Download Examination of plasma current spikes and general analysis of H

Examination of plasma current spikes and general
analysis of H-mode shots in the tokamak COMPASS
Arne Van Londersele
Supervisor: Ereprof. Dr. Ir. Guido Van Oost
Counsellor: Dr. Jan Stockel
Master’s dissertation submitted in order to obtain the academic degree of
Master of Science in Engineering Physics
Department of Applied Physics
Chairman: Prof. Dr. Ir. Christophe Leys
Faculty of Engineering and Architecture
Academic year 2013-2014
Examination of plasma current spikes and general
analysis of H-mode shots in the tokamak COMPASS
Arne Van Londersele
Supervisor: Ereprof. Dr. Ir. Guido Van Oost
Counsellor: Dr. Jan Stockel
Master’s dissertation submitted in order to obtain the academic degree of
Master of Science in Engineering Physics
Department of Applied Physics
Chairman: Prof. Dr. Ir. Christophe Leys
Faculty of Engineering and Architecture
Academic year 2013-2014
i
Allowance to loan
The author gives permission to make this master dissertation available for consultation and
to copy parts of this master dissertation for personal use. In the case of any other use, the
limitations of the copyright have to be respected, in particular with regard to the obligation
to state expressly the source when quoting results from this master dissertation.
Arne Van Londersele
June 2, 2014
ii
Preface and acknowledgement
This thesis discusses research performed on the tokamak COMPASS. This device is installed
in the Institute of Plasma Physics (IPP) in Prague. I lived in this city for four months as part
of an Erasmus exchange project in the winter semester of 2013. In the beginning, the subject
of my thesis was not sharply defined. The primary goal was to discuss some H-mode shots
with NBI heating. The current spikes were discovered in the middle of my stay in Prague
and they became a new part of my thesis. Generally, I had a lot of freedom in this thesis.
I decided to make it my goal to explain the fusion research performed at the IPP as good
as possible to someone with very basic knowledge of science. I also took the liberty to say
something more about the energy problem and fusion research in general in the first chapters.
My whole Erasmus project and work at the IPP was an amazing experience. Although, I had
underestimated the amount of work a little bit. It was very instructive to work in this technical environment. I learned a lot about fusion research and the di↵erent kind of diagnostic
tools, but also about Czech culture and habitats. Further, I also followed some courses at the
Czech Technical University and I lived in the Masarykova student dorm where I met a lot of
new friends with di↵erent nationalities.
I would like to thank everyone who contributed to this thesis. In the first place, prof. J.
Stockel, not only for answering all my questions, but also for his experience as a thesis
counsellor. He motivated me from the beginning to already do a lot of work in Prague, so
that I would not get in troubles once I would be back in Belgium. I also want to thank all
other scientists and technicians at the IPP that helped me, especially J. Havlicek for sharing
his knowledge about the current spikes and a lot of other things, and R. Dejarnac for giving
me the information I need to analyse the Langmuir probe data. But also E. Stefanikova
and M. Peterka for their Thomson scattering profiles (Figure 3.25) and T. Markovic for his
statistics about the ELM frequency and the power through the separatrix (Figure 4.8). Many
thanks go to prof. G. Van Oost to recommend me this thesis and to be my thesis supervisor,
and also to prof. J.-M. Noterdaeme who also shared his ideas about the current spikes. I
think I could have contacted both of them much more than I did.
iii
Onderzoek van pieken in de plasmastroom en algemene
analyse van H-mode shots in de tokamak COMPASS
door
Arne Van Londersele
Masterproef ingediend tot het behalen van de academische graad van
Master in de ingenieurswetenschappen: toegepaste natuurkunde
Promoter: Ereprof. Dr. Ir. Guido Van Oost
Begeleider: Dr. Jan Stockel
Vakgroep Toegepaste Natuurkunde
Voorzitter: Prof. Dr. Ir. Christophe Leys
Universiteit Gent
Academiejaar 2013-2014
Samenvatting
Deze master thesis situeert zich in het vakgebied van de kernfusie. In onze moderne wereld
is een nieuwe vorm van propere energie een punt bovenaan onze verlanglijst - of dat zou het
alleszins moeten zijn. Een mogelijke oplossing hiervoor zou kunnen geboden worden door
kernfusie, de manier waarop sterren zoals de zon hun energie creëren. Deze energiebron
zou ons, indien ze uitvoerbaar is op Aarde, voor eeuwig kunnen voorzien in onze energiebehoefte. De moeilijkheid bestaat erin om de juiste omgeving te creëren waarin fusiereacties
kunnen doorgaan. Een mogelijkheid is de tokamak configuratie. Hierbij wordt een heet
plasma gecreëerd dat in evenwicht wordt gehouden door sterke magneetvelden. Sinds de jaren
zeventig zijn al heel wat tokamaks gebouwd over heel de wereld. Één ervan is COMPASS. Dit
toestel bevond zich oorspronkelijk in Culham, maar is ondertussen verplaatst naar het Institute of Plasma Physics (IPP) in Praag. Deze tokamak heeft een louter experimentele functie:
het is niet de bedoeling om er energie mee te maken en die om te zetten naar een bruikbare
vorm zoals electriciteit, maar eerder om gegevens te verzamelen die waardevol kunnen zijn
in het kader van grotere en duurdere tokamaks die deel uitmaken van de weg naar centrales
draaiende op fusie-energie. Een volgende stap op deze weg is ITER. Deze tokamak en al zijn
bijkomende infrastructuur wordt momenteel gebouwd door een internationale samenwerking
waarin het merendeel van de industrielanden betrokken is. Het onderzoek dat verricht wordt
in het IPP is heel interessant met het oog op ITER, omdat COMPASS een paar belangrijke
gelijkaardige kenmerken heeft en bijvoorbeeld ook gebruik maakt van zogenaamde neutral
beam injection (NBI), een techniek die gebruikt wordt om de fusiebrandstof op te warmen
om zo de juiste omstandigheden te creëren waaronder fusiereacties kunnen doorgaan.
iv
De studie die uiteengezet wordt in dit werk is tweedelig. Eerst worden vijf COMPASS shots
bestudeerd die allemaal het H-mode regime bereikten. Dit is een toestand waarbij het plasma
zeer goed gecontroleerd wordt door de magneetvelden en er een opmerkelijke reductie is in
het aantal plasmadeeltjes dat botst met de binnenzijde van de tokamak. Het is het standaardregime waarin ITER zal werken. Vier van deze geanalyseerde shots maakten gebruik
van de NBI. Aangezien het extra vermogen dat de NBI toevoegt aan het plasma niet geweten
is, werd in deze thesis getracht hier een schatting van te maken op basis van de energiebalans van het hele systeem. Startend van data afkomstig van spectroscopie, interferometers,
Thomson verstrooiing en sondes worden conclusies getrokken met betrekking tot verschillende
plasmaparameters zoals deeltjes- en energieopsluitingstijden, het drempelvermogen om over
te gaan tot H-mode, de temperatuur en dichtheid van het plasma, enzoverder.
In het tweede deel wordt een fenomeen besproken dat misschien zelfs nog nooit eerder is
waargenomen in andere tokamaks. Het gaat hier om merkwaardige pieken in de plasmastroom
die gelijktijdig optreden met bepaalde instabiliteiten die afgekort ELMs worden genoemd, en
dit op zeer korte tijdschaal. Verschillende plasma parameters worden kwalitatief en kwantitatief onderzocht. Er worden argumenten gegeven die bepaalde verklaringen voor de pieken
afbreken en er worden suggesties gegeven voor mogelijke oorzaken. Er wordt vermoeden dat
de pieken te maken hebben met de zelf-inductie van het plasma en de wederzijdse inducties
met componenten van de tokamak. Een andere denkpiste heeft te maken met zeer korstondige
sprongen in de punten waar het plasma de divertor aan de onderzijde van de tokamak raakt.
Deze werden reeds enkele jaren terug ook gevonden in JET (een andere tokmak, de beste die
er op dit moment is) en daar heeft men aangetoond dat deze kunnen verantwoordelijk zijn
voor een opmerkelijke daling van de plasmastroom. Er zouden simulaties moeten gemaakt
worden om beide hypothesen te testen. De pieken in de plasmastroom op zich zijn niet echt
schadelijk voor de werking van de tokamak, maar de studie ervan kan helpen om ELMs beter
te begrijpen. Deze instabiliteiten vormen een probleem voor ITER aangezien ze gepaard gaan
met grote energieverliezen. Het is daarom van uitermate groot belang dat de oorzaken van
ELMs goed gekend zijn, zodat software en apparatuur gemaakt kan worden om ze onder
controle te houden.
Trefwoorden: kernfusie, tokamak, COMPASS, H-mode, current spikes
v
Examination of plasma current spikes and general
analysis of H-mode shots in the tokamak
COMPASS
A. Van Londersele, J. Stockel, J. Havlicek, E. Stefanikova, R. Dejarnac, G. Van Oost, J.-M. Noterdaeme
Abstract—This paper is written as an extended summary
of a master thesis about the fusion research performed
on COMPASS. A first part treats some typical aspects of
discharges in H-mode regime, such as the improvement in
particle and energy confinement, the edge pedestal and
ELMs. The second part discusses a new phenomenon:
ELM-coupled current spikes not caused by crosstalk between cables or by the feedback system. They could be
a reaction to fast changes in the plasma self-inductance
and/or the plasma-vessel inductance. Another explanation
involves the so-called strike point jumps which were also
observed in JET in the past and are known to be able to
cause significant drops in the plasma current.
Index Terms—Nuclear fusion, tokamak, COMPASS, Hmode, current spikes, strike point jumps
I. I NTRODUCTION
COMPASS is a small-size tokamak (R = 0.56m,
a = 0.20m) with ITER-like plasma shape. At the end
of 2012, it achieved the high confinement mode for
the first time since its reinstallation at the Institute of
Plasma Physics in Prague (CR) after a former life at
Culham Centre for Fusion Energy (UK). The device is
equipped with two neutral beam injectors and a whole
range of diagnostic tools such as an interferometer,
a Thomson scattering device, a tomographic system,
bolometers, SXR and HXR detectors, a fast camera, the
usual magnetic diagnostic coils, Langmuir probes and
ball-pen probes, and recently also a neutron detector.
Since COMPASS is one of the only relatively small
tokamaks that is capable of running in H-mode regime,
it is of big importance for the ITER project. The research
on COMPASS focuses on edge plasma studies, e.g.
pedestal and ELM physics. This is a topical subject as the
expected energy losses caused by ELMs in ITER pose
still an issue. Other research on COMPASS includes LH transition studies and feasibility studies of the NBI
heating and some diagnostics.
II. E XPERIMENTAL SETUP
COMPASS performs deuterium discharges in the
single-null-divertor configuration with high triangularity
Fig. 1. Evolution of the discharge #4073. From top to bottom: plasma
current, line-averaged electron density, D↵ radiation, integral visible
radiation and hard x-ray emission. The yellow area indicates the time
interval when the NBI was active. Unresolved fringe failing at the
end of the discharge make hne i to collapse some milliseconds earlier
than it is the case in reality.
( = 0.35 0.40). The plasma elongation  reaches up
to 1.8 and the toroidal field Bt is about 1.2T for most
of the shots. Higher magnetic fields can be applied if
necessary. Recently, advanced technical experience has
led to bigger plasma currents Ip around 300-350kA. The
preparation of the vessel for a set of shots involves
a bake-out at 150 C, a helium glow discharge and
boronization.
III. H- MODE STUDIES
Fig.1 shows the time evolution for a shot with NBIassisted H-mode. It concerns here the first shot that
reached H-mode at the IPP. The L-H transition is
observed as a sudden drop in the D↵ radiation at
t = 1141ms. The transition is followed by 4 small
ELMs as is better demonstrated in Fig.2. The plasma
current is ramping up at the moment of the transition.
In its flat-top phase Ip is about 200kA. The electron
vi
density shows a steep increase during H-mode. Improved
confinement of the plasma is established as a particle
barrier is formed in H-mode. The total visible radiation
increases linearly while the D↵ radiation maintains the
same level. This denotes the accumulation of impurities
in the plasma. The discharge is ended by a huge spike
in the spectroscopic data, a disruption. It is caused by
radiation losses due to the impurities. It is remarkable
that the HXR signal is different from zero from the
moment the NBI is turned on. Measurements with the
newly installed neutron detector have proven that the
HXR detector registers neutrons created during NBI
activity.
Soft x-ray measurements as the one plotted in Fig.2
show sawteeth from the moment additional heating is
coupled to the plasma. It seems that the sawtooth instability is a trigger for the L-H transition in this shot.
This is interesting as it would mean that instabilities in
the core of the plasma cause changes in the edge of the
plasma.
When COMPASS was still in Culham, it was known
to generate type-1 and type-3 ELMs. However, at that
time COMPASS was running in SND configuration.
With the high triangularities from now, it would not
be so strange if also type-2 ELMs appeared. They are
however difficult to distinguish from type-3 ELMs and
are not yet observed. Recent shots like #6316 (see
Fig.3) show the classical pattern of small high-frequent
type-3 ELMs right after the L-H transition followed
later by bigger low-frequent ELMs. It is tought that
these bigger ELMs could be type-1 ELMs. However,
the statistics executed in the second part of this paper
show only ELMs with a change of less than 3% in the
thermal energy, which contradicts this hypothesis.
The improved confinement in H-mode is situated on
two different levels: matter and energy. Both are expressed by the corresponding confinement time. Starting
from the global particle balance for an ideal deuterium
plasma (Ne : number of electrons in the plasma, IN :
influx of neutral particles in the plasma)
dNe
=
dt
IN
Ne
,
⌧p
(1)
it is possible to estimate the particle confinement time
as (ID↵ : intensity of the D↵ radiation)
ne
⌧p ⇡ const
(2)
ID↵
e
for points where dn
dt ⇡ 0. Unfortunately, the optical system that measures the D↵ line emission is not calibrated.
Hence, the constant in eq.(2) is unknown. We can still
Fig. 2. Sawtooth oscillations observed by the SXR diagnostic
simultaneously with the L-H transition and ELMs as can be read
from the D↵ radiation.
Fig. 3. D↵ radiation of discharge #6316.
use this formula to compare ⌧p at different times. This
way, we can compare the particle confinement time in
ohmic regime and H-mode regime. We find an increase
that is mostly bigger than a factor 4.
The energy confinement time ⌧E⇤ , on the other hand,
can be derived from the global energy balance (W :
themal energy stored in the plasma, POH : ohmic heating
power, PN BI : NBI power)
dW
= POH + PN BI
dt
W
⌧E⇤
(3)
The calculation is however complicated by the fact that
PN BI is not known. It has been attempted to estimate
this quantity starting from the energy balance and making certain assumptions. One could for example add a
second equation in order to solve a system consisting of
two equations and two variables (PN BI and the time t).
This second equation could be a scaling law for example.
Another method assumes that ⌧E⇤ remains constant at
the moment the NBI is turned on and that PN BI is a
constant. A simplified variant of this last one starts from
the assumption that W is more or less constant right
before the NBI is turned on and that (t0 : time when the
NBI starts)
dW
PN BI ⇡
(t0 )
(4)
dt
This last approach is used in Fig.4.
There are three different signals for the thermal energy
W available. Two are obtained from the measurement
of plasma diamagnetism. The difference between both
lies in the way the toroidal field generated by the
TF coils is measured: Wdia uses a compensation coil
whereas WdiaBT uses Rogowski coils around the TF
vii
Fig. 5. Energy confinement time ⌧E⇤ and D↵ radiation of shot #6313
(ohmic H-mode).
Fig. 4. Thermal energy of shot #6109.
coils. The third energy value WEF IT is an output of
the reconstruction performed by EFIT. It is still vague
which of the three signals is more correct. Since WEF IT
is the result of a software-based reconstruction with
several inputs from magnetic diagnostics, it should be
less reliable than direct measurements. Besides, it has a
very high sample period of 0.1-1ms. On the other hand,
it is suspected that the diamagnetic signals are subject
to crosstalk with the plasma current. Furthermore, if one
applies the neo-Alcator relation (see [1]) to COMPASS,
one finds much better results for WEF IT . Values of ⌧E⇤
which are obtained with one of the diamagnetic energies
are 3-4 times too high. Another indication in favor of
WEF IT is that METIS - a fast plasma simulator code agrees best with EFIT. However, we have to be critical
since both codes use more or less the same input.
One finds for the NBI power of shot #6109:
IT
PNEF
BI = 100.3 kW
PNdia
BI = 151.8 kW
Fig. 6. Radial profiles of the electron temperature and electron
density for shot #4267 (in H-mode regime).
PNdiaBT
BI = 146.3 kW
This is 32-49% of the upper bound of 312kW which can
be determined from the preprogrammed current of the
ion source (10A), knowing that the accelerating grids of
the NBI have a voltage of 40kV and that the neutralizer
only has a 78% efficiency.
Fig.5 shows the evolution of ⌧E⇤ for an ohmic Hmode shot (PN BI = 0). The ohmic heating power is
approximated by POH = Ip Uloop . A more accurate
calculation would have been
◆
✓
dIp
dL
POH = Ip Uloop L
Ip
(5)
dt
dt
However, the time evolution of the plasma selfinductance L(t) is not known. A code to determine this
parameter is in progress. We can roughly estimate that
⌧E⇤ has tripled in H-mode.
The improved ⌧p and ⌧E⇤ are physically translated
to the construction of a particle and energy barrier
at the plasma edge. Those are observed as a pedestal
in the electron density and the electron temperature
respectively. Typical pedestal heights are 200-300eV and
4 6 · 1019 m 3 . E. Stefanikova and M. Peterka have developed a fitting method which assigns a modified Gauss
function to the plasma core and a modified hyperbolic
tangent to the edge pedestal (see Fig.6).
IV. C URRENT SPIKES
In the Autumn of 2013, the IPP team was able to
upgrade the plasma current to values above 300kA. Due
viii
Fig. 7. D↵ radiation, plasma current and diamagnetic energy of shot
#6311.
to these high plasma currents, something unexpected
was observed. The plasma current shows distinct spikes
of magnitude 1kA and temporal width 0.2ms, often
proceeded by a drop. An example of the current spikes
is represented in Fig.7. The modulations on the plasma
current are caused by thyristor failure. It can be seen that
there is no relation between the timing of the current
spikes and the phase of the modulations.
The thermal energy Wdia also shows this same type
of spikes, where one would expect to see only drops
as predicted by the ELM model. The other two energy
signals do not show any extraordinary behaviour. For
WEF IT this is probably due to its high sample period,
for WdiaBT it could be due to noise.
A qualitative analysis shows that the ELMs also
induce drops in the poloidal beta - an effect that is
often attributed to drops in the plasma energy. Also, the
plasma vertical position sometimes shows clear drops
and ELMs are preceded by small disturbances in the
vertical magnetic field.
A quantitative analysis of the the D↵ radiation, the
plasma current Ip and the thermal energy Wdia is shown
in Fig.8 and Fig.9. Apparently, there is a positive relation
between the absolute height of the D↵ bursts and the
relative height of the current spikes: if one quantity
increases, the other increases too. This behaviour is more
pronounced for the relation between the relative current
spikes and the relative energy spikes. According to Fig.9,
the spikes are 4 times more dominant in Wdia than in
Ip .
What is the story behind these spikes? They do not
originate from some crosstalk between cables, neither
from the connection to the data-acquisition system or
the connection to MARTe. Another evident explanation
is that the spikes are caused by the feedback control
system. IPR coil measurements of the vertical field
Fig. 8. Relative height of current spikes versus absolute height of
D↵ bursts for 687 data points coming from 33 different shots.
Fig. 9. Relative height of current spikes versus relative height of
spikes in the diamagnetic energy for 382 data points coming from
33 different shots.
for a vacuum shot have however demonstrated that the
magnetic field is too much delayed by the vacuum vessel
in order to create spikes in such a small time-scale.
Another indication that the feedback system cannot be
the source of these spikes is the lack of spikes in the loop
voltage, the current in the feedback coils, the vertical
field and the radial position of the plasma.
One plausible explanation claims that the spikes are
a reaction to fast changes in the plasma self-inductance
and/or plasma-vessel inductance. A simulation should be
made to prove this hypothesis. Another explanation is
based on a physical process that was discovered during
the examination of the current spikes: strike point jumps.
At the moment an ELM takes place, the LFS strike point
jumps radially inward while the HFS strike point jumps
radially outward. Probe measurements are excellent to
ix
Fig. 10. Strike point jumps observed by Langmuir probes for shot
#5943. The HFS strike point (top) moves inward, the LFS strike point
(bottom) moves outward. The green lines indicate the times when D↵
bursts occur. The curves are calculated by searching the probe with
the maximum saturation current for each point in time. The sample
frequency of the Langmuir probes is 5MHz. The resulting curve has
been smoothed by a factor 1000. Hence, the actual jumps are bigger
and faster.
register these fast events, as is demonstrated by Fig.10.
Strike point jumps are already described by the staff
of JET (see [2] and [3]). They are associated with
closed field lines at the plasma edge breaking open and
forming a new, smaller separatrix. Simulations made by
the JET crew have demonstrated that this process can be
responsible for significant drops in the plasma current however many orders too big compared to the observed
effects in COMPASS.
It is not clear whether the observed current spikes are
immediately associated with plasma degradation, but as
they appear simultaneously with ELMs, their study can
be important to expand our knowledge of ELMs. These
instabilities do degenerate the plasma as they diminish
the plasma energy, and pose an issue concerning ITER.
Further investigation of the current spikes may even
show that we have to revise our current models of ELMs.
R EFERENCES
[1] M. Dimitrova et al., ““Plasma Parameters in the COMPASS
Divertor During Ohmic Plasmas”,” Contributions to Plasma
Physics, Vol.54, No.3, p.255-260, 2007.
[2] E. R. Solano et al., ““Current loss and strike point movement
during ELMs in JET”,” 30th EPS Conference on Controlled
Fusion and Plasma Physics, ECA Vol.27A, p.1.106, July 2003.
[3] E. Solano et al., ““ELMs and strike point movements”,” IOP
Publishing. Nuclear Fusion, Vol.48, No.6, April 2008.
Contents
1 Thermonuclear fusion
1.1 Existing energy sources and their problems
1.1.1 The world energy problem . . . . . .
1.1.2 Fossil fuels . . . . . . . . . . . . . .
1.1.3 Nuclear fission . . . . . . . . . . . .
1.1.4 Renewables . . . . . . . . . . . . . .
1.1.5 Energy efficiency . . . . . . . . . . .
1.1.6 Hydrogen fuel cell . . . . . . . . . .
1.2 Thermonuclear fusion . . . . . . . . . . . .
1.2.1 Plasma . . . . . . . . . . . . . . . .
1.2.2 Fusion reaction . . . . . . . . . . . .
1.2.3 Properties of fusion fuels . . . . . . .
1.2.4 Triple product . . . . . . . . . . . .
1.2.5 Confinement . . . . . . . . . . . . .
1.2.6 Historical evolution of the tokamak .
1.3 Fusion: pros and cons . . . . . . . . . . . .
2 The tokamak COMPASS
2.1 Introduction . . . . . . . . . . . . . . .
2.2 Vacuum vessel . . . . . . . . . . . . .
2.2.1 Design . . . . . . . . . . . . . .
2.2.2 Cleaning procedure . . . . . . .
2.2.3 Conservation of vacuum . . . .
2.2.4 Fuel . . . . . . . . . . . . . . .
2.3 Magnetic coils . . . . . . . . . . . . . .
2.3.1 Central solenoid . . . . . . . .
2.3.2 Toroidal and poloidal field coils
2.3.3 Power supplies . . . . . . . . .
2.4 Heating system . . . . . . . . . . . . .
2.4.1 Ohmic heating . . . . . . . . .
2.4.2 Neutral beam injection (NBI) .
2.5 Diagnostics . . . . . . . . . . . . . . .
2.5.1 Control room . . . . . . . . . .
2.5.2 Magnetic diagnostics . . . . . .
2.5.3 Microwave diagnostics . . . . .
2.5.4 Spectroscopic diagnostics . . .
xi
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1
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1
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29
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48
51
xii
CONTENTS
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54
56
59
60
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61
61
62
62
3 H-mode operation in COMPASS
3.1 Introduction . . . . . . . . . . . . . . . . . . .
3.2 General discharge evolution . . . . . . . . . .
3.2.1 Start-up . . . . . . . . . . . . . . . . .
3.2.2 Tokamak confinement modes . . . . .
3.2.3 Edge Localized Modes (ELMs) . . . .
3.3 Shot #4073: the first achievement of H-mode
3.3.1 Preset parameters . . . . . . . . . . .
3.3.2 Spectroscopy . . . . . . . . . . . . . .
3.3.3 Electron density . . . . . . . . . . . .
3.3.4 Global particle confinement . . . . . .
3.3.5 Global energy confinement . . . . . .
3.3.6 Divertor Langmuir probes . . . . . . .
3.4 Shot #4267: first shot after cleaning . . . . .
3.4.1 Preset parameters . . . . . . . . . . .
3.4.2 Spectroscopy . . . . . . . . . . . . . .
3.4.3 Electron density . . . . . . . . . . . .
3.4.4 Global particle confinement . . . . . .
3.4.5 Global energy confinement . . . . . .
3.4.6 Divertor Langmuir probes . . . . . . .
3.4.7 Thomson scattering . . . . . . . . . .
3.5 Shot #5909: NBI power calculations . . . . .
3.5.1 Preset parameters . . . . . . . . . . .
3.5.2 Spectroscopy . . . . . . . . . . . . . .
3.5.3 Electron density . . . . . . . . . . . .
3.5.4 Global particle confinement . . . . . .
3.5.5 Global energy confinement . . . . . .
3.5.6 Divertor ball-pen probes . . . . . . . .
3.5.7 Fast visible camera . . . . . . . . . . .
3.6 Shot #6109: H-L transition . . . . . . . . . .
3.6.1 Preset parameters . . . . . . . . . . .
3.6.2 Spectroscopy . . . . . . . . . . . . . .
3.6.3 Electron density . . . . . . . . . . . .
3.6.4 Global particle confinement . . . . . .
3.6.5 Global energy confinement . . . . . .
3.6.6 Fast Visible Camera . . . . . . . . . .
3.7 Shot #6313: ohmic H-mode . . . . . . . . .
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63
63
63
63
64
66
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68
68
72
74
75
77
82
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90
90
91
91
94
94
94
95
97
97
97
99
2.6
2.7
2.8
2.9
2.5.5 Beam and particle diagnostics
2.5.6 Probe diagnostics . . . . . . .
Feedback control system . . . . . . .
2.6.1 Radial equilibrium . . . . . .
2.6.2 Vertical equilibrium . . . . .
2.6.3 Plasma current control . . . .
Recharge time . . . . . . . . . . . . .
Safety . . . . . . . . . . . . . . . . .
Goals . . . . . . . . . . . . . . . . .
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CONTENTS
3.8
xiii
3.7.1 Preset parameters . . . . . . . .
3.7.2 Spectroscopy . . . . . . . . . . .
3.7.3 Electron density . . . . . . . . .
3.7.4 Global particle confinement . . .
3.7.5 Global energy confinement . . .
3.7.6 Divertor ball-pen probes . . . . .
Conclusion . . . . . . . . . . . . . . . .
3.8.1 ELMs . . . . . . . . . . . . . . .
3.8.2 Impurities . . . . . . . . . . . . .
3.8.3 Particle and energy confinement
3.8.4 NBI . . . . . . . . . . . . . . . .
3.8.5 Thermal energy . . . . . . . . . .
3.8.6 H-mode threshold power . . . . .
3.8.7 Edge pedestal . . . . . . . . . . .
4 Current spikes
4.1 Qualitative analysis . . . . . .
4.2 Quantitative analysis . . . . . .
4.3 Conclusion . . . . . . . . . . .
4.3.1 What is not the cause?
4.3.2 So, what is the cause? .
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99
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99
100
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103
104
104
104
104
105
105
106
106
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107
107
110
114
114
114
5 General conclusions and suggestions for future work on COMPASS
117
Appendices
120
A Drift velocity
120
B Density reconstruction
121
C Divertor Langmuir probes
123
D Estimation of PN BI for shot #5909
124
E Current spikes algorithms
129
E.1 Algorithm 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
E.2 Algorithm 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
Bibliography
132
Chapter 1
Thermonuclear fusion
1.1
1.1.1
Existing energy sources and their problems
The world energy problem
Ever after the industrial revolution at the end of the 18th century, the world energy consumption hasn’t stopped growing. Technical inventions followed each other making daily life a lot
easier. As a consequence, the world population has been booming exponentially during the
last century, increasing the demand for energy. This self-reinforcing process seems unstoppable for the moment and the question is how many people our planet can hold. Eventually,
the world population will have to stagnate, but before that we encounter yet another problem:
is there enough energy to fulfil next generations in their needs and what will be the impact
of this increasing energy consumption on the Earth?
It is difficult to find subjective information about these issues. Economics and politics influence almost all publications. Often is referred to the data collected by Vaclav Smil, presented
in Figure 1.1a. This bar graph demonstrates the strongly increasing use of energy from last
century and the importance of fossil fuels (coal, oil and natural gas). They currently provide more than 80% of our energy. Especially oil plays a big role, which was unfortunately
demonstrated by the oil crisis of the 1970s-1980s. Figure 1.1b confirms that this trend has
continued throughout the last decades and that the economical crisis of 2009-2010 temporarily reduced the energy use. Table 1.1 shows the average energy use per person listed for some
countries. The range is striking: the average inhabitant of Iceland consumed about 150 times
more energy than someone from Eritrea in the year 2011. The energy use is not necessarily
related to the climate in the specific country: the warm Arabic countries - where oil is cheap
- are abundantly present in the top 12. The two giants China and India, with both about
1.3 billion inhabitants, are added to show that their economical growth will have big consequences. Especially India, where the people use about one third of the amount used by the
average earthling, will contribute significantly to a steep increase in energy demand during
the coming decades. Furthermore, still 1.3 billion people lack electricity and 2.6 billion lack
clean cooking facilities according to IEA [1]. These - for Western standards - unthinkable
situations will have to be solved in the near future.
1
2
CHAPTER 1. THERMONUCLEAR FUSION
(a)
(b)
Figure 1.1: World energy mix. [2] [3]
Table 1.1: Energy use per capita and per country in 2011. [4]
ranking
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
58
108
135
136
country
Iceland
Qatar
Trinidad and Tobago
Kuwait
Brunei
Oman
Luxembourg
United Arab Emirates
Bahrain
Canada
United States
Saudi Arabia
Singapore
Finland
Norway
Australia
Belgium
Korea, Rep.
Sweden
Russian Federation
China
India
Bangladesh
Eritrea
world
energy [GJ]
754.51
731.58
659.03
437.15
395.94
350.96
337.93
311.09
308.83
306.74
295.36
283.01
271.00
270.86
238.59
231.20
224.66
219.74
217.99
214.75
85.23
25.78
8.60
5.42
76.67
1.1. EXISTING ENERGY SOURCES AND THEIR PROBLEMS
3
It is not easy to say how long our current energy resources will last. According to the World
Energy Council 2013 [5], still new fuel sources are discovered and new extraction techniques
are invented, the best example being shale gas that is exploited in the US and is also getting popular here. Europe however faces the problem that the continent consists of di↵erent
types of subsoils which impedes the commercialization of shale gas production plants. The
survey [5] also states that if the unconventional oil resources, including oil shale, oil sands,
extra heavy oil and natural bitumen are taken into account, the global oil reserves will be
four times larger than the current conventional reserves. On the other hand, some experts
claim that the fossil fuel supply has almost reached its peak and that other methods will fail
to fill the gap following after it [6]. According to [3], the known conventional resources of
coal, oil and natural gas will supply for 108, 52 and 55 years respectively at the current rate
of consumption. The identified resources of uranium, the fuel for nuclear fission, should be
sufficient for over 100 years of supply based on current requirements. These results are more
or less in accordance with other reliable sources such as [5] and [7].
The impact of the increasing energy consumption is very clear these days. Climate change,
rising sea level, ozone depletion, meltdowns, radioactive waste, nuclear weapons, oil wars,
deforestation, loss of biodiversity, air pollution, smog, ecological footprint, ... are daily media
issues. The answer to the question whether we live in a sustainable society is negative. Climate
conferences and resulting goals (Kyoto protocol, 1997) have to limit the exhaust of greenhouse
gases which is mainly a problem caused by fossil fuels. The Non-Proliferation Treaty of 1968
has to assure the peaceful use of nuclear energy. Several nuclear disasters, amongst them
a very recent one in Japan, have turned the public opinion more than ever against nuclear
power plants. Renewable energy sources have not reached high efficiencies yet and are often
too dependent on geological and/or climatological factors. All of this raises the question if
there is no better way to create our energy. In next subsections, the currently available energy
production methods are discussed. It ends with a brief part about the hydrogen fuel cell which
is rather future stu↵. After that, our journey in the scientific world of nuclear fusion begins.
1.1.2
Fossil fuels
Fossil fuels are the remainder of buried dead organisms of typically millions of years old. As
more and more soil is accumulated above the organic material, the pressure and temperature
increase and it is transformed to fuel by natural processes such as anaerobic decomposition,
i.e. breakdown by microbes in the absence of oxygen. This technique is also used by man for
waste treatment and to create renewable fuels. However, creating renewables with the same
energy content as fossil fuels is impossible in human time-scale.
Fossil fuels react exothermic with oxygen. In other words, when they are burned energy is
released by the breaking of old and the forming of new chemical bonds. The chemical reaction
for natural gas, which is mainly composed of methane, is under ideal conditions
CH4 (g) + 2O2 (g) ! CO2 (g) + 2H2 O (l) + 891kJ/mol
(1.1)
The problem associated with this reaction is that CO2 gas is created, which absorbs and reemits infra-red light warming up the Earth’s surface and atmosphere. Today, carbon capture
utilisation and storage, i.e. the removal and long-term storage of CO2 from the atmosphere
into carbon storage areas, is the only large-scale technology which could make a significant
4
CHAPTER 1. THERMONUCLEAR FUSION
impact on the CO2 emissions from fossil fuels. Natural gas is the cleanest burning fossil
fuel. Coal and oil are chemically more complex than natural gas, and when combusted, they
release a variety of potentially harmful chemicals into the air like toxic and acid rain gases
(NOx , SOx ,...). Crude coal even contains some radioactive uranium and thorium. According
to research of the US Geological Survey [8] this refers only to a concentration of 1-4 ppm in
the feed coal and the tenfold after combustion in the bottom ash, which is still in the range
of common soils and rocks. The leach in the air in the form of fly ash is however a possible
thread. Coal and natural gas are the cheapest way to produce electricity at the moment. Oil
is mainly used in car engines.
1.1.3
Nuclear fission
In contrast to fossil fuel burning, fission reactions are not driven by chemical interactions
but by the much stronger nuclear force. The binding energy1 per nucleon is shown in Figure
1.2. Since this curve is concave and reaches its maximum for iron (Z=56), energy will be
released by splitting heavier nuclei or melting together lighter nuclei. This first process is
called nuclear fission, and is the technique used in nuclear power plants nowadays. The other
process is called nuclear fusion, the subject of this thesis. The general fission reaction executed
in nuclear power plants is the chain reaction
1
0n
+
235
92 U
!
A1
Z 1 X1
+
A2
Z 2 X2
+ N 10 n +
+ 200MeV
(1.2)
with
A1 + A2 + N = 235
Z1 + Z2 = 92
(1.3)
(1.4)
Indeed, the reaction products are not always the same. Common fission products are barium
(Z1 =56) and krypton (Z2 =36). Usually, the number of electrons created per reaction N is
2 or 3. To start the reaction, a free neutron is absorbed by uranium-235, turning it briefly
into uranium-236. This unstable excited state breaks down creating two smaller nuclei, some
neutrons and gamma rays. The neutrons are used to induce subsequent fission reactions. The
kinetic energy of the fission products and the radiant energy of the rays heat the working
fluid in the reactor which is usually water (H2 O, occasionally D2 O). This hot water is used to
produce steam in a secondary circuit that drives the steam turbines and generates electricity.
The gained 200MeV per reaction is a theoretical value, calculated using Einstein’s famous
relation
E = m · c2
(1.5)
where the mass di↵erence between U-235 and the fission products is determined experimentally. A neutron is needed to induce the decay of U-235 since the energy barrier Ethresh as
seen in Figure 1.3 is about 6MeV and the binding energy released by the capture of an extra
neutron is about 7-8MeV as can be seen in Figure 1.2. The surplus of energy brings the
formed U-236 in an excited state. In order to make U-236 even more unstable the kinetic
energy of the neutron can be increased. In this case, one speaks about a fast-neutron reactor,
otherwise a thermal-neutron reactor.
1
The energy input needed to split a nucleus entirely into its constituting particles called nucleons.
1.1. EXISTING ENERGY SOURCES AND THEIR PROBLEMS
5
Figure 1.2: Plot of the averaged binding energy per nucleon. [9]
Figure 1.3: Energy versus distance r between two heavy nuclides. The short-ranged attractive nuclear force
between the nucleons dominates for small r while the long-ranged electrostatic repulsion between the protons
dominates for bigger r. In order to induce a fission reaction, at least the threshold energy Ethresh has to
be added to the system. This is known as the Coulomb barrier. The net energy gain Q is indicated on the
graph. We see that heavy nuclides have Q > 0 for fission. Light nuclei have Q < 0 which means that fusion is
favorable for energy winning. [10]
6
CHAPTER 1. THERMONUCLEAR FUSION
Theoretically, according to reactions (1.1) and (1.2), the fission of one mole U-235 generates
more than 20 million times the energy released by burning a mole of CH4 . Furthermore, the
density of uranium is much higher than that of CH4 . Hence, the energy contained in 1g of
U-235 is many orders of magnitude bigger than that of 1g CH4 , which is of course an asset of
nuclear energy. Another advantage of nuclear power plants is the absence of greenhouse gas
emissions. The bad side of nuclear fission is that the by-products are long-lived -emitters
and that the chain reactions cannot be stopped in worst case scenarios, resulting in a socalled “meltdown” of the fission reactor. The big catastrophic nuclear accidents in Three
Mile Island (US,1979), Chernobyl (Ukrain,1986) and Fukushima (Japan,2011) have slowed
down or even reversed the growth of nuclear fission in a lot of countries. The public opinion
is turned more than ever against fission energy and the extra costs and approval times for
nuclear power plants to fit the safety regulations are out of proportion. Japan used to be one
of the countries with a high share of nuclear power (30%) in its electricity mix. Today, Japan
has only two of its 54 reactors in operation [5]. Belgium, with a nuclear power generation
of more than 50% in its earlier energy mix, signed to close all its nuclear power plants by 2025.
Pressing CO2 standards make that nuclear power still has a future, especially if the thorium
reactor breaks through. This type of reactor, using thorium as input instead of uranium, is
claimed to produce less harmful radioactive waste and to be proliferation-resistant. Besides,
thorium is more abundant than uranium so it could be a way to limit our CO2 emission during
the next centuries. But more importantly, much safer reactor designs are possible. Thorium
alone cannot sustain the chain reaction. It first has to absorb slow neutrons to transform into
U-233, an artificial version of uranium that is fissile. This di↵erent fuel cycle lends thorium
reactors to be designed “sub-critical”, i.e. they need external input of neutrons to keep the
reaction going. These neutrons can for example be created by a proton beam incident on a
lead target. If the proton beam is switched o↵, the reactor stops. With this kind of design,
meltdowns are impossible. The difficulty is to create a proton beam with the right amount
of energy. This should be feasible with the modern particle accelerators. [11]
1.1.4
Renewables
Biomass & waste
Bluntly speaking, biomass energy is generated by the combustion of plants, directly or indirectly after conversion to biofuels like ethanol and biodiesel. It is the most primitive energy
source: historically, humans have harnessed biomass-derived energy since the time when people began burning wood to make fire. This renewable energy source has a recycle aspect:
industrial waste and by-products can often be transformed to biofuels, and for example all
rotting garbage releases methane gas which could be captured and used as an energy source.
Bioenergy is controversial because of the food-or-energy dilemma, which also involves issues
like land and fresh water scarcity. Besides, it is not a clean energy source: CO, CO2 , NOx
and SOx emissions are often intrinsic to these kind of combustions. Nevertheless, biodiesel
could be a good alternative for gasoline.
Water
Hydro power is a widely used form of renewable energy mentioned apart in Figure 1.1a and
1.1b because of its significant contribution in the world energy mix. The working principle
1.1. EXISTING ENERGY SOURCES AND THEIR PROBLEMS
7
is based on the ancient watermill. The flow of water in rivers or the hydrostatic pressure
of water kept in reservoirs (dams) is a mechanical form of energy which is converted with
water turbines into rotational energy and thereafter to electricity. More or less the same idea
can also be used for water which has already been diverted for use elsewhere, in a municipal
water system for example. Besides, water storage can be used to supply high peak demands.
At times of low electrical demand, excess generation capacity is used to pump water into a
higher reservoir. When there is higher demand, water is released back into the lower reservoir
through a turbine. And there are plenty of other techniques where water power is used to
generate electricity. Nevertheless, most hydroelectric power comes from dams. It is a clean
method with no direct waste or emission of harmful gases. Unfortunately, the number of
possible locations for such hydro power plants is limited due to the need for a big lake which
imposes a geographical and climatological condition.
Photovoltaic (PV)
The use of solar energy is growing strongly around the world, partially due to the rapidly
declining solar panel manufacturing costs (see Figure 1.4). In 2007, solar energy accounted
for about 0.1% of the world energy consumption. This share is believed to increase to 1.2% in
2030 [12]. The world’s overall solar energy resource potential is around 5.6GJ/m2 /year [12].
According to Figure 1.1b, this means that an area of 525 000km2 - or 0.1% of the Earth’s
total surface area - covered by ideal solar cells suffices to foresee in all our energy needs at the
moment. You could think that this is feasible, but unfortunately the used resource potential
is an overestimation and solar cells are far from ideal. For the moment, commercial panels
convert about 20% of the incident sun light to electricity. Luckily, a lot of improvement is still
possible. The research group of the Fraunhofer Institute for Solar Energy Systems in Freiburg
published in September 2013 that they constructed a new solar cell with 44.7% efficiency [13].
The concerned solar cell is not of the conventional silicon type, but a III-V multi-layer type,
which originally came from space technology. Here, several cells made out of di↵erent III-V
semiconductor materials are stacked on top of each other. The single subcells absorb di↵erent
wavelength ranges of the solar spectrum, making this technology very efficient. Also the 2010
Nobel Prize winner graphene, i.e. a carbon sheet of one atom thick, looks very promising for
high-performance solar cells [14]. Scientists are optimistic to reach the goal of 50% within the
next years. However, even with these high efficiencies solar parks still need to have immense
dimensions in order to create the same power output as fossil fuel and nuclear power plants.
Besides, solar power is unreliable as it is not always available in the same amount. It is perfect
as an additional clean2 source of energy, but probably not more than that. It is for example
also very useful for stand-alone applications reaching from space stations to parking meters.
There also exist other techniques to convert Sun light to electricity. Concentrated solar
power (CSP) uses mirrors with Sun trackers to concentrate a lot of light in one point to drive
a conventional heat engine. Most of the CSP plants are parabolic-trough plants. Here, linear
parabolic reflectors heat a working fluid that is placed in the focal line. Spain is the world
leader in CSP with a total capacity of 2.2GW.
2
The environmental damage by the production process of the solar cells taken aside.
8
CHAPTER 1. THERMONUCLEAR FUSION
Figure 1.4: Left: Evolution of the global cumulative installed PV capacity. Right: The global PV module
price learning curve for c-Si wafer-based and CdTe modules. [15]
Wind
Wind is in the first place useful to produce mechanical power if we think about sail boats and
old windmills, but it has also proven itself to be an interesting tool to generate clean electricity. Last years, driven by the government’s subsidies, big wind farms were built on land
and at sea. The world wind energy capacity has been doubling about every three and a half
years since 1990. The total electricity generation in 2011 was around 377TWh, roughly equal
to Australia’s annual electricity consumption [5]. China, Germany, Denmark and the US are
some examples of countries that create a lot of wind energy. Unfortunately, wind power also
struggles with the problem that it is not always available. As governments begin to cut their
subsidies to renewable energy, the business environment becomes less attractive to potential
investors. Lower subsidies and growing costs of material input will have a negative impact on
the wind industry in the near future.
The windmill park in Zeebrugge was one of the first wind energy projects in Europe. It was
built in 1986 as a demonstration project to give interested companies the know-how they
needed. So already in the nineties, wind energy was subsidized. If we have to be honest, not
enough progress has been made since then to keep on financing this technology. Luckily, a
revolution is coming soon. The future of wind turbines lays in the sky. As there is more wind
energy available at higher altitudes and this at a constant rate, we have to search for wind
over there. This is of course nothing new: the trend seen in conventional wind turbines is
that they always become bigger and bigger. So, what is the di↵erence? We are now speaking
about an altitude of 300-600m. This is impossible with the classical wind turbine technology.
Therefore, some American companies already have prototypes of how the next generation of
wind turbines will hopefully look like, the so-called airborne wind turbines. The first one is
designed by Makani and looks like a kite that circles around in the air (see Figure 1.5a). A
second type is property of Altaeros and is some kind of balloon with a turbine inside (see
Figure 1.5b). Next to the fact that these airborne wind turbines can catch more wind at
the higher altitudes, they are also easy to install at less convenient locations like for example
above the ocean3 , and besides they are much cheaper than classical turbines with a tower.
On the other hand, this new technology is again a step back in terms of power generated per
turbine. [16]
3
They only need to connect a rope to something on the ground.
1.1. EXISTING ENERGY SOURCES AND THEIR PROBLEMS
(a)
9
(b)
Figure 1.5: (a) The “kite” prototype of Makani compared to classical wind turbines [16] [17]. (b) The
“balloon” prototype of Altaeros [18].
Geothermal
In a geothermal power plant, hot steam is pumped up and cold water pulled down to underground natural reservoirs. These geothermal reservoirs appear in regions of volcanic activity,
i.e. near the boundaries of tectonic plates or at hotspots, and also in regions of above-normal
heat production through radioactive decay of minerals. This renewable energy source is clean
(there is no creation of direct waste or harmful gases) and unlike wind and solar energy, which
are more dependent upon weather fluctuations and climate changes, geothermal resources are
always available. While the carrier medium for geothermal electricity (water) must be properly managed, the source of geothermal energy, the Earth’s heat, will be available indefinitely
in human time-scale. The only disadvantage is that the number of sites where such a power
plant can be built is limited because of the need for a geothermal reservoir. According to
the Geothermal Energy Association [19], the world capacity of geothermal electricity was
about 11.224GW in 2012 which is about 0.0007% of the total energy use that year. However,
the same idea of using the Earth’s heat is recently applied to households under the name
“geothermal heat pumps”. A network of underground pipes - not as deep as for power plants
of course - is used to support the central heating system by exchanging heat with the crustal.
Ocean
The ocean covers 71% of the Earth’s surface and contains a lot of energy in di↵erent forms.
It would be a shame not to exploit this energy resource. The general term ‘ocean power’ can
be subdivided in several techniques to produce electricity such as tidal power, wave power,
ocean thermal energy conversion, ocean current power, ocean wind power and osmotic power.
Of these, the first three are the most well-developed technologies. While the kinetic energy
from marine and tidal waves can be relatively easily converted to electricity by turbines, the
conversion of wave power poses bigger technical challenges. A wide variety of wave energy
converter designs exists. Ocean thermal energy conversion uses the temperature di↵erence
between cooler deep water and warmer surface water to run a heat engine. Osmotic power or
salinity gradient power can be exploited for energy extraction through reverse electro-dialysis
and osmotic processes working between ocean water with high and river water with low salt
concentration. Worldwide, ocean energy’s share in the total electricity generation is negligible.
It is projected to increase by 2030, albeit only modestly. Ocean energy industries are at an
early stage of development. Commercial applications of ocean energy have been limited to
10
CHAPTER 1. THERMONUCLEAR FUSION
tidal barrage power plants in France (240MW) and Canada (20MW), but major new tidal
barrage plants are under construction in the Republic of Korea.[20] [21]
1.1.5
Energy efficiency
As stated by the laws of thermodynamics, energy can be converted from one form to another,
but these actions have a price: the amount of useful energy decreases in every step. Not all
energy stored in for example fossil fuels is used for its final purpose, and also the energy that
has reached its final form is often wasted in many ways. Energy efficiency is associated with
the part of the initial energy stored in fuels that is useful in the end.
Every step of the entire energy conversion chain still has enormous margins for improved
efficiency. However, not only technological innovations but also economics play an important
role in this story. Energy efficient technologies will only break through if there is enough
economical benefit associated with it, and if there are no implementation barriers. Some
possibilities to improve the overall efficiency of our energy are summed here for the main
technology groups:
• In power generation, the average efficiency of coal-fired plants for example is 34% [5],
in sharp contrast with the 94% of the multi-fuel Avedore Power Station in Denmark
[22]. Cogeneration, the combined production of electrical power and useful heat, can
certainly improve the efficiency. Other options are repowering, combined cycle power
stations,...
• In transmission and distribution electricity losses reach up to 12% and above [5]. This
may be diminished by better management, strategically better locations of the power
plants, personal energy generation with for example solar panels, better storage techniques, less resistive cables, .... Promising for this last one is the upcoming carbon
technology which will hopefully introduce low-weight and low-loss conductors. In this
respect, carbon nanotubes seem to be the future [23]. Concerning the better management, an important role will be played in the near future by so-called smart grids. The
increasing amount of solar and wind energy, which are highly variable, forces us to adapt
our current distribution system. Smart grids will be able to act on changes in the local
energy production or consumption in an automated fashion using ICT. Germany for
example has a huge installed capacity of solar and wind power that sometimes - on very
sunny days or when it storms - causes negative electricity prices! The craziest part of
this whole story is that pumped-storage hydroelectricity is purposely wasted when this
happens. And you cannot blame the managers of these water reservoirs because they
are making a lot of money by doing it! Some legislative obstacles at the moment are the
real problem. It is time that the European Union becomes a real union and fully opens
its borders for energy transport from one member state to the other. When Germany
has an excess in energy capacity, this should be easily guided to places elsewhere in
Europe where it can be used. The design of smart grids that regulate all of this, is very
complex but a must for the future.
• Buildings account for nearly 40% of the total energy consumption globally and it is
estimated that potential energy savings in buildings could reach between 20 and 40%
[5]. This can be accomplished with better insulation, the use of fluorescent lamps or even
1.2. THERMONUCLEAR FUSION
11
Figure 1.6: Global electricity demand by application. [5]
sky lights instead of the traditional incandescent light bulbs,... According to Figure 1.6,
about 40% of our energy goes to motors. This means that the development of lighter
vehicles is certainly a help. Of course, also the behaviour of the consumer plays a very
important role.
1.1.6
Hydrogen fuel cell
The basic idea of hydrogen technology is to replace electricity with hydrogen as energy carrier.
This implies the production of hydrogen, the transport and storage of hydrogen and the
conversion to electricity by hydrogen fuel cells in the end application, for example a hydrogen
vehicle. The fuel cell releases electrical energy throughout redox reactions and needs the
continuous input of fuel and oxygen or air for that purpose (see Figure 1.7). Some assets:
• Hydrogen (H2 ) can be easily produced from water, biomass, biogas, natural gas,...
• It poses an efficient way to store energy.
• It provides an efficient solution for combined heat and power generation, both at industrial and domestic level.
• Hydrogen o↵ers a significant reduction of green house gas emissions (hydrogen oxidation
only produces water at point of use) and a reduction in air pollution.
The manufacturers of fuel cell vehicles (FCV) have reached the point where vehicles that
could be sold in 2015 would fulfil the costumers’ expectations. However, the high cost and
the lack of refuelling stations still pose a big problem. We can expect to see more and more
hydrogen vehicles in the near future. Germany for example is currently placing refuelling
infrastructure and wants a self-sustaining FCV business by 2020. [24] [25]
1.2
1.2.1
Thermonuclear fusion
Plasma
Plasmas are ionized gases. Hence, they consist of positively charged ions and negatively
charged electrons, as well as neutral particles. This quasi-neutral ensemble features a collective
behaviour described by the hydromagnetic equations of plasma motion. Plasma is also known
as “the fourth state of matter” next to solids, fluids and gases. Despite that plasmas do not
12
CHAPTER 1. THERMONUCLEAR FUSION
Figure 1.7: Hydrogen fuel cell.
appear very much on Earth (lightening, aurora borealis,...) , it is very common in the rest
of the universe: more than 99% of the known matter is in the plasma state, stars being the
best example. Mankind has succeeded to reproduce plasmas on Earth. Two main groups of
laboratory plasmas exist: the high-temperature plasmas and the so-called low-temperature
plasmas or gas discharges. The last ones are used in TL-lamps, plasma displays, gas lasers,
surface treatment, biomedical applications, air and water cleaning,... From now on, however,
the term ‘plasma’ will refer to high-temperature plasmas, which are used in fusion processes.
1.2.2
Fusion reaction
Fusion occurs when light nuclei are melted together to form heavier nuclei with more average
binding energy per nucleon. One could ask himself which fusion reactions are the easiest to
execute on Earth.
First of all, there is the Coulomb barrier between both nuclei which has to be overcome before the strong nuclear force takes over (recall Figure 1.2). This barrier is proportional to the
product of the charges of both nuclei, so the fuels must have a low atomic number. Mind that
the nuclei do not have to go over the whole barrier. As we know from quantum mechanics,
the nuclei can also tunnel through it.
Secondly, the cross-section of the fusion reaction should be as high as possible in the feasible
temperature range. As we can see from Figure 1.8 , the deuterium-tritium reaction is most
suitable.
2
1D
+ 31 T ! 42 He (3.52MeV) + 10 n (14.08MeV)
(1.6)
This reaction produces helium nuclei, also called ↵-particles, with a kinetic energy of E↵ =
3.52MeV and neutrons with a kinetic energy of En = 14.08MeV. As neutrons are electrically
neutral they can leave the magnetic confinement of a tokamak (see later) and their energy is
used to produce electricity. The ↵-particles, however, are charged and cannot escape. Their
energy is - in the best case - used as an extra heating source for the plasma.
Thirdly, the energy release per reaction should be as high as possible to produce net energy.
1.2. THERMONUCLEAR FUSION
13
Figure 1.8: Fusion cross-sections of di↵erent low-Z fusion reactions expressed in barn units (=10 28 m2 ).
More relevant however is h F vi, the averaging of the product of fusion cross-section and particle velocity over
the velocity distribution. [26]
1.2.3
Properties of fusion fuels
Deuterium
Deuterium (D) is a non-radioactive isotope of hydrogen with one neutron (and of course
one proton and one electron). It can be gained by electrolysis of water (D2 O electrolyses
more difficult and remains behind), by distillation of liquid hydrogen or by various chemical
adsorption techniques. According to estimations the energy content of all deuterium in the
world’s oceans should be enough to supply humanity longer than the Sun will burn. So, it is
important that we learn to use the D-D fusion reaction in the long-term.
Tritium
Tritium (T) is a radioactive isotope of hydrogen with two neutrons. It is a -emitter with a
half-life of about 12.3 years. The decay reaction is given by
3
1T
! 32 He + e + ⌫ e
(1.7)
The electron emitted during the decay hasn’t got enough energy to cross the dead layer of
our skin. So, extracorporeal tritium is harmless. When inhaled or ingested, however, tritium
can be very nasty: it damages our body from the inside and causes cancer. Since tritium
is able to replace one or more ordinary hydrogen isotopes in water or organic molecules, it
easily contaminates our water or food cycle. Fortunately, there is already some experience
with tritium because it is a common by-product in present nuclear power plants. Due to its
short half-life, tritium does not appear naturally in big enough amounts. Therefore, it has
to be created somehow. This will be done by surrounding the vessel with a lithium blanket.
The fusion reaction produces high-energetic neutrons which react with lithium as follows
6
3 Li
7
3 Li
+ 10 n ! 31 T + 42 He + 4.80MeV
+
1
0n
!
3
1T
+
4
2 He
+10
n
2.87MeV
(1.8)
(1.9)
14
CHAPTER 1. THERMONUCLEAR FUSION
The radioactive tritium is therefore made in the fusion reactor and immediately consumed as
fuel. The real fuels of a fusion power station are therefore deuterium and lithium, eliminating
the need to transport radioactive fuels outside of the reactor. [27]
Lithium
Lithium (Li) is a silver-white alkali metal. The only naturally occurring isotopes are Li-6
(7.42%) and Li-7 (92.58%). Due to its high reactivity, lithium never occurs freely in nature,
and instead, only appears in compounds, which are usually ionic. It occurs in a number of
minerals, but due to its solubility as an ion, it is present in ocean water and is commonly
obtained from brines and clays. There exists no accurate information about the world lithium
resources. The booming lithium-ion industry could form a threat, especially if the electric
or hybrid cars become a real success in the next years. However, with its 0.17ppm presence
in sea water, cheaper and more efficient extraction techniques would make lithium virtually
inexhaustible. [27]
1.2.4
Triple product
Three plasma parameters need to be high in order to get sustained fusion: the plasma temperature, the fuel density and the energy confinement time. Their product is called the fusion
triple product. for D-T fusion to occur, this product has to exceed a certain minimum value.
This value was already calculated in 1955 by the British scientist John Lawson. The whole
concept is now known as the Lawson criterion.
Temperature (T)
In order to overcome their natural repulsive Coulomb forces, the positively charged plasma
ions need to have enough energy. In the high-temperature-limit the plasma particles can be
considered being in thermodynamic equilibrium, which implies together with the assumption
of solely elastic collisions that their velocity has a Maxwell-Boltzmann distribution. In other
words, under these conditions a plasma can be described by the kinetic gas theory which says
that the most probable energy ✏ and the average energy hEi of the plasma particles are given
by
✏ = kB T
3
hEi = kB T
2
(1.10)
(1.11)
So, one can conclude that the plasma temperature indeed should be high in order to make fusion possible. As a side note, we mention that equation (1.10) is used to express temperatures
in units of energy: 1eV is about 10 000K.
Density (n)
As seen from Figure 1.8, the cross-sections of the fusion reactions are in general very small.
This means that high fuel densities are needed in order to attain the required reaction rates.
In fact, only the density of the fuel has to be high. Impurity atoms and helium ions from the
fusion reaction itself - the “ash” - have to be controlled, because they dilute the plasma and
hinder optimal operation of the fusion device.
1.2. THERMONUCLEAR FUSION
15
Energy confinement time (⌧E )
The energy confinement time is a measure for how long a plasma is able to retain its heat
right after the external heating sources are turned o↵. It is defined as the ratio of the thermal
energy contained in the plasma and the power losses at that same moment. The energy
confinement time increases substantially with plasma size. This imposes a minimum volume
constraint on fusion devices.
Power balance and Lawson Criterion for D-T fusion
To understand the origin of the Lawson Criterion, one has to look at the power balance of a
D-T fusion reactor:
@W
= P↵ + PH PBr PL > 0
(1.12)
@t
This says that in order to have net accumulation of thermal energy W in the plasma, the sum
of the power generated by ↵-particle heating (P↵ ) and by external heating sources (PH ) has
to be bigger than the power losses. These losses are split up in bremsstrahlung losses (PBr )
on the one hand and all other conduction, convection and radiation losses (PL ) on the other
hand. The energy of the neutrons is not spend on heating the plasma but is converted to
electricity.
Bremsstrahlung losses are well understood. They are caused by the acceleration of charged
particles in the electrostatic field of other charged particles. In fusion devices this concerns
mainly the deflection of electrons in the electric field of ions. Bremsstrahlung occurs in the
x-ray domain where the plasma is optically thin: its energy is not absorbed by the plasma and
consequently it is lost. The bremsstrahlung losses in a plasma of volume V are approximated
by (see [28])
1
2
2
PBr = 5.35 · 10 37 Zef
(T in keV)
(1.13)
f ne ni V T Watt
where Zef f is the e↵ective atomic number defined as
P
i
Zef f = P
ni Zi2
ni Z i
(1.14)
i
The occurrence of Zef f in this equation is easy to understand: nuclei with higher electrical
charge cause higher electron accelerations and consequently higher radiation losses. Therefore, it is very important to prevent the introduction of high-Z impurities into the plasma.
The underlying physics of the other losses is not clear. Experiments show a more or less
exponential drop after switching o↵ the fusion apparatus. This e↵ect is in accordance with
known heat losses: the same happens for example when the central heating of a building is
switched o↵. This exponential behaviour is mathematically translated into
PL =
W
⌧E
(1.15)
where the empirical energy confinement time ⌧E is introduced. Indeed, substituting this into
the power balance (1.12) without any of the other power terms, i.e. there is no external
16
CHAPTER 1. THERMONUCLEAR FUSION
heating (PH = 0) and the ↵-particle heating and bremsstrahlung losses cancel each other out
(P↵ = PBr ), gives
@W
W
=
,
(1.16)
@t
⌧E
and solving this first order di↵erential equation results in the proposed exponential drop.
W (t) = W (0) e
t
⌧E
(1.17)
In what comes next, we will use however yet another energy confinement time which includes
the radiation losses PBr and is easier to measure. It is defined by equation (1.18).
PL + PBr =
W
⌧E⇤
(1.18)
The thermal energy of the whole plasma column is given by
W = 3nkB T V
(1.19)
which is easily calculated using equation (1.11) and keeping in mind that the plasma consists
of ions as well as electrons with the same particle density4 and temperature. The total fuel
density is denoted by n.
For nD = nT = n/2, the total fusion power is given by
PF =
n2
h
4
F viEF V
(1.20)
and the heating by ↵-particles has a similar expression, namely
P↵ =
n2
h
4
F viE↵ V
(1.21)
where F is the fusion cross-section, v the particle velocity and ‘h i’ the averaging over the
velocity distribution. E↵ is the energy released in the form of kinetic energy of ↵-particles
after one fusion reaction, namely 3.52MeV. The total energy released by one fusion reaction,
carried by ↵-particles as well as neutrons, is five times bigger (about 17.6MeV).
The external heating responsible for the contribution PH could be ohmic heating, neutral
beam injection, electron/ion cyclotron heating resonance, or maybe even another technique.
The expression for PH is undefined. However, it can be related to the total fusion power PF
by introducing the so-called power enhancement factor Q.
PH =
PF
5P↵
=
Q
Q
(1.22)
This quantity has two values that need special attention: Q = 1 (break-even) and Q = 1
(ignition). This last one occurs if the number of fusion reactions per second is sufficiently
high, so that the heating caused by the ↵-particles makes the use of external heating systems
4
Assumption of quasi-neutrality of the plasma: nD + nT = ne = n.
1.2. THERMONUCLEAR FUSION
17
redundant. The name ‘ignition’ is in analogy with the burning of fossil fuels.
Based on equations (1.18), (1.19), (1.21) and (1.22), it is now possible to rewrite the power
balance (1.12) as
12kB T
⇣
⌘
n · ⌧E⇤ >
(1.23)
h F viE↵ 1 + Q5
Making use of the approximation (see [29])
h
F vi
24
⇡ 1.1 · 10
· T 2 m3 s
1
(T in keV)
(1.24)
which is valid in the range 10-20keV (see Figure 1.9a), this results in the Lawson criterion5
breakeven : n20 · T · ⌧E⇤ > 5 m
ignition : n20 · T ·
⌧E⇤
3
> 30 m
keV s
(1.25)
3
(1.26)
keV s
An estimation of the minimum temperature needed for D-T fusion can be made by solving
(1.27) for T .
PF = PBr
(1.27)
This describes the hypothetical situation where the plasma energy remains constant, there
are no external heating sources (ignition), the only losses are due to bremsstrahlung of the
fusion fuel (Zef f = 1) and all energy released by the fusion reactions - also the energy of the
neutrons - is used to cancel these bremsstrahlung losses. These are the absolute minimum
conditions that have to be fulfilled in order to be able to create an ignited plasma that does
not create electricity. The actual lower bound for the temperature is certainly much bigger,
since impurities are unavoidable and also non-radiative losses occur in reality. Using equations
(1.13) and (1.20), the condition (1.27) can be transformed to
h
F vi
= 1.52 · 10
25
1
T2
We can solve this equation by using experimental data for h
It shows that
Tmin ⇡ 2 keV
(1.28)
F vi.
This is done in Figure 1.9b.
(1.29)
This is an estimation of the minimum ignition temperature executed by the writer of this
master thesis. It is in reasonable consistence with the value of 4keV which is claimed in [30].
Typical desired values for tokamaks (see next paragraph) are
n = 1020 m
3
(1.30)
8
T = 10 keV (= 10 K)
⌧E⇤
= 3s
(1.31)
(1.32)
Stars like our Sun reach the ignition condition for multiple fusion reactions. Their huge mass
creates gravitational forces strong enough to confine their plasma and reach high densities.
Besides, their big volume implies a high energy confinement time and the large amount of
plasma particles makes that there are enough particles in the tail of the Maxwell-Boltzmann
distribution with enough energy - or in other words temperature - to undergo fusion.
5
The notation n20 is used to denote n · 10
20
.
18
CHAPTER 1. THERMONUCLEAR FUSION
(a)
(b)
Figure 1.9: Maxwell averaged cross-section h F vi for D-T fusion according to experimental fitting performed
by Bosch and Hale (see [29]). (a) The parabolic approximation (1.24) is reliable for temperatures in the range
10-20keV. (b) Determination of the minimum ignition temperature based on equation (1.28). Both curves
intersect at T ⇡ 2keV.
1.2.5
Confinement
Because no material on Earth is capable of withstanding the high fusion temperatures, one
has to appeal to non-contact methods to confine the plasma. Two main techniques are used:
inertial confinement and magnetic confinement.
Inertial confinement
In the first technique, a cryogenic (supercooled) pellet of fusion fuel is heated by powerful
lasers or ion beams. The outer layers are turned into plasma which expands due to heat
absorption. As a reaction to this, the rest of the pellet implodes due to its inertia so that the
ignition condition is fulfilled and fusion reactions in the pellet create energy. This principle is
used in hydrogen bombs but is also attempted in controlled fusion reactors. It is particularly
popular in the United States, where at the end of last year a breakthrough took place in
the National Ignition Facility (NIF): for the first time in history, the released fusion energy
exceeded the energy deposited in the fusion fuel during the implosion. The setup and working
principle are explained in Figure 1.10. However, a lot of energy was first wasted to reach the
state of implosion and besides a lot of the laser energy was lost throughout the conversion
from UV light to x-rays. This makes that the energy production is still less than 1% of the
total laser energy. The most important problems are the non-symmetrical shape of the pellet
when it is heated and the mixing of the plastic of the fuel capsule with the fuel itself. To
control these two e↵ects, the laser energy has to be somewhat lowered, while its full capacity
is needed to reach ignition, i.e. a fusion chain reaction that burns a significant portion of
the fuel. The process of self-heating by ↵-particles, which is vital for ignition, has been
demonstrated during the experiments at NIF. [31]
Magnetic confinement: the tokamak concept
The other technique uses high magnetic fields to confine the fusion fuel that is first ionized.
This is the principle used in tokamaks such as COMPASS and is the topic of this thesis. Theoretically speaking, the biggest di↵erence between both confinement methods is that inertial
fusion speculates on a high fuel density n, while magnetic fusion rather aims at a large ⌧E .
1.2. THERMONUCLEAR FUSION
19
(b)
(a)
(c)
Figure 1.10: Inertial confinement fusion at NIF. (a) The interior of the target chamber. A scientist can be
seen on the left. The target positioner is on the right. The target is a metallic case called a hohlraum that
holds the fuel capsule. (b) The golden hohlraum cylinder is just a few millimetres wide. (c) Illustration of
the working principle. A series of laser beams is pointed to the apertures at both ends of the hohlraum, which
contains a fusion target the size of a small pea. The laser beams strike the inside walls of the golden can
converting their UV light into x-rays. These x-rays then bathe the capsule creating tremendous pressure and
crushing the fuel capsule. Now, conditions are reached for fusion reactions to occur. [32]
The temperature has the same order of magnitude for both.
For particles with charge q in the presence of a magnetic field Newton’s second law of motion
states
dv
m
= q(v ⇥ B)
(1.33)
dt
In physical terms, this means that the particles gyrate around the magnetic field lines. This
can be better understood if one transforms the expression to
dv
=!⇥v
dt
(1.34)
where ! is the angular speed of the gyration given by
!=
qB
m
(1.35)
Given the fact that for circular motion v? = !⇢ where v? is the component of the velocity
vector v in the gyration plane, the radius of gyration is given by
⇢=
mv?
qB
(1.36)
The easiest way to invoke electromagnetic confinement would be by using a cylindrical setup
where electrical currents in the windings at the cylinder surface create a homogeneous magnetic field in the cylinder body (see Figure 1.11a). However, it is clear that this setup causes
losses at both open ends of the cylinder. An obvious solution is to bend the cylinder and
form a torus. However, in this case the problem of electromagnetic confinement has become
a lot more difficult. According to Ampère’s law, the toroidal magnetic field is then given by
Bt =
µ0 N I
2⇡r
(1.37)
with N the number of toroidal coils, I the current driven through them, and r the distance
from the main axis of the torus. The appearing r-dependence is very important since it
20
CHAPTER 1. THERMONUCLEAR FUSION
(a)
(b)
(c)
(d)
Figure 1.11: (a) Cylindrical confinement with leaks at both ends [33]. (b) Toroidal confinement with charge
separation [33]. (c) Transformer principle with ferromagnetic core. (d) Central solenoid. Remark the helical
trajectory of the magnetic field lines/plasma particles in the last two figures.
implies a non-zero B ⇥ rB drift. This means that plasma particles with opposite signs drift
in opposite directions, as is demonstrated in Figure 1.11b. This charge separation induces an
electric field which - together with the magnetic field - pushes the plasma away from the main
axis of the torus (see Appendix A). As a conclusion, one sees that it is necessary to counteract
the charge separation. This can be done by using a higher current through the toroidal field
coils as the drift velocity is inversely proportional to this current, but a better way is to deform
the magnetic field a little bit, which can be done by means of a plasma current combined with
some poloidal field coils that are positioned around the perimeter of the vessel (tokamak) or
by creating specifically shaped external coils (stellarator). The plasma current referred to
is induced in the tokamak by means of the transformer principle. The tokamak can have
a ferromagnetic core - for example iron - as showed in Figure 1.11c. In this case a current
through the primary winding induces a current in the secondary winding, namely the plasma.
The tokamak may also have a so-called air core, which means that there is a central solenoid
going through the center of the toroidal tokamak vessel having a mutual inductance with the
plasma ring. When this central solenoid conducts a varying current again a plasma current
will be formed. This can be seen in Figure 1.11d. The transformer mechanism makes the
tokamak a pulse device. The ultimate goal of tokamak research is that after the pulse the
plasma is ignited, i.e. that the plasma keeps burning due to self-heating by ↵-particles.
1.2.6
Historical evolution of the tokamak
The “Prehistoric Period” (1905 - 1938). After Einstein’s publication of the massenergy equivalence E = m c2 in 1905, it took a few years until scientists discovered its real
importance. In the nineteen twenties, the British physicist F.W. Aston measured the mass
1.2. THERMONUCLEAR FUSION
21
defect of helium and suggested nuclear fusion as a possible energy source. It would not take
long before astronomers made the link with the stars. The first experiments with magnetic
confinement were set up in the United States as early as 1938. [34]
The time of the pioneers (1946 - 1958) Shortly after the Second World War, thermonuclear fusion became internationally a hot topic. This was notable in the United Kingdom,
where Thomson and Blackman patented in 1946 the concept for a first fusion reactor that
would become known as the Z-pinch. This device already featured two important characteristics of today’s tokamaks: a torus-shaped vacuum vessel and current generation by radiofrequency waves. In the 1950s, during the Cold War, fusion was stamped top-secret. The
Americans, Russians and the British intensified their research and were joined by the French,
the Germans and the Japanese in the late 1955s. Fusion easily found its way to the weapon
industry. Unfortunately, it is often told that this resulted in 1951 in the “first successful
man-made fusion device”, namely a detonator for a fission bomb. [34]
The first international collaboration (1958 - 1968) An important milestone is the unveiling of secret research at the Atoms for Peace conference in Geneva (1958). The di↵erent
countries revealed the magnetic configurations they had been working on: toroidal pulses,
stellarators, mirror machines, Z- and theta-pinches. The physicists realised this was an important step in fusion research but simultaneously had to admit that mastering fusion would
not be an easy task, due to plasma instability, losses in magnetic configurations and so on. It
was the start of collaboration on international scale. At the European level, associations were
set up between the European Atomic Agency EURATOM and the research organisations of
the member countries. These structures predated the current international organisation of
research (EFDA). [34]
The era of the tokamaks (1968-today) In 1968, the amazing results from controlled
fusion experiments with a specific magnetic configuration, the tokamak6 , surprised the whole
fusion community. Russian scientists claimed that the temperatures reached in their T3
tokamak were over an order of magnitude higher than in other existing fusion devices. These
allegations were confirmed in 1969 by a British team, which - right in the middle of the
Cold War - went to Moscow. This revolutionary result opened the era of the tokamaks.
They would rapidly replace the other magnetic configurations. Today, only the stellarator
is still considered as a possible alternative for tokamaks, although its current performance is
significantly lower than that of the latter. [34]
30 years of considerable progress (1968-1998) During the last 30 years of the 20th
century, considerable advances have been made towards the achievement of controlled thermonuclear fusion: the triple product has increased by a factor 100 000! This huge leap forward
is even bigger than the growth in the performance of micro-processors (Moore’s Law, see Figure 1.12a). At the end of the 1990s, the tokamaks JT60-U (DD fuel) and JET (DT fuel)
were close to break-even as can be read from Figure 1.12b by looking at the fictive horizontal
line at QDT = 1. In parallel to this progress in performance, the duration of pulses in the
large tokamaks such as Tore Supra was extended up to two minutes, hence paving the way
6
Acronym of “toroidal’naya kamera s magnitnymi katushkami”, translated “toroidal chamber with magnetic coils”.
22
CHAPTER 1. THERMONUCLEAR FUSION
(a)
(b)
Figure 1.12: (a) The evolution of the triple product is faster than Moore’s law for transistors [36]. (b)
Triple product vs. plasma centre temperature with indication of existing fusion devices and reactor relevant
conditions like break-even and ignition [27].
for continuous operation of future reactors. Another major achievement is the production of
17MW of fusion power obtained in JET in 1997. These major breakthroughs are the result
of 30 years of progress achieved on tokamaks. Our technological know-how as well as our
knowledge of the physical processes have been significantly enhanced in this period. Some of
the improvements to the tokamak design invented those years include non-circular plasmas,
internal divertors and limiters, but also superconducting magnets, and operation in the socalled high confinement mode or H-mode. Table 1.2 sums most of the operational tokamaks7
around the world. This is only a small portion of the estimated 200 tokamaks that existed
once. [34]
Current state of a↵airs: focus on ITER In order to reach the ignition condition needed
for future fusion reactors, the triple product still has to be improved by a factor of around
10, including some margin. Furthermore, the duration of the pulses must be lengthened since
power plants require reactors in continuous operation. The achievement of these goals need
extra funds and since the further development of fusion technology is to everyone’s advantage, this lead to the idea of an international cooperation on the Geneva Superpower Summit
(1985). Seven parties - the European Union, China, India, Japan, South Korea, Russia and
the United States - decided to join their forces. The project was named ITER which is Latin
for “the way”. It is a large-scale scientific experiment intended to prove the viability of fusion
as an energy source. The two main goals are a power enhancement factor Q = 10 and a
pulse duration of about 300s. “ITER will not produce electricity, but it will resolve critical
scientific and technical issues in order to take fusion to the point where industrial applications
can be designed [37].” The ITER Agreement was officially signed by ministers from the seven
members on 21 November 2006. A Broader Approach agreement for complementary research
and development was signed in February 2007 between Europe and Japan. It established a
framework for Japan to conduct R&D in support of ITER over a period of ten years. ITER is
currently under construction in Cadarache, a small village in South-France. The deadline is
7
It is difficult to find reliable sources concerning this matter. Table 1.2 is based on Wikipedia and [35].
1.2. THERMONUCLEAR FUSION
23
Table 1.2: Operational tokamaks around the world.
name(s)
TM1-MH, Castor, Golem
T-10
TEXTOR
JET
Novillo Tokamak
HT-6B, IR-T1
JT-60
DIII-D
STOR-M
Tore Supra
Aditya
COMPASS, COMPASS-D
FTU
ISTTOK
ASDEX Upgrade
H-1 NF
Alcator C-Mod
TCV
TCABR
HT-7
Pegasus Toroidal Experiment
MAST
NSTX
HL-2A
SST-1
HT-7U, EAST
KSTAR
first operation
1960
1975
1978
1983
1983
1983
1985
1986
1987
1988
1989
1989
1990
1991
1991
1992
1992
1992
1994
1995
1998
1999
1999
2002
2005
2006
2008
current residence
CTU, Prague (Czech Republic)
Kurchatov Institute, Moscow (Russia)
Julich (Germany)
Culham (UK)
Mexico City (Mexico)
Tehran (Iran)
Naka (Japan)
General Atomics, San Diego (US)
Saskatoon (Canada)
CEA, Cadarache (France)
IPR, Gandhinagar (India)
IPP, Prague (Czech Republic)
Frascati (Italy)
IPFN, Lisbon (Portugal)
Garching (Germany)
ANU, Canberra (Australia)
MIT, Cambridge (US)
EPFL, Lausanne (Switzerland)
Sao Paulo (Brazil)
Hefei (China)
Madison (US)
Culham (UK)
Princeton (US)
Chengdu (China)
IPR, Gandhinagar (India)
Hefei (China)
Daejon (South Korea)
24
CHAPTER 1. THERMONUCLEAR FUSION
Figure 1.13: Left: ITER scaling law for ⌧E . [38] Right: Scale of European tokamaks with cross-section
similar to ITER. [39]
planned for 2020 and one hopes to execute discharges with the proposed properties in 2027.
[37]
Half a century of tokamak research has resulted in following scaling law for the energy confinement time of ITER-like machines running in H-mode (see [38]):
0.15 0.19
⌧E = 0.0562 R1.97 a0.58 0.78 Ip0.93 n0.41
A P
19 Bt
0.69
(1.38)
with
R the major radius8 [m],
a the minor radius9 [m],
 the elongation10 [-],
Ip the plasma current [MA],
n19 the electron density [1019 m
3 ],
Bt the toroidal magnetic field [T],
A the mean atomic mass of the main plasma species [amu],
P the power externally applied to the plasma [MW].
In order to attain the energy confinement time necessary for the proposed pulse duration
and power enhancement factor, ITER will be much larger than any existing tokamak, with
a plasma volume of 830m3 . Furthermore, superconducting coils will generate high magnetic
fields of about 13 Tesla. Therefore, they have to be cooled by supercritical helium at 4K.
Together with the aimed plasma temperatures of 150 million K, this poses a real challenge:
8
Distance from the central axis of the tokamak to the center of the plasma.
Radius of the cross-section of the plasma (not the vessel).
10
Ratio of the height of the plasma measured from the equatorial plane and the plasma minor radius.
9
1.2. THERMONUCLEAR FUSION
25
(a)
(b)
(c)
Figure 1.14: (a) Model of the ITER site [40]. (b) Picture of the ITER site, August 2013 [41]. (c) Picture
of the tokamak foundations, March 2014 [37].
26
CHAPTER 1. THERMONUCLEAR FUSION
one wants to create the highest and lowest temperatures on Earth a few metres removed from
each other. The scaling law is tested for real tokamak data in Figure 1.13. In order to obtain
a reliable scaling law, tokamaks of di↵erent sizes are needed. This makes small tokamaks like
COMPASS with a lot of ITER similarities very valuable. For more information about the
evolution of the ITER project as well as some details about the di↵erent parts of the machine
- the magnetic coils, the vessel, the divertor array, the lithium blanket, the cryostat,... - one
can surf to the official ITER website [37]. Some models and pictures of the ITER site are
shown in Figure 1.14.
And what after ITER? Hopefully ITER will show that it is indeed possible to use fusion
for commercial energy production. The next step then is the construction of DEMO, a
demonstration power plant. Scientists and engineers of the Broader Approach are already
thinking about the conceptual design of this machine. According to the original agreement,
DEMO should put its first fusion power into the grid as early as 2040. Probably, there
will however be some delay, because ITER experiences already some difficulties and is not
perfectly on schedule any more. The cost of the project has already been tripled since its
start, and for example the US is already thinking to set a limit to its annual funding, which
would slow the project further down. [42]
1.3
Fusion: pros and cons
Some major advantages of fusion are:
• The needed amount of fuel is very small in contrast to fossil fuel burning. The fuels
have a very large energy density: 1g DT = 26000kWh, 1g coal = 3Wh. [43]
• The fuels are abundant and geographically widespread. Deuterium can be extracted
from sea water. Tritium is made by neutron bombardment of lithium, which eventually
should also be possible to extract from sea water. Almost everywhere on Earth fusion
fuels are available. There is no motivation for an “oil war”.
• Fusion does not give rise to toxic, greenhouse or acid rain gasses in contrast to fossil
fuel burning.
• The reactors are inherently safe. “Meltdown” situations are physically impossible.
There is only a small amount of fuel present in the reactor region, enough for a few
tens of seconds operation. Accidents are self-limiting.
• Fusion o↵ers no efficient way to create nuclear weapons. The only useful substance
present is tritium, but it is produced and consumed in the reactor. There is some
tritium inventory, but it is too small. The heavy water (D2 O) storages present in the
deuterium production site could be used to form nuclear weapons if they are in bad
hands.
• Fusion leaves no long-lived highly radioactive waste. The small tritium inventory and the
neutron-activated structural materials of the reactor form the biggest threats. However,
tritium is short-lived and only dangerous in case of incorporation, and the structural
1.3. FUSION: PROS AND CONS
27
Figure 1.15: Radiotoxicity.[44]
materials can be selected so that after 100 years only low level radioactive waste remains.
The total amount of radioactive material produced is of the same order of magnitude as
for fission reactors, but the radiotoxicity11 is much smaller: there is a huge drop during
the first 50-100 years to the level of coal ash and even lower (see Figure 1.15). A good
selection of the used reactor materials permits after 100 years to clear 30-40% of the
waste and to (partially) recycle about 60%. Only 1% of the waste is long-living, but
has a low level of radioactivity. [43]
• Fusion allows quite compact large-scale power plants of 1GW and more in contrast to
renewables.
• Fusion allows to build baseload power plants. It has no variable character such as solar
and wind power.
Some major disadvantages of fusion are:
• The fusion reaction is difficult to start. Fusion research had already taken o↵ very well
in 1950 and still no net energy producing fusion device is manufactured. The physical
modelling of plasmas in fusion devices is very complex as is the technical design. High
temperatures have to be reached in pure high vacuum amongst other challenges.
• The costs for high-technological fusion research is enormous. There are not enough
investments and the governments’ subsidies were for a long time insufficient.
• Nuclear waste is unavoidable. Neutron radiation originating from the fusion reactions
will induce radioactivity in surrounding materials and the inside of the reactor will be
contaminated with tritium. Careful material selection and design can however limit the
amount and lifetime of the nuclear waste.
11
Radiotoxicity is a measure for the detrimental e↵ect of an incorporated radioactive substance on the human
body. It is defined as the ratio of the radiation dose (expressed in Sv=J/kgequivalent ) and the incorporated
activity (expressed in Bq=# decays/s) summed over all isotopes.
28
CHAPTER 1. THERMONUCLEAR FUSION
• As the energy confinement time ⌧E increases with plasma volume, fusion reactors must
have a minimum size and small-scale power plants are infeasible.
[27] [43]
Chapter 2
The tokamak COMPASS
2.1
Introduction
All experiments treated in this work were performed on the COMPASS tokamak at the Institute of Plasma Physics (IPP) of the Academy of Sciences in Prague (Czech Republic).
Originally, COMPASS was designed and built in Culham Centre for Fusion Energy (United
Kingdom) in the eighties. Its name, which is a contraction of the words ‘compact’ and ‘assembly’, points to the fact that it is a rather small device. The appendix ‘D’ is now often added
because of its D-shaped vacuum vessel. This vessel replaced the original circular shaped one
in 1992 and enabled the achievement of high plasma confinement (H-mode). The most important parameters of COMPASS are listed in Table 2.1.
Due to its size, shape and capability of operating in H-mode regime, COMPASS plays an
important role in the ITER project. There are only two other tokamaks in Europe with
similar ITER-like properties: JET (Culham,UK) and ASDEX-U (Garching, Germany). JET
is the biggest in rank, COMPASS the smallest. Given the huge complexity of the physical
processes acting during tokamak discharges, it is impossible to make one stable simulation
that takes everything into account. So, one has to rely on experiments and extrapolations to
determine the design parameters of ITER. These extrapolations improve if more data from
di↵erently sized tokamaks is available. Since COMPASS is one of the only small tokamaks
capable of H-mode operation, its data is very valuable.
Table 2.1: General parameters of COMPASS. [45]
parameter
major radius R
minor radius a
plasma current Ip
toroidal magnetic field Bt
vacuum pressure
elongation 
plasma shape
pulse length
NBI heating
current max value
0.56m
0.23m
350kA
1.8T
2 · 10 6 Pa
1.8
circular, elongated, D-shape
0.35s
undetermined
29
predicted max value
0.56m
0.23m
350kA
2.1T
1 · 10 6 Pa
1.8
circular, elongated, D-shape
0.50s
2 ⇥ 350kW
30
CHAPTER 2. THE TOKAMAK COMPASS
Figure 2.1: COMPASS vacuum vessel.
In 2002, the emphasis of the research in Culham shifted to the bigger, spherical tokamak
MAST. Because the funds did not suffice to keep both tokamaks in operation and because
of the importance of COMPASS in the ITER project, COMPASS was given for free to the
IPP in 2004. The IPP was chosen because of its long-time experience with the very small
tokamak CASTOR - now known as GOLEM and property of the Czech Technical University in Prague. In December of 2007, COMPASS was installed in the new tokamak hall of
the IPP. About one year later, the first plasma was observed. And about 4 years later, on
29/11/2012, the first operation in H-mode was performed, thanks to improved plasma control,
upgraded conditioning of the first wall, and additional heating by neutral beam injectors. [46]
In what follows a basic description of the most important parts of COMPASS is given, i.e.
the vacuum vessel, the magnetic coils, the central solenoid, the heating system and of course
the diagnostics for research and control of the plasma.
2.2
2.2.1
Vacuum vessel
Design
As mentioned in the introduction, the first vessel of COMPASS had a circular cross-section.
This was changed to a D-shape, so that a divertor configuration could be applied. Table 2.2
sums some of the vessel’s properties. It is made of inconel-625, an alloy armed against high
temperatures. The torus consists of 8 pieces joined together by D-shaped rings which can
contain magnetic diagnostics (see Figure 2.1). There are 69 ports with copper gasket flanges
to ensure a high quality vacuum.
It is very important to avoid impurities in the plasma as much as possible, because they cool
the plasma down through bremsstrahlung. Therefore, COMPASS is equipped with limiters
and a divertor (see Figure 2.2). The limiters form a material shielding between the plasma
and the vessel wall that at the same time results in a deflection of the magnetic field lines.
In a divertor configuration the outermost magnetic lines are bended in the direction of the
divertor ring at the bottom of the vessel so that the plasma particles that normally would
collide with the vessel wall are now colliding with the target plates of the divertor or with
neutral gas. It also allows an easy way to get rid of the fusion ash. Both the limiter and the
divertor tiles are made from high-density isotropic graphite.
2.2. VACUUM VESSEL
31
Figure 2.2: Left: Inside of the COMPASS vessel. Right: Picture made by EDICAM with indication of the
separatrix, i.e. the boundary between closed and open field lines, and other nomenclature for a D-shaped
plasma.
Table 2.2: Vessel parameters. [47]
parameter
material
thickness
volume
surface area
toroidal resistance
poloidal resistance
basic vacuum
bake-out temperature
limiter/divertor material
value
inconel-625
3mm
1m3
8m2
0.63m⌦
0.25m⌦
10 6 Pa
150 C
graphite
The vessel is pumped by a vacuum system, which consists of a vacuum pump and two turbo
molecular pumps with a pumping speed of 500l/s each. All vacuum pumps are oil-free to
prevent the release of impurities. [47]
2.2.2
Cleaning procedure
After the vessel has been opened for maintenance, adjustments or repairs the inside has to be
cleaned from impurities and the vacuum has to be re-established. The first action is pumping the vessel down to about 19Pa by a vacuum pump. When the pressure is at this level,
the turbo molecular pump starts and decreases the pressure down to values in the order of
10 6 Pa. Because there is an equilibrium between the molecules in gas and the molecules absorbed by the surface of the vessel, some molecules will always stay on the vessel wall. When
the pressure drops and so less gas molecules are present, more of these absorbed molecules
will be released and pumped away. To speed up this process the vessel is being heated to
about 150 C for several days1 . The absorbed molecules at the surface of the vessel get more
kinetic energy and are able to leave the surface this way. This process is called bake-out.
We already saw in paragraph 1.2.5 how one uses the transformer principle in a tokamak to
induce a plasma current. The beauty of this transformer configuration is that when there are
no charged particles in the vessel, it is not the plasma but the vessel itself that acts as the
1
About 5, depending on the amount of impurities on the surface.
32
CHAPTER 2. THE TOKAMAK COMPASS
secondary winding. In other words, the vessel is ohmically heated by applying a large alternating current to the central solenoid. A gradual temperature increase is required because
the di↵erent parts of the tokamak have a di↵erent coefficient of expansion and if the heating
would go to fast, some of the components would expand faster than others and cracks could
appear. So therefore it takes about 6 hours to get to the 150 C.
After the bake-out still not all the impurities are removed from the vessel wall. Therefore
a second cleaning process, called Glow Discharge Cleaning (GDC) is performed next. Here,
extremely pure helium gas is put in the vessel. Next, a graphite electrode, located inside the
tokamak vessel in the limiter shadow, is positively biased, so that the helium breaks down
and a part of it is ionized. Finally, the positively charged helium ions bombard the negatively
charged vessel, desorbing the last remaining impurities. These are again removed by the
vacuum pump. [47]
The GDC is often combined with boronization of the vacuum vessel: during the helium
discharge o-carborane (C2 B10 H12 ) is sublimated and forms a hard boron-containing coating
on the vessel wall. During the actual operation of the tokamak this low-Z coating reduces the
interactions of the plasma particles and the impurities with the wall material in addition to an
improvement of the vacuum condition by gettering oxygen. Oxygen is in particular important
for carbon-based plasma-facing materials - like the limiters and divertor in COMPASS - due
to its ability to form CO and CO2 with very high erosion yields near to unity, i.e. almost
every O-atom falling in on the C-containing PFM will chemically react and erode the PFM.
Boronization is an inevitable procedure to achieve H-mode. [48] [49] [50]
2.2.3
Conservation of vacuum
To ensure that there are no leaks at the connection pieces between the vessel and the equipment, copper rings are used. This technique requires the two couplers to have a knife edge
which deforms the copper ring placed between them when they are pressed together. This
results in a very tight seal. Normally, copper rings can only be used once.
It is possible to install appliances to the vacuum vessel while it is vacuum because there are
airtight valves between the vacuum vessel and the appliance. After installation the valve
can only be opened if the appliance itself is cleaned and made vacuum. Therefore about the
same procedure as for the vacuum vessel is followed: first the appliance is pumped to a very
low pressure, and then heating strips are put on it to bake the appliance in order to remove
impurities from the contact surfaces.
In order to detect leaks, one applies helium gas pu↵s near the weak spots where leaks can be
expected. For example, after installing an appliance, one will introduce a pu↵ of helium in
the surroundings of the new appliance2 and analyse the air pumped from the appliance by
a spectrometer to see whether there is helium present and in what quantity. Helium is used
because it is almost the smallest molecule and it has a very low appearance in the atmosphere.
[47]
2
At the outside of course.
2.3. MAGNETIC COILS
2.2.4
33
Fuel
The working gas was originally hydrogen, but nowadays deuterium is used because this makes
the research more ITER-relevant. Experiments with tritium will never happen at COMPASS
because of safety reasons, but several attempts have been done with helium as working gas.
[47]
The D-D fusion reaction
2
1D
+ 21 D ! 31 T + 11 p (50%)
! 32 He + 10 n (50%)
(2.1)
(2.2)
has a very low h F vi and by consequence its occurrence is almost zero. For typical electron
temperatures in COMPASS, which is about 1keV, h F vi is not even mentioned in Figure 1.8.
It is definitely far below 10 26 m3 s 1 . Hence, the fusion energy released by the few reactions
that occur in this machine is negligible.
2.3
Magnetic coils
2.3.1
Central solenoid
During operation, a gradually increasing current Is is sent through the central copper solenoid.
This creates a toroidal electric field
Et =
Ls,p dIs
2⇡r dt
(2.3)
Here, Ls,p is the mutual inductance of the solenoid and the plasma. This electric field exerts a
toroidal force on the charged plasma particles. As the electrons are much lighter than the ions,
they are more accelerated. A plasma current is produced. It is clear that the pulse length
of the central solenoid is limited since Is cannot increase forever. Compared to tokamaks
with ferromagnetic cores however very high current can be reached. These last ones have the
disadvantage to be subject to hysteresis: Beyond a certain maximum current through the
primary winding, the magnetic flux does not change enough any more due to the occurring
saturation.
2.3.2
Toroidal and poloidal field coils
As mentioned in paragraph 1.2.5, the magnetic coil system of a tokamak consists of toroidal
field (TF) coils, maintaining the basic confinement of the plasma, and poloidal field (PF)
coils, correcting the plasma position in the horizontal as well as the vertical direction. COMPASS has got 16 TF coils which are located outside the PF coils and which are positioned
at an equal distance from each other. They each consist of two L-shaped pieces connected
by screws. The electromagnetic expansion forces acting on the two joints are countered by a
hydraulic preload system. Both the TF and PF coils are made of copper which implies energy losses due to their resistance. Therefore, these copper coils have to be water-cooled. In
ITER these losses are unacceptable and thus superconducting coils will be used. The major
drawback of superconductivity is that it is lost above a critical magnetic field.
34
CHAPTER 2. THE TOKAMAK COMPASS
Figure 2.3: PF coil configuration of COMPASS.
The PF coils are depicted in Figure 2.3. The whole PF coil system is made up of four di↵erent
parts, each with its own power supply and its own function:
• Magnetizing field (MF) coils: Together with the central solenoid they set up and sustain
the plasma current. They strongly reduce the stray magnetic field of the central solenoid.
• Shaping field (SF) coils: They create the desired plasma shape. Di↵erent configurations
are possible: circular, single-null-divertor configuration (SND)3 , single-null-divertor
configuration with high triangularity (SNT)4 ,... For all shots that will be discussed in
this thesis, the shape was programmed to be SNT.
• Equilibrium field (EF) coils: They correct the position of the plasma over long timescales. The vertical magnetic field prevents the plasma column from expanding in the
radial direction.
• Feedback (F) coils: The fast feedback coils provide position control of the plasma on
short time-scales. The BR circuit creates a horizontal (radial) magnetic field for fast
feedback control of the vertical plasma position, the BV circuit creates a vertical magnetic field for fast feedback control of the horizontal plasma position.
[27] [51]
2.3.3
Power supplies
COMPASS needs an electrical input power of 50-60MW for about 2-3 seconds. Since the
grid at the campus of the Academy of Sciences in Prague can only deliver 1.5MW, an energy
storage system had to be designed and constructed. The choice fell on the installation of
two flywheel generators. These machines are able to store huge amounts of rotational energy
carried by a very heavy rotor that is kept in the horizontal plane by bearings and is “flying”
on a thin layer of oil. The flywheel generators are each able to deliver 35MW during a pulse
of about 3s. They are first loaded for 40 minutes to get a rotation speed of 1700rpm. After
3
The single-null-divertor configuration (SND) has a plasma shape with only one x-point. The x-point can
be seen in Figure 2.2. It is the point where the magnetic field lines cross each other.
4
The plasma triangularity is defined as the horizontal distance between the plasma major radius and the
x-point. An average value for the discharges performed with COMPASS is = 0.35-0.40. Remark that in
Table 2.1 SND and SNT are present under the name ‘D-shape’.
2.3. MAGNETIC COILS
35
Figure 2.4: Scheme of the power supply system. [45] [52]
the pulse, 1300rpm remains and it takes another 10 minutes to regain the used energy. The
output is an AC current of 85Hz. Note that thanks to the flywheel generators COMPASS
doesn’t need any capacitor banks to store energy and release it as a pulse in contrast to other
tokamaks like for example GOLEM. [47] [52]
Every big energy user among the components of COMPASS (the TF and PF coils, the NBI)
all have their own power supply that has to be fed by the flywheel generators. The circuit that
regulates all this, is shown in Figure 2.4. The two flywheel generators (A and B) provide their
power to the local three-phase 6.3kV grid. Switches allow to uncouple generator B which then
only supplies the TF coils. Generator B is only used when maximal toroidal fields (Bt = 2.1T)
are required, which is not always the case. Afterwards, the AC voltage three-phase 6.3kV is
transformed by three-winding transformers (T3A, T3B, T4, T5 and T6) and rectified in 12- or
24-pulse thyristor converters (⇠ / =), which control the DC current in the tokamak coils. The
PF coils are connected by four cables in quadrupole configuration (see Figure 2.5e) and an
assembly of eight copper plate busbars with alternating polarity is used for the TF coils (see
Figure 2.5c), leading to minimization of the stray fields in the vicinity of the tokamak. The
current needed for the TF coils is so high that the repulsive forces between the cables would
be too big to form a quadrupole. Transformers T8, T9 and T10 supply the auxiliary systems
(NBI and feedback system) by AC three-phase 400V. The converter control system and other
equipment are supplied via transformers T17 and T18. The magnetizing field power supplies
contain some auxiliary capacitor banks (see the box with ‘OH start’). These are used for
example in the start-up circuit to turn o↵ the thyristors in order to get a plasma start-up as
efficient as possible. The flywheel-generators are placed outside the assembly hall in a special
36
CHAPTER 2. THE TOKAMAK COMPASS
sound-proof building with a 6m thick concrete base to counteract the vibrations, while the
local control of the power supply system, transformers, and the switching station are located
in the assembly hall. The thyristor rectifiers are installed in the tokamak hall. Figure 2.5
creates an image of the IPP building. [52]
2.4
2.4.1
Heating system
Ohmic heating
Ohmic heating is inherent to the tokamak concept. The plasma current Ip heats the plasma
according to
POH = Rp Ip2
(2.4)
Since the plasma resistance Rp obeys
Rp / T e
3
2
,
(2.5)
ohmic heating becomes less efficient after a while and a limited plasma temperature of around
2-3keV can be reached. We saw however in paragraph 1.2.4 that for a satisfying fusion reaction
rate 10-20keV is required. So additional plasma heating sources are needed. COMPASS uses
two neutral beam injectors, but other options are heating by electromagnetic waves (ECRH,
ICRH) and internal heating by ↵-particles in case of D-T fusion which is only possible if
the ↵-particles have enough time to give their energy to the plasma, i.e. they do not collide
immediately with the vessel wall. [47] [53]
2.4.2
Neutral beam injection (NBI)
Working principle
The basic idea of neutral beam injection is to shoot neutral atoms with a large unidirectional
kinetic energy into the plasma, where they ionize, get captured by the confining magnetic
fields and exchange their energy with the other plasma particles by collisions resulting in an
increasing plasma temperature. Remark that the atoms indeed have to be neutral to penetrate the magnetic fields. On the one hand the beam needs to have sufficient energy so that
the atoms are ionized in the plasma center and not in the plasma edge, but on the other hand
this energy may not be too large to avoid shine-through losses, i.e. losses due to the collision
of the beam with the vessel wall.
Briefly summarized, the NBI system makes ions, accelerates them and neutralizes them before entering the tokamak vessel. The basic internal mechanism of a neutral beam injector is
demonstrated in Figure 2.6a. First, the neutral gas5 is pu↵ed to the plasma box, where it is
ionized by an RF source and a dense plasma is formed. Next, the plasma ions are extracted
and accelerated by four grids as seen in Figure 2.6b. These grids are bended to focus the
beam and are at an electrical potential of respectively 40kV, 32kV, -0.5kV and 0kV. One can
see from the total potential di↵erence that the ions will have a maximum energy of 40keV
when they pass the last grid. Then, the ion beam enters the neutralizer chamber where the
5
Normally, atoms with the same atomic number as the plasma fuel. In case of COMPASS usually hydrogen
(in the past) or deuterium (now) is used.
2.4. HEATING SYSTEM
37
(a)
(c)
(b)
(d)
(f )
(e)
(g)
Figure 2.5: (a) ground plan of the IPP, (b) the tokamak COMPASS itself on the 2nd floor of the tokamak
hall, (c) TF coil busbars, (d) 1st floor of the tokamak hall, (e) PF coil cables, (f ) transformers, (g) flywheel
generators.
38
CHAPTER 2. THE TOKAMAK COMPASS
(a)
(b)
Figure 2.6: (a) Basic working principle of NBI. (b) Accelerating grids. [54]
ions are converted to fast neutral particles by charge exchange collisions. The third grid
with negative voltage is used to prevent secondary electrons created in the neutralizer from
going back in the direction of the plasma box. At last, after the remaining unneutralized ions
are deflected by a magnet to the ion dump, the created neutral beam is ready to enter the
tokamak vessel. Of course it is undesirable that some neutral particles of the neutralizing gas
enter the tokamak vessel. These “cold” particles would only cool the plasma down. Hence, a
cryopumping system removes the slow neutral particles that passed the magnet.
In case that the neutral gas for the NBI system of COMPASS is deuterium (D2 ), the ion beam
going from the plasma box to the neutralizer chamber will consist mainly of deuterons (D+ ),
+
but also of molecular ions like D+
2 or even D3 , and impurity ions. In the neutralizer chamber,
these ions collide with neutral deuterium gas and with 78% chance they pick up an electron
from the low-energetic molecule and thus become neutral6 . The particles practically conserve
their energy and momentum after the collision. The general charge exchange reaction for
deuterium is as follows
D+ + D2 ! D + D+
(2.6)
2
But as mentioned before, there are also these molecular ions. These ions will be dissociated
in the neutralizer into single ions and atoms.
+
D+
2 + D 2 ! D + D + D2
D+
2
D+
3
+ D2 ! D + D +
(2.7)
D+
2
+ D2 ! D + D + D +
(2.8)
D+
2
(2.9)
The consequence is that the original energy and momentum of the molecular ion is equally
divided among its constituents after the dissociation reaction. The resulting atoms of D+
2 have
an energy of only half the original energy, these of D+
only
one
third.
A
similar
argumentation
3
can be made in case the NBI gas is hydrogen. According to the manufacturer the neutral
particle beam will then have following energy spectrum: 70% of the particles will have the
full energy of 40keV, about 25% will have only 20keV and about 5% will have an energy of
about 13keV. The impurities only represent a very small fraction of the neutral beam. These
values still have to be confirmed by measurements. Besides, the corresponding percentages
for deuterium have to be determined. This is planned for the near future. [47]
6
In case of hydrogen this chance is only 68%.
2.4. HEATING SYSTEM
39
(b)
(a)
(c)
(d)
Figure 2.7: COMPASS Neutral Beam Injectors. Technical schemes of (a) lateral view and (b) top view with
cryopump system. Pictures of (c) lateral and (d) frontal view. [54]
40
CHAPTER 2. THE TOKAMAK COMPASS
Detailed description of the COMPASS Neutral Beam Injectors
The ion source is essentially a RF discharge plasma generator (specs 4MHz, 30kW) that
creates ions, equipped with 4 grids on di↵erent potentials to accelerate the ions. Each grid has
887 holes of 4mm diameter. The total ion beam has a diameter of 167mm. The whole system
is surrounded by an electrostatic and a magnetic shield to protect the ion source against the
stray fields from the tokamak (see Figure 2.7d). During shots the grid edges are cooled with
water, whereas between shots they are cooled through radiation. Cooling is necessary to avoid
deformation of the grids. A few tenths of a millimetre can lead to poor focus.
The neutralizer contains a thick gas target. In case of COMPASS, the deuterium gas flow
used for the ion source suffices. No extra gas puffing is needed. The ion beam undergoes subsequent charge exchange reactions (ion, neutral, ion, neutral,...). The efficiency is determined
by the ratio of the cross-sections of both reactions. These cross-sections depend on the energy
of the incoming ions. For a voltage of 40kV over the grids 78% of the ions is neutralized. The
bending magnet is a coil of 26 turns and a current of 338A is flowing through it to send the
positively and the negatively charged ions to the right ion dump.
There are two copper ion dumps. The lower one has to catch the positively charged ions. It
is water-cooled because the power of the positively charged beam can be up to 200kW. The
upper one has to catch the negatively charged ions. It is not cooled because only about 1.5%
of the ions is negatively charged.
The cryopump is composed of two cryopanels, each with an active surface of 0.3m2 (see
Figure 2.7b). These cryopanels are connected to a 4K closed-cycle refrigerator system which
works with liquid nitrogen7 . By condensing and even solidifying the slow (“cold”) neutral particles in the vacuum tank on the 4K cryoplates these unwanted particles are kept away from
entering the tokamak vessel. The cryopanels provide a pumping speed of about 100 000 l/s.
To test the neutral beam injector it is possible to place a calorimeter as a target on the beam
path. This calorimeter is V-shaped in order to reduce the power density at the copper surface.
There are 4 thermocouples at each side of the target: left, right, above and below. These
thermocouples are placed 2mm from the irradiated surface so they can give an estimation
of the beam power at the beam axis, the beam position and the eventual divergence of the
beam. The calorimeter has to be cooled with water, but even correctly cooled it cannot survive
a pulse at full power (300ms, 350kW). For tests the pulse length is therefore limited to 100ms.
The aiming device is a diaphragm located at the output of the vacuum tank. It uses 4
detectors to adjust the beam axis. These detectors measure the flux of the neutral particles
using secondary emission. Like all the other equipments, the aiming device is water-cooled.
The COMPASS tokamak has got two such neutral beam injectors as described above. These
are placed in a co-injection configuration, as seen in Figure 2.8a, which increases the plasma
rotation. If for example in other tokamaks this extra plasma rotation is unwanted, one can
opt for the balanced injection configuration (Figure 2.8b). The two COMPASS neutral beam
7
Remark that liquid nitrogen is only responsible for the precooling to a temperature of 70K. The remaining
cooling is done by a sophisticated compressor refrigerator.
2.4. HEATING SYSTEM
41
(a)
(b)
Figure 2.8: NBI duo configurations: (a) co-injection and (b) balanced injection. [56]
injectors have a tangential orientation, in contrast to ITER where the injectors are oriented
perpendicular to the vacuum vessel. Due to the small size of COMPASS there would be a lot
of shine-through losses if the NBI was perpendicular to the vacuum vessel. [55]
Beam power delivered to the plasma
In next chapter, we will often encounter the standard applied grid voltage of 40kV accompanied by a current expressed in Ampères. These two quantities are preprogrammed by the
tokamak operators at the IPP and can be adjusted for every shot. Their product gives the
NBI power right behind the accelerating grid. In order to know the power added to the
plasma, some complications have to be kept in mind:
• The neutralizer has an efficiency of 78% according to the manufacturer.
• Reactions (2.7)-(2.9) cause part of the neutral particles to have 1/2 and 1/3 of the
maximum energy of 40keV.
• Due to the geometry of COMPASS, the injectors are not installed at the foreseen distance from the plasma. The longer beam trajectory certainly decreases the beam power
added to the plasma. It definitely has also negative consequences for the focus of the
neutral beam.
• There may be shine-through losses.
The exact e↵ects of the second and third point are unknown for the moment. This is very
impractical since the NBI power is an important quantity to solve the energy balance and
to determine the energy confinement time. Both neutral beam injectors have a design value
of 350kW. However, until now only measurements with one injector at full power and one
injector at half its power are possible. These are issues that still have to be investigated.
Attenuation of the neutral beam in the plasma
In the plasma there are 3 ionization channels:
ionization by plasma electrons :
ionization by plasma ions :
charge exchange collision :
D + e ! D+ + e + e
+
+
+
+
+
D+D !D +D +e
D+D !D +D
h e ve i/vb
(2.10)
i
(2.11)
ch
(2.12)
42
CHAPTER 2. THE TOKAMAK COMPASS
Here, vb is the begin velocity of the neutral deuterium atoms, ve is the velocity of the plasma
electrons and ‘h i’ represents the integration over the electron velocity distribution. All crosssections depend on the velocity vb , and e also depends on the electron temperature.
The intensity of the neutral beam decreases along the path through the plasma by the di↵erential equation
✓
◆
dI(x)
h e ve i
= n(x)
+ i + ch I(x)
(2.13)
dx
vb
For the beam energy of COMPASS - approximately 40keV - holds:
h e ve i/vb = 1.0 · 10
i
= 1.4 · 10
ch
= 6.5 · 10
20
m
20
2
20
m2 (Te ⇡ 1keV)
2
m (dominating)
(2.14)
(2.15)
(2.16)
This means that the total cross-section for the beam attenuation is given by
tot
= 9.0 · 10
20
m2
(2.17)
If we assume a homogeneous plasma with density n(x) = n0 , the beam intensity attenuates
exponentially by
I(x) = I0 e tot n0 x
(2.18)
and the normalized beam power delivered by the neutral beam to the plasma is then given
by
P (x)
I(x)
=1
= 1 e tot n0 x
(2.19)
P0
I0
For a path length through the COMPASS plasma of about 1m - considering the tangential
setup of the neutral beam injectors - one can estimate the density n0 at which the beam
power is almost fully absorbed by the plasma before reaching the vessel wall as
n0 = 6.0 · 1019 m
3
(2.20)
For this average density P (1m)
< 1%. This gives us an idea when we have to start the NBI
P0
to avoid big shine-through losses. [54]
2.5
2.5.1
Diagnostics
Control room
During operation of COMPASS the control room looks like Figure 2.9. By ways of introduction to this diagnostics section, we summarise the data shown on the six panels in front of
the room. From left to right the panels show
1. Plasma temperature and density as a function of the distance from the plasma center,
using the Thomson scattering diagnostic.
2. Time evolution of the main plasma parameters: plasma current, plasma density, loop
voltage, total visible radiation, D↵ emission, hard x-ray radiation,...
2.5. DIAGNOSTICS
43
Figure 2.9: Control room in the IPP building. The chief operators sit in front of six big screens that show
data about the last discharge.
3. Reconstruction of the magnetic flux surfaces (also surfaces of constant pressure); observation of the plasma by the fast camera.
4. Basic technical data of an ongoing experiment.
5. Monitoring the tokamak and its main systems using cameras.
6. Commentary to an ongoing experiment.
In the next paragraphs the techniques used to measure this data will be explained. Therefore
a subdivision of the di↵erent diagnostics is made: there are magnetic diagnostics, microwave
diagnostics, spectroscopic diagnostics, beam and particle diagnostics and probe diagnostics.
2.5.2
Magnetic diagnostics
There are 440 magnetic diagnostic coils in total positioned all over the vacuum vessel of
COMPASS (see Figure 2.10). These enable the measurement of
• basic plasma parameters: plasma current, average toroidal magnetic field, loop voltage,
total energy content, etc.
• plasma position and shape
• magneto-hydrodynamic instabilities
• reconstruction of magnetic surfaces (EFIT program code)
Table 2.3 sums some magnetic diagnostics and their purposes. In what follows some more
information is given about three important magnetic diagnostics: the inductive loops in general, the Rogowski coil and the diamagnetic coil. The last paragraph treats EFIT.
Inductive loops (flux loops)
By measuring the voltage over inductive loops as shown in Figure 2.11, we are able to determine the magnetic flux B passing through them. Indeed, starting from Faraday’s law
r⇥E=
@B
@t
(2.21)
44
CHAPTER 2. THE TOKAMAK COMPASS
Figure 2.10: Left: Magnetic diagnostics attached to the COMPASS tokamak [46]. Right: Other diagnostics,
pumping and NBI [57].
Table 2.3: Magnetic diagnostic coils. [46]
name of the coils
full toroidal loops
(flux loops)
location with
respect to the
vessel
purpose of the measurement
loop voltage and poloidal flux
(used for real-time control and EFIT)
the di↵erence in poloidal flux
(used for real-time control and EFIT)
loop voltage and poloidal flux
perpendicular beta ?
saddle loops
remote loops
diamagnetic loops
diamagnetic
compensation loops
FCA coils
ext
ext
int
8
22⇥4 and
2⇥8
5
2
int
ext
2
16⇥3
discrete Mirnov
coils
high n coils
divertor Mirnov
coils
int
3⇥24⇥3
int
4
int
2⇥8
internal partial
Rogowski coils
int
16
ext
1 ext and
1 int
16
toroidal field
horizontal, vertical and toroidal field
local poloidal, radial and toroidal
fields (hence 3 times), 24 at one crosssection (used for halo currents study)
n-number of MHD instabilities
coils embedded in divertor plates
(used for ELMs study)
local magnetic field parallel to the
vacuum vessel (used for poloidal
current density distribution, real-time
control and EFIT)
local magnetic field parallel to the
vacuum vessel, eddy currents
2
plasma and vacuum vessel current
external partial
Rogowski coils
full Rogowski coils
ext
number of
coils
2.5. DIAGNOSTICS
45
and integrating both sides over the surface enclosed by the loop combined with Green’s
theorem, we find
I
@ B
✏ = E · dl =
(2.22)
@t
@S
or
B (t)
=
Zt
✏(⌧ ) d⌧
(2.23)
0
with ✏ the voltage across the loop. The appearing integration over time is executed by an
analogue integrator circuit.
Figure 2.11: Flux loop.
The 8 full toroidal loops are a type of inductive loops that is worth extra mentioning. In
this case ✏ is the so-called loop voltage. From this loop voltage, one can easily determine the
toroidal electric field by
Uloop
Et =
(2.24)
2⇡r
where r is the radius of the toroidal loop. These loops are also used to measure the poloidal
magnetic flux, which is used by EFIT to reconstruct the magnetic flux surfaces.
Rogowski coils
Rogowski coils are used in Ampère meters but also in tokamaks to measure the plasma current
and the vacuum vessel current. They are composed of a helically wound solenoid with a return
center conductor so that the coil has no net loop around the current carrying conductor or
plasma, and are usually encased in a Faraday shield to avoid electrostatic pickup (Figure
2.12). If we define A as the surface area of the windings, N the total number of windings and
l the length of the return loop, than Faraday’s law (see equation (2.22)) says
✏=
NA
@Bp
@t
(2.25)
There is no contribution of the toroidal magnetic field because there is no net loop around
the plasma. Next, applying Ampère’s law
r ⇥ B = µ0 J + µ0 ✏ 0
@E
@t
(2.26)
reveals
Bp l = µ0 Itor
(2.27)
46
CHAPTER 2. THE TOKAMAK COMPASS
where the electric field is channelled by the Faraday shield. Combining equations (2.25) and
(2.27) we find the relationship between the voltage over the Rogowski coil and the plasma
current (Ip = Itor )
µ0 AN @Ip
✏=
(2.28)
l
@t
or
Zt
l
Ip (t) =
✏(⌧ ) d⌧
(2.29)
µ0 AN
0
Again an analogue circuit is used to solve the time integration. The shape of this contour is
irrelevant, as is the angle between the Rogowski coil and the enclosed current.
Figure 2.12: Rogowski coil with basic integrator circuit.
Diamagnetic coils
The toroidal field is a superposition of
• Of course, the magnetic field generated by the TF coils which is the biggest contribution.
• The diamagnetic e↵ect: the particle gyration decreases the toroidal field.
• The paramagnetic e↵ect: the poloidal component of the plasma current increases the
toroidal field.
Since the first contribution is so much bigger than the others, very sensitive diagnostic devices
are needed in order to measure the diamagnetic and paramagnetic e↵ects. Next figure shows
one setup used to measure these e↵ects. The so-called diamagnetic coil consists of two coils
wound around the vessel, their radii smaller than that of the TF coils. The Bt coil contains
the plasma column and consequently measures the total magnetic flux. The vacuum field coil
or compensation coil is wound around the vessel many times, is then moved a few millimetres
radially outwards and finally wound back. It measures only the contribution of the TF coils.
The di↵erence in magnetic flux
between both coils is given by
=
para
+
dia
=
µ20 2
I
8⇡Bt p
µ0
W?
Bt
(2.30)
Here, W? denotes the thermal plasma energy in the poloidal cross-section [J/m]. This formula
allows to calculate the total thermal energy stored in the plasma as
3
Wth = W? 2⇡R
2
(2.31)
2.5. DIAGNOSTICS
47
Figure 2.13: Diamagnetic coil. [58]
with R the major radius. The factor 3/2 is needed for the transition from two to three dimensions, the factor 2⇡R describes the path length of the plasma center in the toroidal direction.
[58]
The data measured by the diamagnetic coil from above is stored under the name ‘diamagnet PP Energy’. Another method to measure W goes exactly the same except that the field
generated by the TF coils is derived from measurements of the TF coil currents with Rogowski
coils. This data can be found in ‘diamagnet PP EnergyBT’. Both methods should give the
same result. The problem is the presence of crosstalk from di↵erent sources to the compensation coil and the Rogowski coils. The majority of them can be quantified in a vacuum shot,
but the crosstalk from the plasma current cannot. The di↵erence between the two signals is
directly proportional to Ip . It is not known which of the two is correct... if there even is one
exactly correct. [59]
EFIT
EFIT, or Equilibrium FITting code, performs an equilibrium reconstruction based on several
input parameters (plasma parameters and tokamak geometry) by iteratively solving the GradShafranov equation
rp = J ⇥ B
(2.32)
which expresses the balance of pressure forces and magnetic forces in a fusion device in
quasi-stationary state. In this way information is obtained about the magnetic configuration,
plasma shape and position, current and pressure profile, stored energy, plasma- and safety
factor q. The actual Grad-Shafranov equation is another form of equation (2.32), namely
L =R
@p
1 @(RBt )
+
@
2µ0 R @
(2.33)
with L the elliptical operator
L=
and
@
@R
✓
1 @
µ0 R @R
◆
@
@Z
✓
1 @
µ0 R @Z
◆
(2.34)
the poloidal flux function defined as
1
=
2⇡
Z
S
B · dS
(2.35)
48
CHAPTER 2. THE TOKAMAK COMPASS
Figure 2.14: Microwave interferometer.
More details about the derivation of this equation and the algorithm used in EFIT can be
found in [58].
2.5.3
Microwave diagnostics
2-mm interferometer
The phase shift undergone by microwaves propagating through a plasma is used as a diagnostic
to determine the electron density. Figure 2.14 shows a simplified scheme of a 2-mm microwave
interferometer:
• A microwave oscillator (klystron) creates waves with ⌫ = 133GHz or
⇡ 2.3mm.
• A beam splitter (magic T) divides the wave between the plasma and a reference path.
This reference path contains a controllable attenuator and a phase shifter.
• A square-sensitive detector (intensity detector) registers the interference pattern formed
by the superposition of both waves. In other words, the phase di↵erence between both
waves is measured.
Since the electron plasma frequency is given by
e 2 ne
✏ 0 me
(2.36)
p
⌫p,e ⇡ 9 ne
(2.37)
2
!p,e
=
or
and the resolution of microwaves with frequency ⌫ to observe electrons is limited to ⌫ ⌫p,e ,
one finds that the electron densities visible for the 2-mm microwave interferometer are limited
to
ne  2.2 · 1020 m 3
(2.38)
Since the aimed fuel density of tokamaks is 2 · 1020 m 3 , this upper bound is a very good one,
what shows that microwaves are the best choice to measure the electron density.
The phase of a wave propagating in the x-direction is given by
= !t
This means that
d'
d
=
(
dx
dx
kx
vac )
= kvac
(2.39)
k
(2.40)
2.5. DIAGNOSTICS
49
with ' the phase di↵erence between the plasma wave and the reference wave. Using the
simplified8 dispersion relation of transversal waves in a plasma
2
! 2 = !p,e
+ c2 k 2
this can be written as
2
d' 4 !
=
dx
c
!
c
s
1
(2.41)
3
2
!p,e
5
!2
(2.42)
Supposing not too high electron densities we can assume that
2
!p,e
⇡0
!2
(2.43)
This allows a first order Taylor expansion resulting in
!
2
d'
! 1 !p,e
1 2
=
=
!
2
dx
c 2 !
2!c p,e
The experimental observed phase shift
1
'=
2!c
ZL
2
!p,e
dx
0
(2.44)
' is then
1 e2
=
2!c ✏0 me
ZL
ne dx =
0
1 e2
hne iL
2!c ✏0 me
(2.45)
with L the transmission length through the plasma. In this way we obtain the line-integrated
average electron density hne i.
Since for the total intensity observed by the detector of the interferometer holds that9
Itot = 2I0 [1 + cos( ')] ,
(2.46)
the output will show interference fringe jumps when ' is a multiple of 2⇡. The number
of these jumps in a plasma discharge depends on hne i and L. The phase shift generated by
the COMPASS plasma on the frequency 133GHz reaches commonly several tens of fringes.
Utilization of two near frequencies, namely ⌫1 = 133GHz (interferometer 1) and ⌫2 = 131GHz
(interferometer 2), propagating through the plasma in opposite directions, enables to avoid
the fringes as much as possible. The total setup is a so-called unambiguous interferometer. An
output without fringes is a necessary condition for a feedback system controlling the density.
For this purpose, not only the phase di↵erence between the reference and probing wave is
determined (as is done in the case of both interferometer 1 and 2), but the mutual phase
di↵erence between both probing waves is registered as well. According to Figure 2.15 and
equation (2.45), this mutual phase di↵erence is given by
'm =
8
'2
'1 =
1 e 2 !1 !2
hne iL
2c ✏0 me !1 !2
(2.47)
Assumptions: (1) influence of magnetic fields, i.e. of cyclotron frequencies, can be neglected (2) plasma
frequency of deuterons is negligible compared to plasma frequency of electrons.
9
General expression for interference of waves with the same amplitude. Both plasma beam and reference beam have (approximately) the same intensity when they hit the detector, namely their common initial
intensity I0 .
50
CHAPTER 2. THE TOKAMAK COMPASS
Figure 2.15: Unambiguous interferometer of COMPASS. [46]
This shows that the mutual phase di↵erence increases circa 66.5 times slower with increasing
electron density than the two separate phase di↵erences. The unambiguous interferometer is
installed in the vertical direction at R = 0.56m. This means that the waves cross the plasma
along the plasma vertical diameter, or in other words
L = 2a = 2 · 0.23 · 1.8 = 0.828 m
(2.48)
which holds for maximum minor radius and maximum elongation. We can now make an
estimation of the electron density hne i⇤ for which the unambiguous interferometer output
reaches the first fringe. This is done by setting 'm equal to 2⇡ and solving the equation for
hne i. This results in
hne i⇤ = 7.8 · 1019 m 3
(2.49)
When the electron density reaches this value, the data stored in the COMPASS database will
make a jump and the next data points should be incremented by this value.
At present, the interferometer is equipped with two phase detectors: one is based on AD8302
ICs, the other on logic circuits. This first detector gives two outputs: one that uses six
AD8302 ICs and has a 360 phase range, and one that uses only one AD8302 IC and has a
phase range of 180 . The second detector gives a “triggered” output. All three signals have a
DC component which should be removed. The initial DC level of the triggered interferometer
is set by a trigger signal. The stored hne i values are calculated assuming that the transmission
length is equal to two times the plasma minor radius. Thus, if we want to know the true
value of hne i, we have to divide by the plasma elongation.
Also remark that the linear relation ' / hne i only holds for relatively small electron densities
according to the assumption (2.43). So, for higher densities - starting from about 1020 m 3 this is not true any more and a more exact formula has to be used. [30] [46] [60] [61]
Microwave reflectometer
Plasmas are reflective for certain waves. This fact is for example used by radio stations that
use the ionosphere to reflect their radio waves so that regions that are normally unreachable
2.5. DIAGNOSTICS
51
due to the spherical surface of the Earth, are nevertheless able to receive them. This same
principle is used in tokamaks: the reflectometer emits microwaves in the range of frequencies
for which the plasma is reflective and observes the ones that are reflected. Based on the
relation between the cut-o↵ frequency of the plasma and the electron density, this method
is able to measure the electron density in the plasma edge. As seen from equation (2.41)
the cut-o↵ frequency can be approached by the plasma frequency10 and so the relation with
the electron density is immediately clear11 . On the COMPASS tokamak frequencies between
18GHz and 90GHz are used to measure electron densities of 0.4 10 · 1019 m 3 . Starting from
the delay of the received microwave the reflectometer knows at which position in the plasma
the wave was reflected. Advantages of this technique are that no mathematical transforms
are needed to calculate the density in one point and that the low power waves do not perturb
the plasma . The reflectometer is installed and it often does measurements, but the electron
density is not routinely reconstructed from the raw data. [46]
ECE/EBW radiometer
According to its most general definition a radiometer is a sensitive microwave receiver that
is able to determine the temperature of an object by analysing its thermal noise. Besides its
wide use in astronomy it is also used to study radiation of tokamak plasmas. It focuses on
the electron cyclotron emission (ECE). This is the radiation generated by the gyration of an
electron along a magnetic field line. We know from equation (1.35) that this radiation has a
frequency
eB
!c,e =
(2.50)
me
But also harmonics of !c,e are emitted. Since the magnetic field and thereby the ECE frequency is inversely proportional to the radial position r of the electron, the inner electrons
will emit higher frequency radiation than the outer electrons. The radiometer of the COMPASS tokamak can measure in two frequency bands: 26.5-40GHz and 60-90GHz. The first
range is devoted to the study of the 1st harmonics or the so-called electron Bernstein waves
(EBW). The second range is used to study the 2nd harmonics. Since these last ones radiate
like a black body, they are used to determine the radial profile of the electron temperature.
The radiometer is capable of doing measurements, but it is not routinely used. Currently, the
device is not installed. [46]
2.5.4
Spectroscopic diagnostics
Thomson scattering
Thomson scattering is a laser-aided diagnostic used to perform well localized measurements
of the electron temperature and density. It uses the physical principle of Doppler broadening:
monochromatic light reflected from particles moving at relativistic velocities will be broadened
due to the Doppler e↵ect, which is described by the formula
r
c+u
!=
!0
(2.51)
c u
10
For the wave number k to be real, the frequency of the wave ! has to be bigger than the electron plasma
frequency !p,e .
11
It is namely given by equation (2.36).
52
CHAPTER 2. THE TOKAMAK COMPASS
(a)
(b)
Figure 2.16: (a) Poloidal cross-section with laser path and view of the objectives. (b) Laser operating
modes. [62]
where c is the speed of light, u is the velocity component of the reflecting particles in the
direction of the objective, and !0 is the original frequency specified by the laser. As the
electrons are the particles with the lowest mass present in the tokamak, they will have the
highest velocities and consequently they will be responsible for the dominant Doppler shift.
This means that the spectral width of the scattered light is a measure for the electron temperature: a higher electron temperature implies higher velocities of the electrons - and so a
higher u in equation (2.51) - and by consequence bigger Doppler shifts. On the other hand,
the intensity is a measure for the plasma density: as more plasma particles are present, more
reflections will occur and more light will be captured by the objectives.
COMPASS uses two Nd:YAG lasers (1064nm wavelength, 1.5J energy, 7ns pulse duration,
30Hz repetition rate). The laser beams are guided by optical fibres to a quartz window positioned under the Brewster angle at the top of the vacuum vessel (see Figure 2.16). The
scattered light is captured by two objectives: one for the core plasma and one for the edge
plasma. Then, it is sent to a polychromator that by use of mirrors, filters and photodiodes
unravels the spectral composition of the scattered light in the form of multiple analogue electrical signals. Finally, these signals go through an analogue-digital converter and are further
analysed to determine the electron temperature and density. The laser light that passes the
plasma without scattering leaves the vessel and is stopped by the so-called beam dump. [46]
The two lasers can operate in di↵erent regimes: they can be fired simultaneously, with double
repetition rate (60Hz) or in “double-pulse mode” with arbitrary pulse separation from 1µs
to 16.6ms (see Figure 2.16b). The first case is used to measure low electron densities and to
reduce the statistical error. The last one allows observation of fast events in the plasma, like
the influence of edge localized modes (see later) on the pedestal profiles. [62]
2.5. DIAGNOSTICS
53
(a)
(b)
Figure 2.17: (a) MOS visible radiation diagnostic [64]. (b) AXUV bolometers: position and orientation of
the 6⇥20 photodiodes [46].
Fast visible cameras (EDICAM)
This camera system monitors the visible light that is emitted with the help of an “Event
Detection Intelligent Camera” (EDICAM). This is a fast video camera system that is mainly
used to monitor the plasma shape and position, the plasma behaviour (like the transition to
H-mode) and plasma-wall interactions. A typical camera frame resolution is 1280x1024 pixels
at milliseconds time-scales. However, the resolution can be decreased to reach extremely fast
frame rates of 100kHz if required. [46]
Multichannel Optical System (MOS) for Visible Plasma Radiation (VIS)
This tomographic system measures the integral plasma radiation in the visible range 4001000nm both from the core and edge plasma. By analysing specific spectral lines using
interference filters, it is able to determine the deuterium and impurity emission of the plasma.
The e↵ective atomic number Zef f can be evaluated from measured bremsstrahlung radiation
in the line-free region if the plasma density and temperature profiles are known. The device
consists of two equally designed components which are installed at two di↵erent ports in the
same poloidal cross-section so they can view the plasma from two di↵erent poloidal angles
almost perpendicular to each other (see Figure 2.17a). The ultra wide-angle objectives each
achieve a 110 field of view, covering almost the whole poloidal cross-section. The signals
are sent through 20m long optical cables to the visible light detectors which are located in
a separate room because, beside the visible range 400-1000nm, they are also sensitive to xrays emitted by the tokamak. Di↵erent types of detectors such as the impurity spectrometer
HR2000+ by Ocean Optics and the 35-channel detector S4114-35Q by Hamamatsu analyse
the light signals. [46] [63]
Bolometric diagnostics
In COMPASS, so-called fast bolometers are used to get the radiated power distribution and
to examine fast radiating events connected to plasma instabilities. Since time-scales of the
54
CHAPTER 2. THE TOKAMAK COMPASS
order of microseconds are required, photo-detectors are used as they provide a high temporal
resolution in contrast to for example temperature-dependent resistors. Six arrays (A, B, C,
D, E and F) of twenty photodiodes record the total radiation in a spectral range from ultraviolet up to soft x-rays in the poloidal cross-section of COMPASS (see Figure 2.17b). These
measurements do not give information on local properties. To this end, special mathematical transformations have to be performed. Under certain assumptions of symmetry these
calculations can be simplified and only an inverse Abel transformation has to be applied. [46]
Soft x-ray diagnostics
The SXR diagnostics are bolometers - arrays of 35 silicon photodiodes on a chip - that only
measure soft x-ray intensities. This selection is achieved by using a thin beryllium foil. Soft
x-rays are linked to bremsstrahlung (see paragraph 1.2.4) and therefore they are extremely
valuable to examine impurities. [46]
Hard x-ray diagnostics
High-energetic x-rays, better known as hard x-rays, are measured by a detector placed somewhere in the tokamak hall separated from the tokamak itself. The detector consists of a
scintillator and a photomultiplier. The scintillator converts the high-energetic photons to visible photons. The photomultiplier then converts the energy of these photons to an amplified
electrical current making use of the photoelectric e↵ect and secondary emission by well positioned electrodes in a vacuum tube. Unfortunately, this detector is also sensitive to neutrons.
[45]
High dispersion spectrometer
This device is used to determine amongst others the toroidal and poloidal rotation velocity of
the edge plasma starting from Doppler shift measurements of carbon triplet lines 1s2 2s3s !
1s2 2s3p (⇡465nm). Next to this, it is also used to measure the motional Stark e↵ect of the D↵
line (⇡656nm) from the NBI. The spectrometer is equipped with a high speed camera with
high quantum efficiency, which enables time resolutions up to 2ms. The rotation velocities
are still not measured, and currently the spectrometer is not installed. At the moment, the
COMPASS team is working on CXRS12 diagnostics. Rotation measurements will be part of
this new project. [46] [57] [59]
2.5.5
Beam and particle diagnostics
Lithium beam emission spectroscopy (BES)
In the BES system of COMPASS, a beam of neutral Li atoms is directed into the plasma,
where the Li atoms excite or ionize by colliding with the plasma particles. The excited Li
atoms then radiate at a wavelength of 670.8nm (2p-2s transition) to get back to their lower
energy state. This radiation is detected by a slow-measuring CCD camera on top of the vessel
and by fast-measuring avalanche photodiodes (APD) at the bottom of the vessel. This can
be seen in Figure 2.18a. In case of Li, this radiation is very weakly dependent on the electron
temperature, and so the intensity measured by the detectors is a measure for the electron
12
Charge eXchange Recombination Spectroscopy.
2.5. DIAGNOSTICS
55
(a)
(b)
Figure 2.18: (a) Li-BES system [46]. (b) Scanning method of Li-BES [46].
density. The detection system measures the beam radiation along multiple lines of sight. The
light detected in a measurement channel originates from the intersection of the beam and the
line of sight. If the beam is scanned up and down using deflection plates, di↵erent points in
the plasma are investigated. Performing a series of measurements at a set of di↵erent beam
positions, the whole two-dimensional density profile can be reconstructed, although not on
a rectangular grid of points, as can be seen in Figure 2.18b. For the moment, there are no
reliable experimental data from the Li-BES system. [46]
In Figure 2.18a also an atomic beam probe (ABP) detector is shown. It is used to determine
the poloidal magnetic field perturbation and the edge plasma current profile. For a profound
description is referred to [65].
Neutral particle analyser
The charge exchange reactions in the hot plasma also create neutral particles, namely hydrogen and deuterium, which can leave the magnetic confinement. A neutral particle analyser
is positioned outside the tokamak vessel and captures some of these neutral particles. These
particles first pass through a gas which ionizes them. The resulting ions keep their energy
and momentum. Then, a bending magnet separates protons and deuterons based on their
di↵erent masses. Finally, they are each detected by an array of 12 detectors which determines
the energy distribution. The NPA is not yet connected. [46]
56
CHAPTER 2. THE TOKAMAK COMPASS
Figure 2.19: Neutral particle analyser. [46]
Neutron detector
Very recently, a neutron detector is installed. It is actually the same device as the HXR detector - consisting of a scintillator plus photomultiplier and placed somewhere in the tokamak
hall 5m removed from the tokamak itself - but shielded by a 10cm wide wall of lead bricks to
avoid the registration of HXR emission from the tokamak plasma. [45]
2.5.6
Probe diagnostics
An electric probe is basically a conducting object placed in the plasma and connected to a
circuit to measure the voltage or current induced in it. Probes have to fulfil two requirements:
they have to withstand the high temperatures of the plasma and they have to be small in
order to disturb the plasma as little as possible. Scientists play with externally applied probe
potentials and currents, to measure
• the IV characterstic (V is swept)
• the ion saturation current (V <
100V)
• the floating potential (I = 0)
Probe diagnostics are loved for their extremely high frequency, which is only limited by the
quality of the data acquisition system.
Divertor probes
Langmuir Probes. The COMPASS tokamak is equipped with an array of 39 Langmuir
probes embedded in the divertor tiles (see Figure 2.20). A triangular shaped time-varying
voltage is applied to these probes allowing them to sweep between a positive and a negative
potential. Assuming that the electron velocity has a Maxwell-Boltzmann distribution, which
is typical for high-temperature plasmas, the IV characteristic obtained by comparing the
measured current through the probe to the applied voltage can be fitted by

V Vf
+
I = Isat 1 ↵(V Vf ) e Te [eV]
(2.52)
2.5. DIAGNOSTICS
57
Figure 2.20: Langmuir probe array (39 probes) in the divertor region of COMPASS. [46]
with I the current through the probe, V the probe voltage, Vf the floating potential13 , ↵ a
parameter to cope with a possible lack of saturation, Te the electron temperature expressed
+
in eV and Isat
the ion saturation current given by
+
Isat
= eZni cs A
(2.53)
where Z is the atomic number of the ions (equals 1 without impurities), ni the ion density
which equals the electron density for a quasi-neutral deuterium plasma, A the contact surface
of the probe and cs the ion sound speed. This last quantity is in turn given by
s
kB (ZTe + i Ti )
cs =
(2.54)
mi
with mi the ion mass and i the adiabatic coefficient of the ions which can take on values between 1 and 314 . Assuming thermodynamic equilibrium (Ti ⇡ Te ) one is able to find ne and Te .
A typical IV characteristic is given in Figure 2.21. The current obviously saturates for negative
values of V meaning that ↵ = 0. A high enough negative probe potential repels all electrons
from entering the probe and only the current caused by the positively charged plasma ions
is what remains. For increasing probe potential the behaviour of the curve is determined
by the electron current. The exponential decrease leads to the determination of the electron
temperature. The current will be zero for a positive value of V , namely the floating potential.
This phenomenon can be explained as follows: for a small positive value of V the plasma
electrons will form a Debye shield around the probe repelling other electrons while they are
not inducing a current in the probe. There exists no equivalent ion shield because ions have a
much higher mobility than electrons. The encircled part of the graph is called the ion branch.
Formula (2.52) is applicable to this part of the IV curve. As you might guess, the other
part is called the electron branch. There, the exponential behaviour is determined by the ion
temperature and the saturation current consists solely of electrons. This current is given by
1
Isat = e ne ce,th (1
4
see )A
(2.55)
where the factor 1/4 accounts for the isotropic spatial dimensions and see for the secondary
electron emission at the probe surface. As mentioned before, the electrons are assumed to
13
14
Remark that I = 0 for V = Vf .
In a classical gas is related to the degrees of freedom N :
= 1+ N2 . It is a measure for the compressibility.
58
CHAPTER 2. THE TOKAMAK COMPASS
Figure 2.21: Representation of a Langmuir probe measurement (left) and a typical resulting IV characteristic
(right). [47]
have a Maxwell-Boltzmann velocity distribution, meaning that the saturation current is a
function of the thermal velocity
r
8kB Te
ce,th =
(2.56)
⇡me
[66]
The above described fitting method starts from the assumption that we are dealing with a
Maxwellian plasma. Since this is not always the case, especially for low-temperature plasmas,
it is more reliable to use the theory of Druyvesteyn [67]. He starts from an expression for the
electron energy distribution function (EEDF), which is proportional to the second derivative
of the IV characteristic, to calculate the electron density and the electron temperature. Yet
another method, based on the first derivative of the IV characteristic, is discussed in [68].
Ball-pen probes. Ball-pen probes consist of a conical conductor (the collector) placed in
a ceramic tube at adjustable height. This height determines the e↵ective probe surface A in
equations (2.53) and (2.55). Due to the di↵erent gyration radii of electrons and ions and a
lot of other more complicated e↵ects like E ⇥ B drift, the e↵ective surfaces of electrons and
ions are di↵erent. Well thought out design of the ball-pen probes makes it possible to have a
+
wide range of collector heights for which Isat
⇡ Isat , which implies that they directly measure
the plasma potential
if they are in floating potential mode. This can be theoretically
demonstrated as follows. Equation (2.52) is equivalent to
+
I = Isat
V
Isat e Te [eV]
(2.57)
if the plasma potential is taken as reference instead of the floating potential. Using the fact
that I = 0 for V = Vf , we derive
✓
◆
Isat
Vf =
Te ln
(2.58)
+
Isat
which shows indeed that Vf = if both saturation currents are the same. Very interesting is
the combination of a ball-pen and Langmuir probe close to each other, since their data allows
to calculate the electron temperature with very high time resolution:
BP P
Te [eV] =
2.2
VfLP
(2.59)
2.6. FEEDBACK CONTROL SYSTEM
59
Figure 2.22: Draft of a ball-pen probe with non-withdrawn collector showing the di↵erent used materials
and the bigger gyration radius of ions compared to electrons (left), and a picture of the corresponding real
ball-pen probe (right). [69]
Here, 2.2 is a typical value for the natural logarithm occurring in equation (2.58) in case of a
deuterium plasma15 . [66] [69]
Reciprocating probes
Next to the divertor probes also horizontal reciprocating probes are installed on the COMPASS tokamak to gather data deeper into the plasma, namely in the scrape-o↵ layer. These
are probes mounted on a fast pneumatic manipulator reciprocating quickly (within 0.1 second) in and out to avoid overheating, which would cause impurity release and destruction of
the probe head. The probe head consists of 5 Langmuir probes and 3 ball-pen probes, which
measure
• radial profiles of the plasma potential , electron density ne and temperature Te
• plasma velocity along the magnetic field
• fluxes of particles and energy towards the wall
• ion temperature Ti
[70]
2.6
Feedback control system
To maintain plasmas as long as possible, especially non-circular shaped ones, a fast feedback
system controlling the radial and vertical plasma position is indispensable. The choice of the
data fed to the feedback system is far from obvious since it has to be inert to changes in
other plasma parameters. Therefore, data extracted from di↵erent diagnostic coils is tested
in simulations with elliptical shaped plasmas (see Figure 2.23) [71]. Following combinations
of internal partial rogowski (IPR) coils seem to be the best choice.
Bh (R, Z) = 3 · IP R5 + IP R3
3 · IP R13
IP R15
Bv (R, Z) = 1.2 · IP R8 + IP R9 + 1.2 · IP R10
15
In case the working gas is hydrogen this is 2.8
(2.60)
(2.61)
60
CHAPTER 2. THE TOKAMAK COMPASS
The values of the newly introduced variables Bh and Bv form look-up tables for the radial
position R and vertical position Z, which are used in the feedback code implemented in the
real-time controller MARTe (Multi-threaded Application Real-Time executor). MARTe is
running in two threads with two di↵erent speeds. The fast thread runs in a loop of 20kHz
and contains amongst others the module for the calculation of the plasma position. The slow
thread runs in a loop of 2kHz and is used mostly for communication with the main power
supplies. [71]
2.6.1
Radial equilibrium
In the approximation of a circular and high aspect ratio plasma16 , radial equilibrium is fulfilled
by the vertical magnetic field17
Bz =
 ✓ ◆
µ0 Ip
8R
ln
4⇡R
a
3
+
2
p
+
li
2
(2.62)
where R is the radial plasma position, a the plasma minor radius, p the poloidal beta18 and
li the internal inductance between the plasma center and the edge at r = a. As mentioned
in paragraph 2.3.2, two types of PF coils are responsible for the radial equilibrium: the
equilibrium field coils (EF) and the fast feedback coils (BV). As its name says, the last one
acts much faster. The EF circuit uses a proportional-integral (PI) control scheme:
IEF,req = KP 1 · Ip + KP 2 · (Rreq
Rmeas ) + KI1 ·
Zt
0
(Rreq
Rmeas ) dt + KP 3 · IBV,meas (2.63)
Here, the radial position Rmeas is determined by the algorithm based on IPR coil measurements as described above. The BV circuit takes care of the fast disturbances. It calculates
its requested current IBV,req starting only from the radial position error Rreq Rmeas , also
with a PI controller (though PID19 is available). In theory, the superposition of the vertical
magnetic fields generated by both circuits, should approximate equation (2.62). However,
three parameters do not appear in the controller code, namely a, p and li . They are indirectly taken into account by the Ip -term of equation (2.63) since they all influence the current
distribution inside the plasma. The tokamak operators can manually preset Rreq on shot to
shot basis to achieve the desired plasma position. [59] [73]
2.6.2
Vertical equilibrium
The radial field (BR) circuit handles vertical disturbances by use of a PD regulator. [73]
16
The major radius is much bigger than the minor radius, i.e. R
a.
For a derivation of this formula, see [72].
18
BT
The plasma- is defined as the ratio of the plasma pressure to the magnetic energy density: Bnk
2 /2µ . It is
0
a measure for the efficiency of the magnetic confinement. The toroidal depends on the external magnetic
field created by the TF coils. It has an economical aspect: since the TF coils are the biggest reactor cost, a
high toroidal is desired. The poloidal contains the current-induced poloidal field and is important for the
radial equilibrium.
19
Proportional-integral-derivative controller.
17
2.7. RECHARGE TIME
61
Figure 2.23: IPR feedback simulation with elliptical shaped plasma. Note the positions of the IPR coils
along the vessel surface. [71]
2.6.3
Plasma current control
The output of the power supply of the central solenoid is controlled by a PID regulator that
minimises the error Ip,req Ip,meas . Since Is needs to increase gradually as explained in
s
paragraph 2.3.1, this means that the PID controller determines the change dI
dt . The current
in the central solenoid (and more generally in the MF coils) can be expressed as
✓
◆
dIs
Is = Is,meas +
t
(2.64)
dt P ID
where
2.7
t is the time between two iterations. [59] [73]
Recharge time
COMPASS needs typically 30 minutes between two consecutive discharges. The major time
consuming actions are
• pumping the vessel again to a good vacuum (takes the most time)
• recovery of the speed of the flywheel generator(s)
• reading and storing data in the database
• performing some calculations (for example by EFIT)
• performing some modifications to the torus hall if necessary
• preprogramming the next shot
• charging the auxiliary capacitor banks
EFIT processes the data from important shots with a higher sampling rate at night to minimize the time lost between shots. [45]
62
2.8
CHAPTER 2. THE TOKAMAK COMPASS
Safety
COMPASS does not produce any radioactive waste. However, during operation some neutron
radiation and x-rays are produced. These are harmless outside the tokamak hall. Further,
a protection system is made for the two high power lasers used for the Thomson scattering
diagnostic.
2.9
Goals
COMPASS is an experimental reactor, not aimed to produce actual fusion reactions. Its
research is focused on the edge plasma studies relevant to ITER, e.g. pedestal and ELM
physics (see later in paragraph 3.2.3). Also the L-H transition is intensively examined. More
exactly its power threshold and hysteresis behaviour. Further, the feasibility of NBI heating
and some diagnostics, for example the atomic beam probe, is studied. And the development
of new techniques for improved data acquisition and analysis was originally a main goal. [39]
Chapter 3
H-mode operation in COMPASS
3.1
Introduction
In this chapter, useful data from COMPASS experiments will be shown and widely discussed.
Here, we examine in particular the behaviour of the plasma parameters around the transition
from L-mode to H-mode, and we try to learn more about H-mode. We also focus on the
influence of neutral beam injection. The reader is first informed about the di↵erent phases
and confinement modes of a standard tokamak discharge with special attention for ELMs.
Then, the analytical part of this thesis begins. Data from di↵erent diagnostics are discussed
for five H-mode shots: the very first shot that reached H-mode at the IPP (#4073), a shot
immediately after a glow discharge cleaning (#4267), a shot with three NBI intervals and more
accurate data of the ohmic heating power (#5909), a shot with an H-L transition (#6109)
and finally a shot with only ohmic heating (#6313). Indeed, the last shot is the only shot
without additional heating from the NBI. At the end of the chapter, some conclusions are
made by comparing the di↵erent shots.
3.2
3.2.1
General discharge evolution
Start-up
After vacuum pumping, the tokamak vessel is filled with deuterium to a pressure in the range
0.02-0.2Pa. The first step in the actual start-up process is the pre-ionization: some free
electrons are generated in the vessel by an external electron source. In COMPASS this is
a VUV lamp, but other possibilities are an electron gun, an RF wave generator or just the
cosmic background radiation. In the next step, a sequence of processes is triggered, namely:
1. activation of the data acquisition system
2. powering of the TF coils
3. powering of the central solenoid
The third trigger pulse is sent when the toroidal magnetic field has reached a reasonable level.
The changing current in the central solenoid induces a toroidal electric field in the vacuum
vessel.
63
64
CHAPTER 3. H-MODE OPERATION IN COMPASS
The following step, namely the plasma breakdown, can be split up in two phases, each with different underlying physics: the avalanche phase and the Coulomb phase. During the avalanche
phase collisions between electrons and deuterium molecules dominate. The electrons from the
pre-ionization are accelerated by the toroidal electric field and once they have enough kinetic
energy they will ionize deuterium when they collide resulting in one extra electron for each
ionizing collision. Thus, the ionization happens exponentially. For an ionization of about 5%
the density of ions and electrons has reached the point where the Coulomb interactions between them are so strong that electron-ion collisions start to dominate. The current increases
and magnetic surfaces are formed during this Coulomb phase so that the confinement of the
plasma increases significantly. At the end of the Coulomb phase the plasma is fully ionized.
[74]
3.2.2
Tokamak confinement modes
After the plasma breakdown, the current starts ramping up going hand in hand with ohmic
heating. This phase is characterized by the lack of additional heating. The plasma confinement is very good. Years of research have shown that confinement deteriorates with increasing
power coupled to the plasma (see for example the ITER scaling law (1.38)). However, since
the plasma resistance has a bad temperature dependence, additional heating is needed to
reach the ignition condition for future fusion reactors.
From the moment extra heating sources are applied (e.g. NBI), the tokamak is said to be in
low confinement (L) mode. As its name says, the discharge has now stepped back with regard
to confinement. Be careful: the term ‘L-mode’ often has a more general meaning and is not
always related to additional heating. In the literature, ohmic heating and L-mode are often
mixed which may be confusing. In this master thesis is started from the definition given above.
When the heating power has reached a certain threshold, the discharge enters the high confinement (H) mode. A transport barrier is set up at the plasma edge, retaining heat and
particles in its core (see Figure 3.1). This transport barrier is physically translated into a
high gradient in the plasma pressure p = nkT at the plasma edge: a pressure pedestal. Also
the density and temperature profiles show such a pedestal. These can be interpreted as particle and energy barriers respectively. Both theoretical models and experimental observations
indicate a strong dependence of the overall confinement in the core on the pedestal height. [75]
Other tokamak operation modes exist. Their appearance is often dependent on tokamak geometry and know-how of controlling certain plasma parameters.
3.2. GENERAL DISCHARGE EVOLUTION
Figure 3.1: Radial plasma pressure profile for di↵erent operation modes. [76]
Figure 3.2: Evolution of an ELM crash. [77]
65
66
CHAPTER 3. H-MODE OPERATION IN COMPASS
3.2.3
Edge Localized Modes (ELMs)
In H-mode, especially right after the L-H transition, the plasma is very sensitive to certain
instabilities called edge localized modes (ELMs). This is a phenomenon where the pressure
pedestal falls down and rebuilds itself. An ELM cycle is typically described by 4 steps (see
Figure 3.2):
1. A steep pressure gradient is built during H-mode.
2. The pressure gradient exceeds a certain critical value leading to the onset of many small
turbulent eddies at the edge.
3. The edge plasma is lost to the scrape-o↵ layer where it flows along the magnetic field
lines towards the divertor.
4. The lost plasma hits the divertor plates hereby producing a distinctive peak in the D↵
radiation1 .
During the instability, the edge pressure is reduced until the plasma becomes stable again.
Then the process is ready to repeat itself. In theory, the cycle can go on indefinitely if nothing
changes to the conditions.
ELMs can be classified in 3 groups according to the emerging changes in plasma parameters
during the crash:
• Type-1: These ELMs are also known as “large” or “giant” ELMs because the D↵
radiation shows large isolated bursts. The pressure gradient at the edge is close to the
theoretical stability limit (“ideal ballooning”, see Figure 3.3) or even beyond it. The
repetition frequency is 10Hz or less - which is very low compared to the other ELM
types - and increases together with the heating power. They are known to cause up
to 10-15% drops in the plasma energy. The degradation of the plasma confinement is
smaller than with other ELMs. They are, on the other hand, most detrimental to the
divertor plates.
• Type-2: These ELMs require strongly-shaped plasmas, i.e. with high elongation and
triangularity, and a rather high plasma density and edge safety factor. The D↵ bursts
are smaller and the repetition rate is higher than that of type-1 ELMs, while the confinement stays almost as good. Virtually nothing is known about how the frequency
and amplitude of type-2 ELMs depend on the power coupled to the plasma. They
are sometimes called “grassy” ELMs. This terminology is somewhat confusing because
type-3 ELMs also look grassy.
• Type-3: These ELMs are characterised by small and frequent D↵ bursts. Therefore,
another name is “small” ELMs. The instability is driven by electric currents and appears
when plasma resistivity is rather high, i.e. when the edge temperature is rather low.
The repetition frequency is found to decrease with increasing heating power. They are
observed for powers near the H-mode threshold power and produce small energy dumps.
More exactly 1-3% of the stored energy is lost. The plasma confinement is degraded
more than with other ELMs. Compared to type-2 ELMs, they appear in poorly confined
plasmas.
1
Visible light emitted by excited deuterium, see later.
3.2. GENERAL DISCHARGE EVOLUTION
67
Figure 3.3: Peeling and ballooning model of ELMs. [80]
While they have many negative e↵ects, the beneficial e↵ect of ELMs in providing density control and limiting the core plasma impurity content in high confinement discharges should not
be overlooked. Indeed, H-mode has the advantage of having an improved energy confinement
time ⌧E , but the disadvantage of having a particle barrier which keeps radiating impurities in
the plasma core. ELMs could be used to remove impurities from the plasma core from time
to time, if one succeeds to control them. They however do more harm than good.
In fact, ELMs represent a big problem for ITER. It is not yet clear whether an efficient way will
be found to suppress or mitigate them without loss of energy confinement. Therefore, a new
operation regime, the so-called improved confinement (I) mode is now experimentally studied.
This regime exhibits improved energy confinement and is ELM-free, but the density remains
constant. This implies that impurities are not accumulated in the plasma. Technically, this
regime can be achieved by reversing the toroidal magnetic field, so that the B ⇥ rB drift of
the ions is directed upwards and not towards the x-point (recall Figure 1.11b). [45] [77] [78]
[79]
68
CHAPTER 3. H-MODE OPERATION IN COMPASS
3.3
3.3.1
Shot #4073: the first achievement of H-mode
Preset parameters
Shot #4073 is the first discharge in COMPASS where H-mode is reached. Important preset
parameters are the gas pu↵, NBI activation, plasma position profile and plasma current profile.
They are shown in Figure 3.4. Some useful information that can be derived from this figure,
is summed next:
• gas pu↵: 930-1120ms
• NBI2: 1130-1180ms (40kV,6.5A)
• breakdown: 959ms
• flat-top phase: 1150-1190ms
• end of the discharge: 1190ms
Other preset parameters are the currents of the di↵erent power supplies for the magnetic coils.
These are not important for our discussion of H-mode. An upper bound2 for the NBI power
is given by 40kV ⇥ 6.5A ⇥ 0.78 = 202.8kW. The actual value can be everything between zero
and this upper bound, though the enhanced achievement of H-mode with NBI makes zero
very unlikely.
Figure 3.4: Plots of plasma current, vertical position and radial position of the plasma center relative to the
center of the COMPASS vessel (R=0.56m, Z=0m) for shot #4073. The measured values as well as the preset
wave form are shown. Also the time intervals when the gas pu↵ and NBI are active, are indicated.
3.3.2
Spectroscopy
Figure 3.5 shows the most important spectroscopic data of shot #4073. It contains respectively the D↵ radiation, the visible radiation (All Vis) and the emission of hard x-rays (HXR).
The measured quantities are voltages generated by the di↵erent detecting systems. These detectors are not calibrated, thus the vertical scales of the di↵erent graphs cannot be compared
to each other.
2
Remember paragraph 2.4.2.
3.3. SHOT #4073: THE FIRST ACHIEVEMENT OF H-MODE
69
D↵ and visible radiation
First of all, we remark that the two first curves are very similar. This may not surprise you
since the All Vis signal is a superposition of all visible wavelengths and thus also includes the
dominating D↵ line. Secondly, it has to be stressed that the D↵ radiation is an extremely
important signal for our discussion of H-mode: the D↵ signal contains the signature of Hmode. This will be explained... During operation, the deuterium fuel gas in the tokamak is
excited and ionized. The excited deuterium atoms emit light with a wavelength of 656.3nm
(D↵ line) radiated by electrons jumping from the 3th to the 2nd shell. This light is captured
by the Multichannel Optical System3 . The D↵ radiation is strongest during the plasma startup because the lower amount of energy available in the tokamak at that moment increases
the chance of an excitation reaction against an ionization reaction. This peak is omitted
from Figure 3.5 since we are more interested in the L-H transition. After the start-up phase
the plasma is fully ionized and the D↵ radiation is coming from newly injected neutral fuel
particles4 , but also from fuel particles that are desorbed by the vessel wall - a process that is
called wall recycling. As the confinement of the plasma keeps increasing less and less particles
collide with the vessel wall. H-mode implies that this second source of D↵ radiation, namely
desorption of deuterium from the vessel wall, is very small. The transition from L- to H-mode
can be observed as an abrupt drop in the D↵ radiation. Scientists are very glad to see this
drop. From Figure 3.5 it is clear that the transition to H-mode took place around t=1141ms:
at that moment the average intensity of the D↵ radiation is approximately divided by two.
We see in Figure 3.5 that around this transition the D↵ radiation shows distinct spikes. These
are Edge Localized Modes. There are 3 ELMs at the end of L-mode, the first one occurring at
t=1140ms, and 4 ELMs in the beginning of H-mode, the last one being at t=1145ms (see also
Figure 3.9). During the subsequent ELM-free H-mode the D↵ radiation stays constant while
the All Vis radiation slowly increases, because impurities are better confined and consequently
more excited. The better confinement implies that the plasma touches the wall less which
means that there should be less impurities. However, there is obviously an impurity influx.
This impurity accumulation goes on until a major instability occurs and a lot of the thermal
energy is lost at once, ending the discharge at t=1190ms. Such an instability is called a
disruption. As a last note, remark that the fluctuations in the D↵ and all visible radiation
are reduced after switching o↵ the NBI at t = 1180ms.
Hard x-rays
The HXR signal is not well understood yet. Hard x-rays are produced by plasma-wall interactions and by runaway electrons. These are electrons that are produced “when the collisional
drag force is lower than the electric driving force [81]”. In other words, these electrons
collide less with other plasma particles than normal and are accelerated until they are nonMaxwellian particles with a lot of energy. They are only produced during abnormal events
such as disruptions. The HXR scintillation detector is completely separated from the rest of
the tokamak and is placed somewhere outside the tokamak vessel. For some unknown reason
the x-rays are initiated by the neutral beam injection. You could say that it is the signature
of the NBI operation, but be carefull: the HXR signal keeps showing high values after the
NBI is turned o↵. The most reasonable explanation for the correlation between the NBI
3
4
See paragraph 2.5.4.
Deuterium puffing and neutral beam injection.
70
CHAPTER 3. H-MODE OPERATION IN COMPASS
Figure 3.5: Spectroscopic data of #4073. The yellow area indicates the NBI.
operation and the increased HXR values is the creation of neutrons. Indeed, neutrons are
also registered by the scintillation detector. Recently, a neutron detector was installed and
confirmed this hypothesis.
Soft x-rays
Another interesting spectroscopic signal is the soft x-ray radiation. As the SXR signal measures the bremsstrahlung radiation, we know from equation (1.13) that following proportionality holds for the measured intensity
1
2
2
ISXR / n2e Zef
f Te
(3.1)
The SXR intensities registered by detectors 18-30 are plotted in Figure 3.6. The position and
line of sight of these SXR detectors are shown in Figure 3.7. The data is detrended so that
we can clearly observe the appearance of a sawtooth pattern from the moment the NBI is
turned on. These sawteeth indicate a build-up of electron density and temperature, followed
by an instability causing a fast drop. The sawtooth oscillation is one of the fundamental
instabilities in tokamaks, and is therefore also indicated in Figure 3.1. This phenomenon
seems to happen when additional heating is coupled tot the plasma. When a sawtooth
crash occurs, hot electrons are sent rapidly from the plasma core to the cooler plasma edge,
flattening the temperature profile. Figure 3.6 shows this electron transport throughout the
plasma: the sawteeth in the plasma edge (detectors 18-20 and 30) are inverse with respect to
the sawteeth in the plasma core (detectors 23-26). The inversion occurs at the q=1 surface
which designates the most stable part of the whole plasma. The safety factor q expresses
how many toroidal rotations are necessary for a single rotation of a magnetic field line in the
poloidal direction. For tokamaks with circular cross-section and large aspect ratio (R
a),
this is approximately given by
a Bt
q=
(3.2)
R Bp
This tells us something about the stability of the plasma: If q is a rational number, the magnetic field line bites in its own tail after several turns, but if it is an irrational number the
field line travels around the whole magnetic surface. You can feel intuitively that the latter
is less stable. The most stable situation occurs when q equals one.
3.3. SHOT #4073: THE FIRST ACHIEVEMENT OF H-MODE
71
Figure 3.6: Soft x-ray radiation for shot #4073. The data is detrended and smoothed. All signals are on the
same scale. The vertical distance between two consecutive signals is 0.2µW. Photodiode 22 did not work well
and is omitted.
(a)
(b)
Figure 3.7: Reconstruction of the q=1 surface at (a) t = 1140ms and (b) t = 1170ms.
Figure 3.8: Radial distribution of the safety factor q in the midplane calculated by EFIT.
72
CHAPTER 3. H-MODE OPERATION IN COMPASS
Figure 3.9: D↵ and SXR radiation.
Estimations of the q=1 surface at di↵erent times are drawn as a blue circle in Figure 3.7.
We know from Figure 3.4 that the plasma center deviates from its original position by
Z = +35mm and R = 18mm. Around t = 1140ms the inversion occurs at photodiodes 19 and 30, around t = 1170 this is 21 and 27. It is clear that the inversion radius
becomes smaller for increasing t. In the estimation the q-surface was assumed to be circular.
Its radius is about 90mm at t = 1140ms and 50mm at t = 1170ms. In this way, sawtooth
oscillations could be used to cross-check EFIT calculations of the safety factor. Unfortunately,
EFIT claims that there is no q=1 in the midplane (see Figure 3.8). This is not consistent with
what we read from Figure 3.7 at Z = 0. This discrepancy between SXR data and EFIT data
is because the EFIT reconstruction is not perfect for diverted plasmas. As will be seen in the
discussion of next shots, the kinetic energy from EFIT is usually lower than from diamagnetic
measurements. Also, the position of the separatrix at LFS is about 2cm deeper than in reality.
Figure 3.9 nicely shows the correlation between the sawteeth, the ELMs and the transition
to H-mode. It seems that the sawtooth instability is a trigger for the L-H transition. In
other words, it turns out that the sawteeth instability, usually assumed to develop in the core
plasma, modifies conditions at the plasma edge. This e↵ect has to be studied more in detail.
Further information about sawtooth oscillations in COMPASS can be found in [82].
Summary
Spectroscopic diagnostics are very valuable for tokamak research. They do not interfere with
the plasma and give fundamental information. The D↵ radiation is used to detect the L-H
transition as well as ELMs. The total visible radiation shows the impurity accumulation. Soft
x-rays have a similar purpose, but also show sawteeth which can be used to localize the q=1
surface. It has to be investigated if sawtooth oscillations are a trigger for the L-H transition.
There clearly is some connection between sawteeth and ELMs. Finally, hard x-rays are an
indication for plasma-wall interactions and run-away electrons. However, the detector used
here also registers neutrons. It is remarkable that neutrons are generated from the moment
the NBI is switched on, and they keep on being generated even when the NBI is again switched
o↵.
3.3.3
Electron density
The electron density is a trouble maker: its line-averaged value is measured by the 2-mm
interferometer and as discussed in paragraph 2.5.3 the resulting data are subject to fringe
3.3. SHOT #4073: THE FIRST ACHIEVEMENT OF H-MODE
(a)
73
(b)
Figure 3.10: (a) Raw line-averaged electron density divided by the maximum elongation max = 1.8 for the
three di↵erent ambiguous interferometer signals. (b) Plasma elongation calculated by EFIT.
failing. Figure 3.10a is a plot of the raw data from the COMPASS database divided by the
maximum plasma elongation, namely 1.8. This is of course an underestimation of the real
electron density since the elongation is most of the time smaller then 1.8 as can be seen in
Figure 3.10b. We first of all remark that there is an o↵set on each channel which has to be
removed. Secondly, we notice that the red and green curves are physically impossible: the
electron density should rise in ohmic regime and certainly in H-mode. Besides, the green
channel even has negative values if the o↵set is removed! Everything suggests to take the
blue channel to discuss the electron density of shot #4073.
However, also the blue curve (6xAD8302) performs strange behaviour: during H-mode it
reaches hne i = 7.45 · 1019 m 3 and then suddenly drops to its o↵set value. This drop can be
explained by the plasma reaching its first interference fringe. In paragraph 2.5.3 we estimated
the critical value hne i⇤ for this fringe to be 7.8 · 1019 m 3 for a plasma elongation of 1.8. So,
this is a plausible explanation. In Figure 3.11 is the corrected electron density hne i plotted
based on the blue channel (6xAD8302). This plot was made by using the algorithm described
in appendix B. We see how the electron density gradually rises, then it suddenly drops a little
bit around t=1040-1045ms due to the ELMs that go along with the transition to H-mode,
thereafter it increases very fast during H-mode and finally it falls down very fast when the
disruption takes place. It is remarkable that between the gas pu↵ and the NBI activity, the
density keeps rising. Apparently, there is some kind of improved particle confinement at that
moment. As explained before, once the NBI is turned on, the discharge goes per definition
over to L-mode.
As a last remark, we note that the red curve (1xAD8302) only has two di↵erences compared
to the blue one (6xAD8302):
• It has a slightly di↵erent o↵set.
• When the electron density reaches the value hne i = 3.361 · 1019 m 3 (about half the
first-fringe-density of the blue curve) it goes over to mirroring the blue curve.
The fringe-failing occurs at exactly the same moment. The mirror behaviour is explained by
the fact that the red channel has a phase detector with a range of only 180 . This phase
detector is therefore never used in data analysis.
74
CHAPTER 3. H-MODE OPERATION IN COMPASS
Figure 3.11: Reconstructed line-averaged electron density for shot #4073.
3.3.4
Global particle confinement
In its most general form the global particle balance is given by
dN0 dN+
+
=
dt
dt
IN
(3.3)
OU T
This equation says that the change in the amount of neutral and positively charged plasma
particles equals the influx of neutral particles5 minus the outflux of neutral and positively
charged particles. In other words, it expresses the conservation of the number of nuclei in the
absence of fusion reactions.
For a deuterium plasma without impurities these neutral particles are deuterium atoms (N0 =
ND ) and these positively charged particles are deuterons (N+ = ND+ ). We further use
following assumptions (and facts):
• The plasma is fully ionized: ND =0 ; and as a consequence the outflux
only of charged particles and is assumed proportional to ND+
• The ingoing neutral particles ionize immediately:
dND
dt
OU T
consists
=0
• Deuterium has only one electron: ND+ = Ne
Now, we can rewrite the particle balance as
dNe
=
dt
IN
Ne
⌧p
(3.4)
where
IN
=
Ne
=
⌧p
5
gas puf f
OU T
=
+
N BI
+
re emission by wall
absorption by wall
Charged particles cannot penetrate the magnetic field.
+
divertor pump
(3.5)
(3.6)
3.3. SHOT #4073: THE FIRST ACHIEVEMENT OF H-MODE
75
Table 3.1: Data used to measure the relative increase in particle confinement time.
OH phase
1129
5.01
0.03916
t [ms]
ne [1019 m 3 ]
ID↵ [V]
H-mode
1185
11.79
0.01652
We here introduced the particle confinement time ⌧p . It is a measure of the time that the
plasma particles stay confined after the influx of neutral particles has been stopped. We can
make an estimation of ⌧p based on the data from Figure 3.5 and 3.11 since
N e / ne
IN
If we select a point in time where
dne
dt
(3.7)
/ ID↵
(3.8)
⇡ 0, we can derive the particle confinement time from
⌧p =
Ne
IN
⇡ const
ne
ID↵
(3.9)
Unfortunately, the D↵ detector is not calibrated meaning that we are not able to calculate
the absolute value of ⌧p since the constant is unknown. However, we can calculate the ratio
of ⌧p at two di↵erent points in time. In this way, we can estimate the improvement of the
particle confinement in H-mode compared to ohmic heating phase:
⌧p (H)
ne (H) ID↵ (OH)
=
⌧p (OH)
ID↵ (H) ne (OH)
(3.10)
Since the influxes from the gas pu↵ and NBI happen at fixed points in the vessel, the D↵
detectors do not necessarily observe them, in contrast to the re-emission of neutral particles
by the vessel wall which happens everywhere in the vessel and so also in the sight of the
D↵ detectors. So, if we select for ohmic heating a point in the range 1120-1130ms and for
H-mode a point in the range 1180-1190ms, there is no contribution of the gas pu↵ or the NBI
in equation (3.5), and the approximation (3.9) reaches maximum accuracy. The results are
summarised in Table 3.1. In this way, we calculate
⌧p (H)
⇡ 5.58
⌧p (OH)
(3.11)
meaning that the particle confinement at the end of H-mode has improved by more than
a factor 5 with respect to the end of ohmic heating. Impurities were neglected for this
estimation.
3.3.5
Global energy confinement
The energy balance of COMPASS is given by
dW
= POH + PN BI
dt
PBr
PL
(3.12)
saying that the change of total thermal energy of the plasma column equals the sum of the
ohmic heating power and NBI heating power minus the power losses - the radiation losses
76
CHAPTER 3. H-MODE OPERATION IN COMPASS
Figure 3.12: Left: Ohmic heating power. We assume L = 1µH. Right: Thermal energy calculated by EFIT.
due to bremsstrahlung separately mentioned. If we compare this to equation (1.12), we see
that PH = POH + PN BI and that PF = 0 as there is no mentionable amount of fusion power
created by COMPASS. Substituting equation (1.18), we find for the energy confinement time
⌧E⇤ =
POH
W
+ PN BI
dW
dt
(3.13)
The total thermal energy W stored in the plasma can be deduced either from plasma diamagnetism or from EFIT calculations. The NBI power injected in the plasma is an uncertainty
(remember paragraph 2.4.2). Therefore, we can reasonably estimate the energy confinement
time before and after the neutral beam injection. The most general equation for the ohmic
heating power is
✓
◆
dIp
dL
POH = Ip Uloop L
Ip
(3.14)
dt
dt
Here, Uloop is the loop voltage felt by the plasma, which is slightly di↵erent from the loop
voltage felt by any toroidal flux loop6 , Ip is the plasma current and L is the total plasma
self-inductance. Indeed, the total self-inductance of the plasma changes during operation.
Scientists at the IPP are working on a program code to calculate L(t), but for now we just
neglect this term. Besides, we are interested in H-mode, which usually occurs at the flattop phase of the discharge, so we can normally also omit the second term. However, shot
#4073 only has a small flat-top phase at the end of the discharge as can be seen from Figure
3.4, so we will need the second term. We can estimate the total plasma self-inductance by
using the formula for a homogeneous current through a 1-turn loop with circular cross section
(µ0 = 4⇡ · 10 7 Hm 1 , R = 0.56m, a = 0.20m)7
 ✓ ◆
8R
L = µ0 R ln
1.75 = 0.96 µH
(3.15)
a
This agrees pretty well with the value of 1µH obtained by EFIT. There are 8 flux loops to
measure the loop voltage. Because some of them are used in the feedback control system,
their voltages are integrated over time. This makes it difficult to average the voltages of
all loops which should normally be the best solution. Therefore, we only use the signal
‘loop voltage Flux loop 01’. This flux loop is localized in the mid-plane at the high field
side. The ohmic heating power POH and thermal energy W are shown in Figure 3.12. Only
6
7
Other mutual inductances regarding the poloidal field coils for example.
Table 2.1 gives a maximum value. More common achieved minor radii are approximately 0.20m.
3.3. SHOT #4073: THE FIRST ACHIEVEMENT OF H-MODE
77
Table 3.2: Data used to calculate the energy confinement time and NBI power.
t [ms]
W [kJ]
dW
dt [kW]
POH [kW]
PN BI [kW]
⌧E⇤ [ms]
OH phase
1109.5
3.243
41.47
270.1
0
14.18
start NBI
1130
3.692
64.54
195.6
129.3
14.18
H-mode
1185.2
5.490
-10.64
311.2
0
17.06
EFIT data was accessible for the plasma energy of this shot due to the adoption of another
data-acquisition architecture8 after shot #4609. Remark that the corrected ohmic heating
power shows negative values which is impossible. To obtain an estimation of the energy
dI
confinement time as accurate as possible, we select points where dtp ⇡ 0, i.e. where the red
and green curve of Figure 3.12 overlap. The chosen data are summed in Table 3.2 together
with the resulting energy confinement times. We assume that the plasma energy curve is
intrinsically smooth. If we would not smooth this data out with the Matlab smooth-function
or with a polynomial fit, the derivative would contain very high values which are physically
impossible. According to Table 3.2, ⌧E⇤ has improved by a factor 1.20 between ohmic heating
at t=1109.5ms and H-mode at t=1185.2ms. More accurate calculations demand better data
for Uloop as well as knowledge of L(t) and PN BI . We can make an estimation of PN BI if we
assume that ⌧E⇤ remains constant in the time interval 1109.5-1130ms. Like Table 3.2 shows,
we find as estimation for PN BI a value of 129.3kW.
3.3.6
Divertor Langmuir probes
As seen in paragraph 2.5.6, COMPASS has an array consisting of 39 Langmuir probes9 in the
divertor region, LP1 being at the high field side and LP39 at the low field side. A scheme of
the circuit used for the probe measurements is shown in Figure 3.13. The tokamak operators
can choose the potential that is applied to the probes. This is represented by the PC-Kepco
branch. The plasma-induced current through the Langmuir probes is measured over a resistor by a di↵erential amplifier and then saved in the COMPASS database. In case of shot
#4073, R is 1⌦ and the amplification factor is 2. This means that the data retrieved from
the database has to be divided by 2 in order to get the real current through the probes. One
chose for a swept potential for this shot in order to be able to derive the IV characteristic as
discussed in paragraph 2.5.6 . The resulting potential and current signals for LP2 around the
time of the L-H transition are also shown in Figure 3.13. We see that the probe potential is
swept with a frequency of 1kHz. The ion-saturation current diminishes in H-mode and shows
spikes caused by the ELMs. If we compare multiple probes (see Figure 3.14), we observe the
same properties but the currents are in general smaller as the probe is located closer to the
low field side and there is an increasing time delay for the ELMs towards the high field side.
8
D-tAcq instead of ATCA.
However, probes 1, 20, 33, 34, 35, 36, 37, 38 and 39 were not activated or did not seem to work fine for
shot #4073.
9
78
CHAPTER 3. H-MODE OPERATION IN COMPASS
Figure 3.13: Lef t: Scheme showing how the probe potential is created and the current measured. Right: the
resulting time-varying potential and current signals for probe 2 of shot #4073.
Figure 3.14: Time-varying current of LP2 (HFS), LP15 (private region) and LP32 (LFS).
Next, some IV characteristics are plotted in Figure 3.15 for some specific points in time together with the corresponding exponential fit following equation (2.52). Hereby, we make the
assumption that we are dealing with a Maxwellian plasma. The algorithm used to determine
the di↵erent parameters uses
• ↵ = 0, i.e. there is saturation
+
• Isat
= mean(Iprobe (Vprobe <
50))
• Vf = mean(Vprobe (|Iprobe | < 0.02))
• Te is determined by searching the minimum error (method of least squares)
E=
X
probe data

Iprobe
✓
+
Isat
1
e
Vprobe Vf
Te [eV]
◆
2
(3.16)
3.3. SHOT #4073: THE FIRST ACHIEVEMENT OF H-MODE
79
Figure 3.15: IV characteristic of LP2 at t=1135-1135.5ms and t=1195-1195.5ms. The black spots are the
+
original data points. The red line is the exponential fit. Isat
, Vf and Te are summed above the graph.
The active surface area A of the Langmuir probes is in the range 5.78-6.89mm2 , the smallest
values for the probes in the private region (see Appendix C). With this information we are
able to calculate the electron density at the probe level. We hereby make the approximations
Z = 1, i.e. there are no impurities, and i =1. The electron temperature and density are
plotted in Figure 3.16 versus time for di↵erent probes. Note that due to the 1kHz swept potential, the best time resolution is only 0.5ms. Therefore, it could be possible that the ELMs
for example are not visible. Apparently, the average electron temperature is about 40eV for
all of the investigated probes. Remark that the data scattering of the Te signal is reduced in
H-mode. There is no extraordinary behaviour at the L-H transition, no observable e↵ects of
ELMs. The electron density is highest for LP19. All three curves show a sudden increase in
density at t = 1032ms. This is the time when the plasma is elongated enough to touch the
divertor. As can be seen in Figure 3.10b, the plasma then reaches its maximum elongation.
The L-H transition is again not very good visible, except maybe for the curve of LP2: there,
the density drops from about 0.85 · 1019 m 3 to 0.55 · 1019 m 3 , accompanied by some spikes
at 1137-1146ms, and thereafter it increases steadily during H-mode.
Maybe more interesting to examine than the time evolution of the divertor parameters, is
the spatial distribution of them along the divertor array. This is plotted in Figure 3.17 for
three di↵erent points in time: t = 1110ms in ohmic regime, t = 1141ms around the L-H
transition and t = 1185ms in H-mode. Only for the second point, the NBI was active. We see
an increased electron temperature around LP10 and LP17 which are probably the positions
of the strike points, i.e. where the open field lines of the D-shaped plasma strike the divertor
plates. The density, on the other hand, shows a down-sloping trend towards the LFS with
some high peaks around LP18-LP21 - especially at the end of H-mode - immediately followed
by some kind of “shadow”, a small well in the pattern at LP22.
The strike points can be localized by plotting the spatial distribution of the ion saturation
current and searching the maxima. Their positions, according to Figure 3.18a on the one
hand and EFIT on the other hand, are summarized in Table 3.3. The time-evolution of the
radial position of the strike points determined by EFIT is shown in Figure 3.18b. This radial
position is converted in Table 3.3 to the nearest Langmuir probe. For the radial position of
each Langmuir probe is referred to Appendix C.
80
CHAPTER 3. H-MODE OPERATION IN COMPASS
(a) Electron temperature at LP2
(b) Electron density at LP2
(c) Electron temperature at LP9
(d) Electron density at LP9
(e) Electron temperature at LP19
(f ) Electron density at LP19
Figure 3.16: Time-varying plasma parameters of LP2, LP9 (HFS strike point) and LP19 (LFS strike point).
(a)
(b)
Figure 3.17: Spatial distribution of (a) Te and (b) ne along the divertor probe array.
3.3. SHOT #4073: THE FIRST ACHIEVEMENT OF H-MODE
(a)
81
(b)
+
Figure 3.18: (a) Spatial distribution of Isat
along the divertor probe array for shot #4073. (b) Timeevolution of the radial position of the strike points (EFIT).
Table 3.3: Position of the strike points (expressed as the position of the nearest Langmuir probe) determined
by the saturation current technique and by EFIT.
time [ms]
ohmic heating (OH)
NBI assisted H-mode
ohmic H-mode
1115
1150
1185
HFS strike point
probes
EFIT
9
9
9
8
6
7
LFS strike point
probes EFIT
21
21
19
20
18
19
82
CHAPTER 3. H-MODE OPERATION IN COMPASS
3.4
Shot #4267: first shot after cleaning
This is an interesting shot, because it is the first shot that is performed after a GDC of the
vacuum vessel. We expect a clear reduction in the amount of impurities.
3.4.1
Preset parameters
Again, we summarize the basic preset parameters and compare them with the measured
plasma current and plasma position.
• Gas pu↵: 930-1100ms
• NBI2: 1120-1175ms (40kV, 9.7A, 302.6kW upper bound)
• breakdown: 959ms
• flat-top phase: 1011-1173ms
• end of the discharge: 1174ms
Figure 3.19: Plots of plasma current, vertical position and radial position of the plasma center relative to
the center of the COMPASS vessel (R=0.56m, Z=0m) for shot #4267. The measured values as well as the
preset wave form are shown. Also the time intervals when the gas pu↵ and NBI are active, are indicated.
3.4.2
Spectroscopy
Due to the preliminary cleaning all radiation intensities are very low. The L-H transition is
now almost invisible in the D↵ radiation. According to the All Vis signal it occurs around
t=1110ms. Almost no impurity accumulation is observed. There are several ELMs: about
10 small ELMs with a frequency of 1kHz and thereafter 16 bigger ELMs with a frequency of
0.3kHz. The repetition rate decreases at t = 1128ms, a few milliseconds after the activation of
the NBI. This negative relation between the repetition rate and the coupled power indicates
that these are type-3 ELMs. The shot ends with a disruption at t = 1174ms. The hard
x-rays appear again when the NBI is turned on. There also is a HXR spike around the L-H
transition. The SXR data again shows the typical sawtooth oscillations. According to Figure
3.19, the plasma center is displaced by Z = +5mm and R = 8mm. An estimation of
the q=1 surface is drawn in Figure 3.20c. Its radius is about 80mm. According to EFIT,
the q=1 surface intersects the midplane at R ⇡ 0.52m and at R ⇡ 0.60m (see Figure 3.20d),
which means that the radius should be about 40mm according to EFIT. We however already
know that EFIT is not 100% correct. On the other hand, the smaller radius could be an
3.4. SHOT #4267: FIRST SHOT AFTER CLEANING
83
(b)
(a)
(c)
(d)
Figure 3.20: (a) Spectroscopic data of #4267. The yellow area indicates the NBI. (b) Soft x-ray radiation
for shot #4267. The data is not detrended. All signals are on the same scale (order of magnitude 1µW).
The impurity accumulation is clearly visible. The graph is flat at the end because the intensity exceeds the
photodiode’s maximum. (c) Reconstruction of the q=1 surface at t > 1120ms. (d) Radial distribution of the
safety factor q in the midplane calculated by EFIT.
indication that the q=1 surface is not circular but rather elliptical, as could be expected for
an elongated plasma.
3.4.3
Electron density
The electron density is low. There even are no fringe jumps. Between the gas pu↵ and
the NBI activity, the density drops, since there is no external source that adds particles
to the plasma10 . Somewhere in this time interval without gas pu↵ or NBI, namely around
t = 1110ms, the spectroscopic signals show improved confinement: H-mode is already reached
without the help of NBI heating. The shot is never in L-mode. There is no significant increase
of the electron density during H-mode.
10
The behaviour of shot #4073 was rather exceptional.
84
CHAPTER 3. H-MODE OPERATION IN COMPASS
Figure 3.21: Reconstructed line-averaged electron density and elongation for shot #4267. There was not
enough elongation data to see the disruption at t=1174ms. This is solved by linear expanding  and assuming
 = 1 at t=1182ms.
Table 3.4: Data used to measure the relative increase in particle confinement time.
t [ms]
19
ne [10 m 3 ]
ID↵ [V]
3.4.4
OH phase
1050
3.21
0.003542
H-mode
1118
4.63
0.001069
Global particle confinement
According to equation (3.10) the particle confinement time has increased by a factor 4.78
between t = 1050ms and t = 1118ms. Remark that for this first point in time, there was gas
puffing.
3.4.5
Global energy confinement
The ohmic heating power, corrected for time-varying plasma current and constant plasma
self-inductance, is plotted in Figure 3.22 as well as a 40th order polynomial fit of the thermal
energy calculated by EFIT. A smooth energy is needed to get reasonable values for the
derivative. The energy confinement time ⌧E⇤ and neutral beam heating PN BI are calculated
using the values summed in Table 3.5 and formula (3.13). However, this time the value for
PN BI found at the moment the NBI is turned on, is very low and not in accordance with our
calculation for shot #4073. For next shot (#5909) more extended calculations of PN BI will
be performed. We see from the linear fit in Figure 3.22 that PN BI ⇡ 46.7kW according to the
third method described in paragraph 3.5.5. This is indeed low and confirms Table 3.5 which
is actually less error-resistant as it is based on some discrete points selected from the curves
and not on average values.
3.4.6
Divertor Langmuir probes
For shot #4267 the Langmuir probes were in saturation current mode (Vprobe ⇡ 95V). We
+
can make some spatial plots of Isat
to search the strike points. This is in very good agreement
with the EFIT data for the low field side (keeping in mind that probe 20 is not connected),
but for the high field side there are some deviations especially for t=1080ms.
3.4. SHOT #4267: FIRST SHOT AFTER CLEANING
85
Figure 3.22: Left: Ohmic heating power. We assume L = 1µH. Right: Thermal energy calculated by EFIT.
Table 3.5: Data used to calculate the energy confinement time and NBI power.
t [ms]
W [kJ]
dW
dt [kW]
POH [kW]
PN BI [kW]
⌧E⇤ [ms]
OH phase
1040.6
4.408
-103.2
325.9
0
10.27
ohmic H-mode
1115.1
3.611
-3.957
224.1
0
15.83
start NBI
1120
3.638
25.55
229.1
26.27
15.83
(a)
NBI H-mode
1139.9
4.586
25.16
240
26.27
19.02
(b)
+
Figure 3.23: (a) Spatial distribution of Isat
along the divertor probe array for shot #4267. Probes 1, 20, 36
and 39 are not connected. The data is averaged over 1ms. (b) Time-evolution of the radial position of the
strike points (EFIT).
Table 3.6: Position of the strike points (expressed as the position of the nearest Langmuir probe) determined
by the saturation current technique and by EFIT.
time [ms]
ohmic heating (OH)
NBI assisted H-mode
ohmic H-mode
1080
1120
1160
HFS strike point
probes
EFIT
7
11
11
10
9
8
LFS strike point
probes EFIT
19
20
19
20
19
19
86
CHAPTER 3. H-MODE OPERATION IN COMPASS
3.4.7
Thomson scattering
The Thomson scattering device measures the Te and ne profiles along the vertical chord. The
vertical distributions of Te and ne for shot #4267 are shown in Figure 3.24 for four di↵erent
values of t around the L-H transition. We note in particular the increase in temperature of the
core plasma for t > 1110ms. It seems that the maximum pedestal height is reached earlier by
the electron density than by the electron temperature. The particle barrier is formed faster
than the energy barrier.
(a)
(b)
Figure 3.24: Vertical distribution of (a) the electron temperature and(b) the electron density according to
Thomson scattering.
One is able to map these vertical profiles to the mid-plane by using the EFIT reconstruction11 .
The radial profile of Te in the core plasma is well fitted by a modified Gauss function (mgauss)
F = Te,P + (Te,0
Te,P )e
⇣
r
WC
⌘1+W 2
C
while the radial profile of Te in the pedestal is fitted by

✓
◆
Te,P Te,SOL
M r
F =
mtanh
, s + 1 + Te,SOL
2
2WP
(3.17)
(3.18)
where the modified hyperbolic tangent (mtanh) is defined as
mtanh(x, y) =
(1 + xy)ex
ex + e
e
x
(3.19)
x
and with
r the horizontal distance with respect to the plasma center, not a parameter but the
variable on the horizontal axis
Te,0 the electron temperature at the plasma center (
n
= 0)
Te,P the electron temperature at the “knee” of the pedestal
11
This is reflected in the n (pronounced “psi”) on the horizontal axis of Figure 3.25, which is a normalized
form of the poloidal flux function introduced in paragraph 2.5.2. The generally used normalization is: n = 0
in the plasma center and n = 1 on the separatrix.
3.4. SHOT #4267: FIRST SHOT AFTER CLEANING
87
Te,SOL the electron temperature at the scrape-o↵ layer, i.e. the plasma region with open
field lines (see Figure 2.1). This parameter is an o↵set value and is often fixed to zero.
WC the width of the plasma core (achieved by for example least squares fitting)
WP the width of the pedestal, approximately given by the horizontal distance between
the “knee” and the separatrix ( n = 1)
M the pedestal position read from the horizontal axis, which is approximately given by
the middle of the segment defined by WP
s the slope of the mtanh where it connects to the core profile
The mgauss-fit for the core plasma is invented by E. Stefanikova and M. Peterka, who both
work at the IPP. The mtanh-fit of the pedestal was already described in the literature. At the
moment, they are working on an improved version of their fitting code that will automatically
generate a smooth transition between the mgauss and the mtanh. Now, they are connected
by using weighted averages which is not optimal. The corresponding fit for shot #4267 at
t = 1165ms is drawn in Figure 3.25. [48] [83]
(a)
(b)
(c)
(d)
Figure 3.25: Radial distribution of the electron temperature Te and electron density ne measured by Thomson
scattering. The fitting parameters are indicated in figures (a) and (b).
88
CHAPTER 3. H-MODE OPERATION IN COMPASS
3.5
Shot #5909: NBI power calculations
This shot is interesting to make an estimation of the NBI power absorbed by the plasma:
there are three short NBI pulses in a row and more accurate data about POH is available.
Further, the ball-pen probes were activated for this shot. This is interesting to check the
ELMs in another way.
3.5.1
Preset parameters
Again, we summarize the basic preset parameters and compare them with the measured
plasma current and plasma position.
• Gas pu↵: 970-1060ms
• NBI1: 1060-1069ms, 1076-1084ms, 1091-1105ms (250kW upper bound)
• breakdown: 959ms
• flat-top phase: 1073-1122ms
• end of the discharge: 1122.5ms
Figure 3.26: Plots of plasma current, vertical position and radial position of the plasma center relative to
the center of the COMPASS vessel (R=0.56m, Z=0m) for shot #5909. The measured values as well as the
preset wave form are shown. Also the time intervals when the gas pu↵ and NBI are active, are indicated.
3.5.2
Spectroscopy
The L-H transition takes place around t=1065ms. This shot shows about 15 clear ELMs.
There is no recognizable period between the ELMs, probably due to the on and o↵ switching
of the NBI. The discharge ends with a disruption.
3.5.3
Electron density
This time, the fringe jumps really cause big problems to reconstruct the line-averaged electron
density: the jumps are incomplete (see red part in Figure 3.27d), which destroys the algorithm.
The triggered signal (green curve) looks the best one for this shot. However, Figure 3.27b
shows an unrealistic spike right before the disruption. It is caused by the fact that the density
data remains high while the elongation is already dropping. There is probably an error in the
density data: there are no fringe jumps that bring the curve back to the actual zero.
3.5. SHOT #5909: NBI POWER CALCULATIONS
(a)
(c)
89
(b)
(d)
(e)
Figure 3.27: (a) Spectroscopic data of #5909. The yellow area indicates the NBI. (b) Reconstructed lineaveraged electron density shot #5909. The spike at the end seems to be incorrect. (c) Raw line-averaged
electron density divided by max = 1.8. (d) Incomplete fringe jump in 6xAD8302 interferometer signal.
(e) Plasma elongation calculated by EFIT, linearly extrapolated by making the assumption that  = 1 at
t = 1131ms.
90
CHAPTER 3. H-MODE OPERATION IN COMPASS
Table 3.7: Data used to measure the relative increase in particle confinement time.
OH phase
975
2.53
0.1859
t [ms]
ne [1019 m 3 ]
ID↵ [V]
3.5.4
H-mode
1099.5
6.27
0.06061
Global particle confinement
According to equation (3.10) the time constant ⌧p has improved by a factor 7.60 in the time
interval 975-1099.5ms.
3.5.5
Global energy confinement
For this shot information from plasma diamagnetism is available. The three di↵erent energy curves show big deviations. In December 2013, tests were done with METIS12 , a code
comparable to EFIT that calculates specific plasma parameters by using inputs from several
diagnostics. If we believe METIS, we should trust the EFIT curve. However, we have to be
critical since METIS has partially the same input as EFIT.
Several attempts were done to estimate PN BI and ⌧E⇤ . The general expression for ⌧E⇤ , derived
from the power balance, is given by
⌧E⇤ (t, PN BI (t)) =
W (t)
POH (t) + PN BI (t)
dW (t)
dt
(3.20)
Of course, the problem to determine ⌧E⇤ and PN BI is that we have two variables, but only one
equation that links them. In theory, we could solve this for example by (1) assuming that ⌧E⇤
stays the same at the moment that the NBI is turned on, determining PN BI which is assumed
to be a constant and finally determining ⌧E⇤ (t) by substituting this value of PN BI , or (2) by
using a second equation derived from the ITER scaling law. This second equation would be
✓
◆
POH (t) + PN BI (t) ↵
⇤
⌧E⇤ (t, PN BI (t)) = ⌧E,0
(3.21)
POH,0
⇤ and P
where ⌧E,0
OH,0 are respectively the energy confinement time and ohmic heating power
at the end of the ohmic regime, and the exponent ↵ equals 0.5 for L-mode and 0.69 for
H-mode (see equation (1.38) and [85]). This approach results in two surface plots defined
by equations (3.20) and (3.21) of which the intersection gives us PN BI (t). Method (1) was
actually applied in paragraphs 3.3.5 and 3.4.5. Some results of method (2) can be found in
Appendix D. It has to be said that both methods give disappointing results. They are maybe
too detailed in that way that they depend too much on the smoothing of dW
dt and POH . It
is also questionable if the scaling law is valid in such a short time-scales right after the start
of the NBI. Further, we do not reject the possibility that there is some observable transient
regime after the NBI has started. The method recommended by J. Stockel is (3) to assume
12
METIS is a tokamak plasma simulator featuring a current di↵usion solver and a 2D equilibrium solver.
Through simplified actuator models, it is able to calculate a large number of physical quantities fairly fast.
The tool can use shot parameters as input but can also do estimations for new tokamaks. [84]
3.5. SHOT #5909: NBI POWER CALCULATIONS
91
Figure 3.28: Left: Ohmic heating power. For the red and green curves, we assume L = 1µH. Also, a
more accurate estimation of the real Ohmic heating power calculated by J. Havlicek is shown. This one uses
approximations of L(t) and an artificially determined Uloop . Right: Thermal energy calculated by EFIT and
diamagnetic coils.
PN BI = dW
dt at the moment that the NBI is turned on, hereby literally drawing a tangential
line to W in order to estimate the derivative. This is actually a simplified variant of method
(1), with an extra condition, namely that W is more or less constant right before the NBI
starts. However, even in the raw signal, no change in the pattern of any of the three signals
for this shot is seen at the moments the NBI is turned on. There is no increased slope or
whatsoever. Unfortunately, despite a lot of e↵orts, the conclusion of this paragraph is that it
is very difficult - maybe even impossible - to obtain reliable estimations of PN BI starting from
the power balance, especially for this shot. It is maybe not such a bad idea to just disconnect
the injectors and do a calorimeter measurement13 , so that the NBI power at the end of the
beam duct is at least known. In a second phase one can maybe estimate the power absorbed
by the plasma through calculations like the ones done in paragraph 2.4.2.
3.5.6
Divertor ball-pen probes
The ball-pen probe is invented by J. Adamek who works at the IPP. As discussed in paragraphe 2.5.6, it directly measures the plasma potential. In combination with the floating
potential measured by a very close Langmuir probe, it is possible to determine the electron
temperature with equation (2.59). Probes react extremely fast to the plasma and therefore
the speed of the data acquisition system is the limiting factor here. The measurement has
a sample frequency of 5MHz. For our calculations of the electron temperature, we use the
data from ball-pen probe D and Langmuir probe L, which are located towards the high field
region (see Figure 3.29a). The raw signal of the ball-pen probe and the calculated electron
temperature are respectively plotted in Figure 3.29b and 3.29c. It is seen in Figure 3.29c that
the spikes in Te are indeed ELMs, since they coincide with the D↵ bursts. So, the ball-pen
probes make it possible to localize the ELMs with very high time resolution.
3.5.7
Fast visible camera
For this shot, the EDICAM system was active. Some pictures generated by EDICAM are
shown in Figure 3.30. It demonstrates the typical evolution of an H-mode shot very well.
Before plasma breakdown, there is nothing to see. There are no excited atoms and conse13
With the colorimeter positioned at the end of a beam duct comparable to the situation when the NBI is
connected to COMPASS. Recall paragraphe 2.4.2 for more information about this type of measurement.
92
CHAPTER 3. H-MODE OPERATION IN COMPASS
(a)
(b)
(c)
Figure 3.29: (a) Ball-pen probes and Langmuir probes in a divertor tile. (b) Raw floating potential data
from ball-pen probe D. (c) Electron temperature in the divertor area (HFS) measured by ball-pen probe D
and Langmuir probe L, smoothed by a factor 1000. ELMs are visible in the (divertor) electron temperature
and in the D↵ radiation.
(a) t = 985.7ms
(b) t = 1001.6ms
(c) t = 1041.4ms
(d) t = 1062.6ms
(e) t = 1107.7ms
(f ) t = 1126.3ms
Figure 3.30: (a) circular plasma shape, (b) plasma is elongated, (c) plasma is further elongated and touches
the divertor, (d) plasma reaches H-mode, (e) plasma-wall interactions, (f ) disruption
3.5. SHOT #5909: NBI POWER CALCULATIONS
93
quently there is no visible radiation. Suddenly, there is a flash. This first light is more or
less homogeneous, but very quickly a circular shape is formed. This circle is elongated until
the plasma touches the divertor, which can be seen as a bright strip at the bottom of the
pictures. Then suddenly, the boundaries of the plasma are very sharp: H-mode is reached.
The plasma is now visibly very good confined. The plasma boundary is significantly sharper
at the HFS in H-mode. This could be a sign that this region has an increased density gradient.
During H-mode, some plasma-wall interactions happen and are well captured by EDICAM.
Sometimes the whole picture is very bright for a short time. This is probably due to ELMs.
Finally, a lot of plasma-wall interactions happen and the shot ends. This is the disruption.
94
CHAPTER 3. H-MODE OPERATION IN COMPASS
3.6
Shot #6109: H-L transition
Some of the recent shots, namely #6105, #6106, #6108, #6109, #6110, #6131, #6135,
#6146 and #6147, show extraordinary behaviour: for some reason, the plasma goes from
H-mode to L-mode. It is interesting to examine one of these shots.
3.6.1
Preset parameters
Again, we summarize the basic preset parameters and compare them with the measured
plasma current and plasma position.
• Gas pu↵: 970-1100ms
• NBI2: 1120-1240ms (40kV,10A, 312kW upper bound)
• breakdown: 959ms
• flat-top phase: 1035-1160ms
• end of the discharge: 1244ms
Figure 3.31: Plots of plasma current, vertical position and radial position of the plasma center relative to the
center of the COMPASS vessel (R=0.56m, Z=0m) for shot #6109. The measured values as well as the preset
wave form are shown. Also the time intervals when the gas pu↵ and NBI are active, are indicated. Remark
that the radial plasma position deviates from the preset wave form.
3.6.2
Spectroscopy
Looking at the D↵ signal, we clearly observe di↵erent phases. First the D↵ radiation is flat
and relatively low. This is L-mode. At t=1133.5ms, the plasma goes over to H-mode, which
is visible as a sudden drop in the D↵ radiation. At, t=1168.5ms, the plasma falls back to
L-mode preceded by a big spike in the D↵ radiation. At t=1197ms, H-mode is reached again.
Finally, at t=1244ms, the discharge ends with a disruption. We note that aside from the
expected impurity accumulation, there also clearly is an increase in the fuel particles. This
can be explained by the long activity of the NBI, which actually adds fuel particles to the
plasma. The HXR signal gives away the time when the NBI was started. The H-L transition occurs together with the start of the current ramp-up. Maybe this is a trigger. This
hypothesis is however investigated for the other shots that show H-L transitions and most of
the time the current was in flat-top phase during these events. Plausible explanations for the
H-L transition are the impurity accumulation, or the occurrence of a giant (type-1) ELM, or
a combination of both.
3.6. SHOT #6109: H-L TRANSITION
(a)
95
(b)
(d)
(c)
Figure 3.32: (a) Spectroscopic data of #6109. The yellow area indicates the NBI. (b) Soft x-ray radiation
for shot #6109. The data is detrended and smoothed. All signals are on the same scale. The vertical distance
between two consecutive signals is 1.6µW. (c) Reconstruction of the q=1 surface at t > 1170ms. (d) Radial
distribution of the safety factor q in the midplane calculated by EFIT.
The SXR signals again show sawtooth oscillations. A reconstruction of the q=1 surface is
represented in Figure 3.32c. The plasma center is shifted by Z = +20mm and R = +5mm
and the inversion happens at photodiodes 21 and 31. In the approximation of a circular q=1
surface, we find a radius of about 70mm this way. This time, our estimation is consistent
with EFIT. Figure 3.32d shows that according to EFIT, the q=1 surface should intersect the
Z = 0 line at R ⇡ 0.496m and R ⇡ 0.646m. This is more or less what we see on Figure 3.32c.
3.6.3
Electron density
Again, the triggered interferometer signal (green curve) seems to be the best choice, but
unfortunately there are again some errors in this data because fringe jumps are missing at
the end to let the signal go to the actual zero. It was very difficult to reconstruct the electron
density for this shot. After the H-L transition, the data shows strange behaviour. Comparing
to what happens with the blue curve, we decided that the density drops about 1 · 1019 m 3
after the H-L transition. This should not surprise you, since a lower confinement goes hand
in hand with a lower electron density.
96
CHAPTER 3. H-MODE OPERATION IN COMPASS
(a)
(b)
Figure 3.33: (a) Raw line-averaged electron density divided by max = 1.8 for the three di↵erent ambiguous
interferometer signals. (b) Plasma elongation calculated by EFIT. There was not enough elongation data to
see the disruption at t=1244ms. This is solved by linear expanding  and assuming  = 1 at t=1250ms.
Figure 3.34: Reconstructed electron density for shot #6109.
3.6. SHOT #6109: H-L TRANSITION
97
Figure 3.35: Left: Ohmic heating power. We assume L = 1µH. Right: Thermal energy calculated by EFIT
and diamagnetic coils.
3.6.4
Global particle confinement
Since we are not sure about the density data after the H-L transition, we only compare ⌧p ’s
before t=1169ms. According to equation (3.10) the time constant ⌧p has only improved by
a factor 1.51 in the time interval 1083-1157.5.5ms. This may be related to the steep linear
increase of D↵ radiation during H-mode.
Table 3.8: Data used to measure the relative increase in particle confinement time.
t [ms]
ne [1019 m 3 ]
ID↵ [V]
3.6.5
OH phase
1083
5.92
0.1167
H-mode
1157.5
7.63
0.09963
Global energy confinement
This time all three energy signals clearly show an increased slope when the NBI is switched
on at t = 1120ms. So, we can apply the third method based on the time-derivative of the
thermal energy in order to estimate PN BI . According to Figure 3.35, we find this way:
IT
PNEF
BI ⇡ 100.3kW
PNdia
BI ⇡ 151.8kW
PNdiaBT
BI ⇡ 146.3kW
3.6.6
Fast Visible Camera
Some frames captured by EDICAM are shown in Figure 3.36. We see how the plasma originally had a circular shape, is elongated, touches the divertor, reaches the first L-mode followed
by the first H-mode, emits more visible radiation at the end of H-mode compared to the beginning,... Unfortunately the system stopped recording after the first H-mode. There are
strong plasma-wall interactions at the poloidal rings during several milliseconds. Maybe, the
boron layer was not so good there.
98
CHAPTER 3. H-MODE OPERATION IN COMPASS
(a) t = 983.1ms
(b) t = 1049.4ms
(d) t = 1136.9ms
(c) t = 1128.9ms
(e) t = 1158.1ms
Figure 3.36: (a) circular plasma shape, (b) plasma reaches maximum elongation + plasma-wall interactions,
(c) L-mode, (d) H-mode, (e) visible radiation increases during H-mode.
3.7. SHOT #6313: OHMIC H-MODE
3.7
99
Shot #6313: ohmic H-mode
During this shot, H-mode was achieved without help of extra heating by NBI.
3.7.1
Preset parameters
Again, we summarize the basic preset parameters and compare them with the measured
plasma current and plasma position.
• Gas pu↵: 970-1200ms
• NBI: no
• breakdown: 959ms
• flat-top phase: 1072-1168.5ms
• end of the discharge: 1170ms
Figure 3.37: Plots of plasma current, vertical position and radial position of the plasma center relative to
the center of the COMPASS vessel (R=0.56m, Z=0m) for shot #6313. The measured values as well as the
preset wave form are shown. Also the time intervals when the gas pu↵ and NBI are active, are indicated.
3.7.2
Spectroscopy
The L-H transition happens at t=1077ms. This is followed by five small ELMs, an ELM-free
part of about 20 milliseconds, 13 ELMs with increasing repetition frequency - starting with
200Hz which is pretty low - and finally a disruption which ends the discharge. The total
visible radiation indicates the presence of impurities. The discharge ends with a disruption
at t = 1170ms. The HXR signal is zero except at the L-H transition and at disruption.
Apparently, there was a problem with the data acquisition during this shot. The SXR signals
are all flat and incorrect. What we would expect is a signal that increases during H-mode
due to the impurity accumulation and that does not show sawtooth oscillations, because
sawtooth oscillations are related to additional heating. These expectations are confirmed by
the examination of several other ohmic H-mode signals without NBI.
3.7.3
Electron density
Only the 6xAD8302 interferometer measurement was successful for this shot. Unfortunately,
this signal shows again incomplete fringe jumps, and so the whole density profile could not
100
CHAPTER 3. H-MODE OPERATION IN COMPASS
Figure 3.38: Spectroscopic data of shot #6313.
(b)
(a)
Figure 3.39: (a) Raw line-averaged electron density divided by max = 1.8 for the three di↵erent ambiguous
interferometer signals. (b) Plasma elongation calculated by EFIT.
be reconstructed. However, the transition to H-mode is very clear: after a small drop, the
electron density starts to rise very steeply as high confinement is achieved.
3.7.4
Global particle confinement
Again, the known density data is limited, so we are forced to search a point in time nearby the
e
L-H transition with approximately dn
dt ⇡ 0. According to equation (3.10) the time constant
⌧p has improved by a factor 8.67 in the small time interval 1041.1-1085.1ms. This is mainly
caused by a huge relative drop in ID↵ .
Table 3.9: Data used to measure the relative increase in particle confinement time.
t [ms]
ne [1019 m 3 ]
ID↵ [V]
OH phase
1041.1
5.13
0.4227
H-mode
1085.1
5.76
0.05474
3.7. SHOT #6313: OHMIC H-MODE
101
Figure 3.40: Reconstructed line-averaged electron density. It is too difficult to reconstruct the whole curve
due to incomplete fringe jumps.
3.7.5
Global energy confinement
The ohmic heating power as well as the energy confinement time are estimated for this shot.
This time, the NBI was not active so there is no unknown term and the power balance is
exactly solvable. Further, the neo-Alcator scaling relation is checked for this shot. This
empirical relation claims that the energy confinement time of ohmic discharges increases
linearly with electron density for low densities
p
⌧E [ms] = 6.6 a R2 q95  hne,19 i
(3.22)
until it saturates to the value
⌧E,s [ms] = 64 a R Bt
p

(3.23)
Our density data of this shot is only known for t < 1089ms. Further, we only look at points for
t > 1072ms so that the plasma is in flat-top phase14 and has reached its equilibrium position
and maximum elongation. In this time window holds that a ⇡ 0.185m, R ⇡ 0.55m, q95 ⇡ 3.0,
 ⇡ 1.8 and Bt ⇡ 1.21T. Indeed, a new variable appeared in equation (3.22), namely q95 .
This is the safety factor at the 95% flux surface, i.e. at the plasma edge. The resulting
⌧E⇤ (hne i)-plot is shown in Figure 3.42a. Here, ⌧E⇤ was computed using equation (3.24). In
other words, it was taken from Figure 3.41c.
⌧E⇤ =
⇣
Ip Uloop
WEF IT
⌘
dI
L dtp
dWEF IT
dt
(3.24)
In COMPASS’ former life at Culham, the same plot was made. At that time, the energy
confinement time was calculated using equation (3.25)15 .
⌧E =
14
Wdia
Ip Uloop
dWdia
dt
(3.25)
Our estimation of POH is more or less correct in this case.
So, note that ⌧E in Figure 3.42b actually denotes ⌧E⇤ , i.e. the radiation losses due to bremsstrahlung are
included, but to be consistent with this figure the same notation is used here.
15
102
CHAPTER 3. H-MODE OPERATION IN COMPASS
(a)
(c)
(b)
(d)
(e)
Figure 3.41: (a) Ohmic heating power, assuming L = 1µH. (b) Thermal energy calculated by EFIT and
diamagnetic coils. (c)-(e) ⌧E⇤ versus time calculated in three di↵erent ways.
If we compare the neo-Alcator curves for both plots (now and in Culham, see Figure 3.42b),
we see that the saturation occurs at higher density and higher confinement time. This upward shift can be explained as follows: Nowadays, COMPASS is running in a Single Null
Triangularity (SNT) configuration, where the plasma takes up most of the volume in the
vacuum vessel, whereas in Culham COMPASS was running in a Single Null Divertor (SND)
configuration with a much smaller plasma volume and by consequence a smaller confinement
time. Further, we observe some similarities: Most of the data points exceed neo-Alcator,
and the energy confinement time is highest for ELM-free H-mode and lowest in OH regime.
But also some di↵erences occur: The ELMy regime is for example clearly distinguishable
from OH regime in Figure 3.42a while this is not the case for Figure 3.42b. This is probably because only a very limited amount of data was used here, and only for one shot. [68] [86]
We note from Figures 3.41c, 3.41d and 3.41e that if we use the more accurate formula for
POH , non-physical values appear in the beginning of the discharge when the flat-top phase is
dI
not reached yet and dtp can fluctuate a lot. On the other hand, we note that Figure 3.41c
has the best vertical scale to fit the neo-Alcator relation (see Figure 3.42a). Especially the
values for ⌧E⇤ resulting from diamagnetism measurements are much too big. So, an exact
comparison between the data derived from diamagnetism for both Culham and the IPP is
not possible. Also remark that if the less correct formula for the ohmic heating power is used,
namely POH = Ip Uloop , a clear increase in the energy confinement time is observed around
the transition to H-mode.
3.7. SHOT #6313: OHMIC H-MODE
(a)
103
(b)
Figure 3.42: (a) ⌧E⇤ versus hne i for t 2 [1072ms, 1089ms] and the neo-Alcator scaling law (black line). The
interval only contains one ELM. (b) The same graph when COMPASS was still in Culham (L-mode here
actually denotes ohmic regime). [68]
Figure 3.43: ELMs visible in the (divertor) electron temperature and in the D↵ radiation.
3.7.6
Divertor ball-pen probes
During this shot, the ball-pen probes were active which means that we can again make a plot
of the electron temperature on the HFS divertor plates. The ELMs are very good visible (see
Figure 3.43). From analysing both Figure 3.29c and 3.43, we can state that there is almost no
correlation between the height of the D↵ bursts and the height of the Te spikes. The electron
temperature is a measure for the energy of the ELM plasma when it hits the divertor plates,
while the spikes in the D↵ radiation are a measure for the amount of neutral gas in front of
the divertor plates that is excited due to the ELMs. So, to excite a lot of neutral gas and
create a large D↵ burst, the ELM has to give up a lot of its energy and by consequence the
temperature registered by the divertor plates will be lower. On the other hand, the ELM
needs to have enough energy and the neutral gas has to be dense enough to create many
excitations. This could explain why we do not observe a clear correlation.
104
3.8
3.8.1
CHAPTER 3. H-MODE OPERATION IN COMPASS
Conclusion
ELMs
There is unclarity about the type of ELMs observed in COMPASS. In the past, when COMPASS was still in Culham, there were type-1 and type-3 ELMs. However, now at the IPP
in Prague, COMPASS is running in SNT configuration with high triangularity and so it
would not be so strange if also type-2 ELMs appeared. Unfortunately, these are difficult to
distinguish from type-3 ELMs. The ELMs of some of the last shots such as #6316, which
is analysed in the next chapter, have a frequency that increases with the power across the
separatrix. These could be type-1 ELMs. Most of the observed ELMs at the IPP are thought
to be type-3 ELMs.
3.8.2
Impurities
It is notable that somehow impurities are accumulated during H-mode. This e↵ect even
occurs in the first shots after glow discharge cleaning, although it is much smaller than for
other shots. Together with the fact that the impurity accumulation also exists during ohmic
H-mode, this tells us that the impurities originate from the vessel wall rather than from the
neutral beam injectors. The impurities are not only observed in the All Vis signal but also in
the AXUV signals as can be seen for example in Figure 3.44. This is the radiation ranging
from UV light to soft x-rays that is captured by fast bolometers. The line of sight of the
di↵erent AXUV bolometer chips is shown in Figure 2.17b. The chosen bolometers point to
the plasma core. Chips D and F are in the divertor region and by consequence their data is
higher in magnitude. Figure 3.44a nicely shows the ELMs in the AXUV F 10 signal. Figure
3.44b clearly illustrates how fast the impurities are lost when H-mode is terminated. This
linear accumulation of impurities is clearly something typical for H-mode. The impurities
released by the vessel wall enter the plasma but have a difficult time leaving the plasma again
because they are so well confined. They emit bremsstrahlung due to their acceleration in the
electromagnetic fields. It is often thought that these radiation losses induce the disruption
that ends the discharge. All shots discussed in this chapter end with a disruption, but this is
certainly not always the case. On the other hand, a lot of other possible causes exist for these
disruptions. Finally, remark that one has to be careful with the interpretation of the AXUV
1/2
signals. As they contain SXR radiation they are possibly proportional to n2e Te Zef f along
their line of sight. The temperature dependence is low enough, but it has to be investigated if
the increase of the signals can be attributed to increasing plasma density or to accumulation
of impurities. Nevertheless, there are enough examples here above where the All Vis radiation
as well as the AXUV signals are rising while the density is more or less constant. Therefore,
the AXUV signals are interpreted as accumulation of impurities.
3.8.3
Particle and energy confinement
In the literature, H-mode is characterized by an increase in particle as well as energy confinement. This last property is one of our goals in improving the triple product. The improved
particle confinement, however, has some disadvantageous consequences. It is the basis of
impurity accumulation in the plasma core during H-mode.
3.8. CONCLUSION
105
(a)
(b)
Figure 3.44: AXUV signals of (a) shot #4267 and (b) shot #6109.
The improved particle confinement has been demonstrated for all five shots. For every shot
except #6109, the particle confinement time increases by a factor 4 or more. The improvement
in energy confinement is less drastic. Energy confinement times lay typically between 10 and
30 milliseconds16 . The expected improvement due to H-mode is not well observed. In the first
four shots, the NBI could be blamed for this, but also in the last shot with ohmic H-mode
no real improvement is established. It has to be mentioned that the data available for the
calculations were not optimal: the thermal energy, the NBI power as well as the ohmic heating
power17 are uncertain. The lack of a big increase in ⌧E⇤ can also be explained physically by
the presence of high radiation losses due to impurity accumulation. These losses could be
responsible for a decrease in ⌧E⇤ which cancels out the e↵ect of H-mode. However, as we can
see from the spectroscopic data, this impurity accumulation happens linearly. This kind of
linear behaviour cannot be found back in graphs of ⌧E⇤ .
3.8.4
NBI
The exact NBI power is a mystery at the moment. The reason why was already explained in
paragraph 2.4.2. Only an upper bound determined by the preprogrammed current of the ion
source and the voltage over the accelerating grids is known. The fraction of this upper bound
that is really transferred to the plasma was estimated in this chapter to be 15-65% (see Table
3.11).
Table 3.10: Fraction of NBI power captured by the palsma (based on EFIT data).
#4073
#4267
#6109
3.8.5
upper bound [kW]
202.8
302.6
312
estimation [kW]
129.3
46.7
100.3
fraction [-]
63.8%
15.4%
32.1%
Thermal energy
A similar problem exists for the thermal energy W . Together with the NBI power, this
quantity is important to solve the energy balance and to determine the energy confinement
16
17
If EFIT data is used for the energy, otherwise it is higher (20-100ms).
Since we do not know the plasma self-inductance and actually also not the exact loop voltage.
106
CHAPTER 3. H-MODE OPERATION IN COMPASS
time. However, three di↵erent signals are given and it is not yet determined which of them
is the best one. For shots #5909, #6109 and #6313, the energy balance was solved for all of
them and every time EFIT came out as “winner”. Actually, none of them gave really good
results, but the values found for the confinement time based on the diamagnetic energies
were the worst. They gave extremely high or even negative confinement times. Furthermore,
METIS - another code that calculates amongst others the thermal energy - also confirms that
EFIT gives the best results.
3.8.6
H-mode threshold power
The H-mode threshold power lost through the separatrix is calculated as
Pth = POH + PN BI
dW
dt
(3.26)
Since the NBI power is unknown, we will estimate it to be 40% of the upper bound specified
by the settings of the tokamak operators. The results can be compared to the scaling law,
adopted from [87] (Bt = 1.2T, a = 0.20m, R = 0.56m).
sc
Pth
[MW] = 2.15 hne,20 i0.78 Bt0.77 a0.96 R ⇡ 0.296 hne,20 i0.78
(3.27)
The resemblance between the scaling law and the measured Pth is very bad.
Table 3.11: H-mode threshold power calculation.
#4073
#4267
#5909
#6109 (1)
#6109 (2)
#6313
3.8.7
POH [kW]
234.5
126.9
311.9
82.6
75.5
530.2
PN BI [kW]
81.1
121.0
124.8
124.8
0
dW
dt
[kW]
35.3
-5.42
38.52
105.2
-3.7
48.9
hne,20 i [1020 m
0.529
0.510
0.577
0.669
0.548
3]
Pth [kW]
280.3
153.32
102.2
204.0
481.3
sc [kW]
Pth
180.1
175.1
192.7
216.3
185.2
Edge pedestal
H-mode is characterized by the presence of an edge pedestal in the radial temperature and
density profiles. This big temperature gradient is the physical translation of the aimed energy barrier, while the density gradient stands for a particle barrier. These pedestals can be
observed with the Thomson Scattering diagnostic. This has been discussed for shot #4267 together with a formula to fit the radial profile. The pedestal height of the electron temperature
is typically 200-300eV, that of the electron density 4-6·1019 m 3 18 .
18
This has been investigated for several other shots.
Chapter 4
Current spikes
In the autumn of 2013, shots were executed with higher plasma currents due to improved
know-how of the IPP scientists and technicians. J. Havlicek was the one who discovered an
interesting phenomenon: the plasma current Ip performs distinct spikes of magnitude 1kA
and width 0.2ms, often preceded by a drop. It was asked to the writer of this thesis to make
some statistical analysis of these spikes and to come with an idea about the origin of the
spikes.
4.1
Qualitative analysis
Various plasma parameters are analysed. The e↵ect of ELMs on them is summed next:
• D↵ radiation: bursts indicating the presence of ELMs, see Fig.4.1
• plasma current Ip : big spikes simultaneously observed with ELMs, see Fig.4.1
• diamagnetic energy Wdia : spikes, see Fig.4.1
• poloidal : drops, see for example Figure 4.2
• line-averaged electron density hne i: no extraordinary behaviour
• loop voltage from FL1 (midplane, HFS): no extraordinary behaviour, see for example
Figure 4.3
• vertical plasma position: sometimes clear drops, see for example Figure 4.4
• radial plasma position: nothing
• vertical field (IPR1 and IPR9): small disturbances before the ELMs are seen in the D↵
radiation
• fast feedback current IBV : no clear correlation (also modulations in ELM-free region)
107
108
CHAPTER 4. CURRENT SPIKES
Figure 4.1: D↵ radiation, plasma current and diamagnetic energy of shot #6311.
4.1. QUALITATIVE ANALYSIS
109
Figure 4.2: p for shot #5943. The sample frequency is 10kHz. The green vertical lines indicate the times
at which ELMs occur according to the D↵ radiation. These green lines will return in a lot of other figures.
Figure 4.3: Loop voltage for shot #5943. There is no extraordinary behaviour during ELMs.
Figure 4.4: Vertical position measured by the feedback control system for shot #5905. The sample frequency
is 20kHz.
110
CHAPTER 4. CURRENT SPIKES
ELMs cause by definition drops in the plasma energy. However, it is strange that also spikes
occur. Besides, only the signal of the diamagnetic coil with compensation coil shows ELMrelated e↵ects. The EFIT signal maybe is not sampled fast enough to see the small spikes and
the other diamagnetic energy signal maybe contains too much noise. However, after sending
the data of this last one through a low-pass filter, still nothing special is observed.
The drops in p are probably related to the drops in Wdia . As can be seen from equation
(4.1), the poloidal beta depends on the thermal energy of the plasma, the poloidal magnetic
field and the plasma volume. The drops in p are not always that clear, so a quantitative
analysis of p was not done.
nkB T
W
/ 2
(4.1)
p =
Bp2 /2µ0
Bp V
Further, ELMs are known to cause drops in the vertical position. According to [88] for
example, these drops can be unreal and the consequence of ELMs influencing the vertical
position measurement. In the case of COMPASS the vertical position measurement is done
by internal partial Rogowski coils. ELMs create short-lived magnetic perturbations1 which
could induce eddy currents in those coils. The observer would think that the plasma was
vertically displaced while there actually was no change. On the other hand, [88] tells that
ELMs can also cause real vertical drops of the plasma position owing to modifications of the
plasma current profile. In up-down asymmetric configurations, such as the SNT configuration
used in COMPASS, these changes in the current profile imply rapid vertical displacements of
the plasma current centroid.
4.2
Quantitative analysis
The measurement of the plasma current spikes is complicated by the presence of modulations
with the same order of frequency which are caused by the non-ideal thyristors of the power
supplies. The oscillations caused by the power supplies can be observed in Figure 4.1. Note
that there is no relation between the current spikes and the phase of the modulations.
What follows is an extended analysis of the spikes visible in the D↵ radiation, the plasma
current and the diamagnetic energy. To this end, a series of short Matlab codes was used.
The algorithms for these codes are found in Appendix E. The measured quantities are the
absolute height of the D↵ bursts (I denotes intensity here)
D↵ = ID↵,max
ID↵,min ,
the relative height of the current spikes given by
Ip,max Ip,min
Ip,rel =
Ip,average
and the relative height2 of the energy spikes given by
Wdia,max Wdia,min
Wrel =
Wdia,average
1
2
These are by the way also observed, see the summation above.
Since there is uncertainty about the correctness of the diamagnetic energy data, this is a necessity.
(4.2)
(4.3)
(4.4)
4.2. QUANTITATIVE ANALYSIS
111
Here, Wdia denotes the diamagnetic energy measured by the diamagnetic coil with compensation coil. The results are shown in Figure 4.5 and Figure 4.6. Apparently, there is a positive
relation between the D↵ spikes and the current spikes: if one quantity increases, the other
quantity increases too. This is even more true for the relation between the current spikes and
the energy spikes. There is obviously a linear behaviour. The datasets obey following linear
fits3 :
Ip,rel = 0.009
D↵ + 0.0006
Ip,rel = 0.2411 Wrel + 0.0002
R2 = 0.2740
(4.5)
R2 = 0.6295
(4.6)
The spikes are four times more dominant in the diamagnetic energy than in the plasma current.
We however have to be careful with this data. It is sometimes suspected that there is crosstalk
between the diamagnetic coils and the plasma current. This would explain the nice linear
relation, and why we do not see only drops but also spikes in the diamagnetic energy. One
would expect to see only a drop in Wdia : the physical description of ELMs implies energy
losses. On the other hand, equation (4.6) shows that the spikes are more dominant in the
energy, which may be an indication that the plasma energy influences the plasma current and
not the other way around. Another reason why we must carefully interpret these two plots,
is because of human errors: The Matlab code generates plots that allow to control whether
the code did a good job, so that the bad data points can be removed. Only the clear spikes
made it to the final plots presented here. This means that for example ELMs without current
spikes are neglected because the spikes were stamped “indistinguishable from the rest of the
curve”.
Remark that all analysed ELMs have a relative energy drop - followed or not followed by
a small spike - of less than 3%, which is an indication that all of them are type-3. Shot
#6316 shows the typical D↵ graph for a discharge with small and frequent type-3 ELMs right
after L-H transition, followed by higher and more isolated type-1 ELMs, as can be seen in
Figure 4.7. Although, some of these bigger ELMs are also mentioned in Figure 4.6 and clearly
have a relative energy drop that is much too small to be type-1. On the other hand, power
calculations for di↵erent shots with similar pattern in the D↵ radiation have shown that for
these bigger ELMs the power increases with the frequency, which is generally accepted as the
signature for type-1 ELMs (see Figure 4.8).
3
R2 is the coefficient of determination calculated with Microsoft Excel 2007.
112
CHAPTER 4. CURRENT SPIKES
0,008
#5905
#5909
#5912
#5914
#5916
#5926
#5928
#5938
#5943
#5944
#5987
#6000
#6007
#6012
#6013
#6058
#6061
#6062
#6064
#6065
#6099
#6105
#6131
#6132
#6133
#6146
#6301
#6306
#6309
#6310
#6311
#6313
#6316
0,007
0,006
ΔIp_rel [-]
0,005
0,004
0,003
0,002
0,001
0
0
0,05
0,1
0,15
0,2
0,25
0,3
0,35
0,4
0,45
ΔDα [V]
Figure 4.5: Data analysis: relative plasma current spikes versus absolute D↵ spikes.
4.2. QUANTITATIVE ANALYSIS
113
0,008
#5905
#5909
#5912
#5914
#5916
#5926
#5928
#5938
#5943
#5944
#5987
#6000
#6007
#6012
#6013
#6058
#6061
#6062
#6064
#6065
#6099
#6105
#6131
#6132
#6133
#6146
#6301
#6306
#6309
#6310
#6311
#6313
#6316
0,007
0,006
ΔIp_rel [-]
0,005
0,004
0,003
0,002
0,001
0
0
0,05 0,005 0,1
0,15
0,01
0,2 0,015 0,25
0,3
0,02
0,35 0,025 0,4
0,45
0,03
ΔDα [V]
ΔW_rel [-]
Figure 4.6: Data analysis: relative plasma current spikes versus relative spikes in diamagnetic energy.
114
CHAPTER 4. CURRENT SPIKES
Figure 4.7: D↵ radiation of shot #6316.
Figure 4.8: Power-frequency plots. [89]
4.3
4.3.1
Conclusion
What is not the cause?
It is intuitive to think that these spikes are caused by some electrical devices in the circuit
that captures the data. However, it has been verified by J. Havlicek that the spikes are not
caused by crosstalk between cables, neither by the connection to D-tAcq or by the connection
between D-tAcq and MARTe.
Another evident explanation is that the spikes are caused by the feedback control system.
However, a vacuum shot like #6413 nicely demonstrates that the vertical field generated by
the fast feedback system is delayed too much by the vacuum vessel in order to create current
spikes in such a small time-scales. Figure 4.9 shows a delay of almost 0.5ms, while the plasma
current spikes are only up to 0.2ms wide. Another indication is the lack of spikes in the loop
voltage, IBV current, vertical field and radial position.
4.3.2
So, what is the cause?
It is certain that the spikes come from inside the plasma vessel. So, the only explanation
is that it is a physical e↵ect caused by the plasma itself. A possible theory relies on the
plasma self-inductance and the plasma-vessel inductance, and more specifically on their time
derivatives. They are dominant for fast events. A computational simulation should be made
in order to investigate this.
Another explanation that is worth investigating, is given in [90] and [91]. These articles
propose that ELMs go along with previously closed edge field lines suddenly breaking open.
4.3. CONCLUSION
115
Figure 4.9: Vacuum shot #6413. IBV : Current in the PF coils of the fast feedback system. The linear drift
caused by the analogue integrator is removed. BIP R1 : Vertical magnetic field measured by the internal partial
Rogowski coil at the low field side of the mid-plane. BIP R9 : Vertical magnetic field measured by the internal
partial Rogowski coil at the high field side of the mid-plane. The setup of the internal partial Rogowski coils
can be seen in Figure 2.23.
When this happens, plasma energy and plasma current are released along the open field lines.
This leads to the formation of a new equilibrium with a smaller separatrix. One could say
that the plasma edge “peels away”. This is actually a new kind of instability that cannot be
categorized under ‘peeling and ballooning instabilities’ since the plasma boundary is typically
held fixed throughout the computational simulation of these last ones. This whole process
is characterized by very fast jumps of the strike points, in time-scales of 1ms and less. If
the divertor tiles are positioned vertically - as is the case for JET - the strike points jump
upwards. In plasmas with strike points arriving at horizontal target plates - as is the case
for COMPASS - the inner strike point would move inward and the outer outward. Modelling
indicates that these jumps can be associated with losses in plasma current and in p . This
“peel-o↵ instability” is however fundamentally di↵erent from the change in equilibrium that
would be derived simply from a reduction in p , as it works in much smaller time-scales.
Figures 4.10-4.12 confirm that the HFS strike point of shots #5943 and #6313 indeed jumps
towards lower R during ELMs and that the LFS strike point of shot #5943 jumps towards
higher R. This last e↵ect is however less clear. We observe jumps of 1cm and more. Since
the curves have been smoothed by a factor 1000, the actual jumps are much bigger and much
faster. The small time-scales of the jumps require a signal with high sample frequency (at
least 1kHz) in order to detect them. The probe data used in Figures 4.10-4.12 is therefore an
excellent choice. The jumps are not so well observed by EFIT which samples at frequencies
of only 1-10kHz. There, the jumps are very small and can only be distinguished from the
other fluctuations in the signal with the help of the D↵ radiation.
116
CHAPTER 4. CURRENT SPIKES
Figure 4.10: Radial position of the HFS strike point of shot #6313. This is computed by searching the
probe with maximum saturation current. Therefore, probes in the HFS region were selected, namely probes
6-12. Appendix C was used to convert probe numbers to radial positions. The sample frequency is 5MHz.
The resulting curve has been smoothed by a factor 1000.
Figure 4.11: Radial position of the HFS strike point of shot #5943. This is computed by searching the probe
with maximum saturation current. Therefore, probes in the HFS region were selected, namely probes 5, 6, 7,
8, 10,12 and 13. Appendix C was used to convert probe numbers to radial positions. The sample frequency is
5MHz. The resulting curve has been smoothed by a factor 1000.
Figure 4.12: Radial position of the LFS strike point of shot #5943. This is computed by searching the
probe with maximum saturation current. Therefore, probes in the LFS region were selected, namely probes
15, 16, 20, 21, 23, 24 and 25. Appendix C was used to convert probe numbers to radial positions. The sample
frequency is 5MHz. The resulting curve has been smoothed by a factor 1000.
Chapter 5
General conclusions and suggestions
for future work on COMPASS
This master thesis consisted of two main tasks: The first one was to analyse several shots that
achieved the H-mode regime. This includes amongst others the examination of ELMs, impurities, energy confinement and particle confinement. The goal of this task was not strictly
delineated. There was a lot of space for experimentation with data from di↵erent diagnostic tools. Besides, it was a continuation of older work such as [50]. The second task was to
gather some statistical data about spikes that were observed in the plasma current and to provide an explanation why they occur. It is the first time that these current spikes are described.
The huge amount of freedom for this thesis permitted to do some additional stu↵ and to be
inventive. An improved reconstruction of the line-averaged electron density hne i was aimed
for example. To this end, a Matlab code was written based on a paper found on the web,
namely [92]. The code removes the o↵set, filters the high-frequent noise, removes the fringe
jumps and takes the plasma elongation into account. The code is certainly useful, though it
fails when incomplete fringe jumps occur. Further, there was also experimented a lot with
probe data and with scaling laws.
Since the D↵ detector is not calibrated, it is impossible to calculate the absolute value of the
particle confinement time. So, we cannot compare ⌧p of COMPASS with ⌧p of other tokamaks
which is a shame. On the other hand, we are still able to compare di↵erent values of ⌧p at different times and examine the improvement of the particle confinement in H-mode for example.
Energy confinement calculations on the other hand struggle with another problem: the power
balance cannot be solved exactly since the NBI power is unknown. We only know that it is
something between zero and some upper bound determined by the preprogrammed current
of the ion source and the voltage over the accelerating grids inside the NBI system, and that
it is very unlikely to be zero. It was attempted to estimate this power term in several ways
starting from the power balance and making certain assumptions, but without good results.
As a consequence it is also difficult to estimate the improvement in energy confinement time
in H-mode when the NBI is active. The attempts to solve the power balance with NBI power
term took a lot of time. For an actual discussion of numerical results is referred to section 3.8.
117
Figures 4.5 and 4.6 definitely form the most important part of this thesis. The height of the
current spikes was examined in more than 30 shots and compared to the diamagnetic energy
and the D↵ radiation. We can conclude from these figures that there is a positive relation
between the height of the D↵ bursts and the relative height of the plasma current spikes, and
that there even is a strongly linear behaviour between the relative height of the current spikes
and the relative height of the diamagnetic energy spikes. Relative heights were used because
there are some uncertainties in the diamagnetic energy. Probably there is some crosstalk
between the plasma current and the diamagnetic coil.
It is proven that the current spikes cannot be caused by the feedback system and further it
is known that they are also not caused by crosstalk between cables. We could think of two
explanations for these current spikes:
1. They are caused by fast changes in the plasma self-inductance and in the plasma-vessel
inductance.
2. They are caused by strike point jumps which are associated to closed field lines breaking
open at the plasma edge followed by the formation of a smaller separatrix. Simulations
performed by the sta↵ of JET have shown that these strike point jumps can be responsible for a significant drop in the plasma current (much too big compared to the 1kA
drops observerd in COMPASS). However, the strike point jumps are clearly observed
in COMPASS using probe data. If they are indeed the cause of the current spikes, we
still have to try to understand why the plasma current (and often also the diamagnetic
energy) first drops a little bit, but then increases a lot more, forming a spike instead of
only a drop.
It is not clear whether the observed current spikes are immediately associated with plasma
degradation, but as they appear simultaneously with ELMs, their study can be important to
enrich our knowledge of ELMs. These instabilities do degenerate the plasma as they diminish
the plasma energy, and pose an issue concerning ITER. Further investigation of the current
spikes could even show that we have to revise our current models of ELMs. But that is still
a long way o↵.
Possibilities for further work on COMPASS are:
• Still improve the reconstruction of the line-averaged electron density from interferometer
data. Find out why those incomplete fringe jumps occur.
• Calibrate the D↵ detector.
• Try somehow to determine which thermal energy signal is correct (WEF IT , Wdia or
WdiaBT ?), maybe by using plasma simulators.
• Disconnect the neutral beam injectors (maybe better both of them since one can work
on full capacity and the other not) and do a calorimeter measurement, so that we at
least know the output power at the end of the beam duct. Maybe there are more
practical methods based on the newly installed neutron detector.
118
119
• Try to calculate the plasma self-inductance L(t) as accurate as possible1 . This helps
to solve the energy balance since it influences the ohmic heating power and will maybe
also help to find an explanation for the current spikes.
• Make a plasma simulation that takes into account the plasma self-inductance (and
maybe also the plasma-vessel inductance), and try to find an explanation for the current
spikes.
• Take contact with the sta↵ of JET and try to link the found strike point jumps to their
observations in JET. Maybe their simulation code can be used.
1
J. Havlicek is working on a code.
Appendix A
Drift velocity
The motion of a charged particle in an inhomogeneous magnetic field is constituted of
1. a gyration around an instantaneous guiding centre due to v? .
2. a translation along the field line of the guiding centre with velocity vk .
3. a drift with velocity vD of the instantaneous guiding centre due to the inhomogeneity.
The drift velocity vD is partially due to v? (the gradient drift) and partially due to vk
(the centrifugal drift). The exact expression is:
vD =
2
mvk2
1 mv?
2
B
⇥
rB
+
[B ⇥ (B · r)B]
4 qB 4
qB 4
(A.1)
Assuming a force-free magnetic field, i.e. B ⇥ (r ⇥ B) = 0, and local thermal equilibrium of
the plasma, this can be simplified to
vD =
kT
B ⇥ rB 2
qB 4
(A.2)
In case of an ideal torus configuration, the magnetic field only has a toroidal component given
by
µ0 Ip
Bt =
(A.3)
2⇡r
ans so
B
rB =
er
(A.4)
r
This gradient causes a drift velocity
vD =
4⇡kT
er ⇥ et
µ0 qIp
(A.5)
The q dependence results in a charge separation, which in its turn generates an electric field
that drifts the plasma away from the central axis. This so-called Hall-drift is given by
vD,Hall =
E⇥B
B2
(A.6)
A vertical equilibrium field is needed to counteract this radially outwards motion of the plasma
column. [30]
120
Appendix B
Density reconstruction
Goal: reconstruct the line-averaged electron density from interferometer data.
Algorithm:
1. Send interferometer data through a (windowing) low-pass filter with cut-o↵ at 10kHz.
2. Remove o↵set.
3. Convolute the resulting data with the kernel function
g(t, wk ) =
8 1
>
< wk M
1
> wk M
:
0
,
wk < t
, t < wk
(B.1)
, rest
where M is the di↵erence between the absolute maximum and absolute minimum of the
density data and wk = wf /↵ with wf an estimation of halve the width of a fringe jump
and ↵ smaller than unity and here chosen to be 1/3.
4. Mathematics claims that this convolution shows distinct spikes with maximum height
equal to 1 ↵/2. So we take a fraction of this value as our threshold. Positive spikes represent downsloping fringe jumps and negative spikes represent upsloping fringe jumps.
5. Now that the fringe jumps are located, we remove the density data that are part of the
jump, which is very accurately estimated by the interval [tjump wk , tjump + wk ], and
we bring the data after the jump on the same level as the data before the jump.
6. Division by the elongation , which is linearly interpolated (and even extrapolated with
some assumptions) to maintain a rich enough amount of data.
This algorithm is based on [92].
121
122
APPENDIX B. DENSITY RECONSTRUCTION
Figure B.1: Left: The basic pattern of a fringe jump, the kernel function and their convolution. tA and tB are
the start and the stop times of a fringe jump. Right: Some mathematical information about the convolution
for the case wf < 21 wk . [92]
Appendix C
Divertor Langmuir probes
Table C.1: Radial position R and e↵ective surface area A of the divertor Langmuir probes.
Probe
1
2
3
4
5
6
7
8
9
10
11
12
13
R [m]
0.3960
0.4000
0.4038
0.4076
0.4114
0.4152
0.4192
0.4236
0.4279
0.4326
0.4373
0.4421
0.4470
A [mm2 ]
6.62
6.53
6.49
6.44
6.44
6.44
6.43
6.40
6.39
6.39
6.36
6.29
6.21
Probe
14
15
16
17
18
19
20
21
22
23
24
25
26
R [m]
0.4520
0.4569
0.4619
0.4669
0.4719
0.4768
0.4817
0.4866
0.4915
0.4963
0.5012
0.5060
0.5108
123
A [mm2 ]
6.13
5.99
5.84
5.78
5.83
5.87
5.96
6.09
6.21
6.32
6.14
6.16
6.23
Probe
27
28
29
30
31
32
33
34
35
36
37
38
39
R [m]
0.5155
0.5202
0.5249
0.5296
0.5342
0.5388
0.5433
0.5478
0.5523
0.5567
0.5611
0.5654
0.5697
A [mm2 ]
6.38
6.52
6.50
6.52
6.65
6.73
6.75
6.77
6.86
6.88
6.91
6.93
6.89
Appendix D
Estimation of PN BI for shot #5909
First of all a short recapitulation of the four methods described in paragraph 3.5.5 to estimate
PN BI :
• Method 1: ⌧E⇤ remains constant during NBI activity and is equal to an average of its
last values before the NBI was switched on.
PN BI (t) =
dW
W (t)
(t) + ⇤
dt
⌧E,0
POH (t)
• Method 2: Search the intersection of the two surfaces given by
8
W (t)
<⌧E⇤ (t, PN BI (t)) =
dW (t)
POH (t)+PN BI (t)
dt ⌘
⇣
↵
POH (t)+PN BI (t)
:⌧ ⇤ (t, P
⇤
(t))
=
⌧
N BI
E
E,0
POH,0
(D.1)
(D.2)
where ↵ is 0.5 for L-mode and 0.69 for H-mode (ITER scaling laws).
• Method 3: Plot W (t) and estimate dW
dt at the moment the NBI is switched on by
drawing a tangential line. The NBI power can be approximated by the found number.
The last method is infeasible for this shot as there is no observable change in W (t) at the moment the NBI is switched on. For all three other methods, smoothing of the di↵erent plasma
parameters is very important, especially for the energy data derived from diamagnetism since
the sample rate is much bigger for these signals. For all figures shown in this appendix, the
datasets Wdia and WdiaBT are reduced by a factor 100, all W are smoothed by a factor 5, and
their derivatives are smoothed by a factor 5 in case of EFIT and by a factor 100 in case of
diamagnetism. The ohmic heating power for Figure D.2, which shows the results of method
1, is smoothed by a factor 50. For Figures D.3-D.5, which show the results of method 2, it is
⇤ and P
smoothed by a factor 50, 100 or 1000. Also the determination of ⌧E,0
OH,0 is important.
For Figure D.2 they are calculated by manually selecting a part of the ⌧E⇤ (t, PN BI = 0) curve
and averaging. For Figures D.3-D.5 they are calculated by averaging over the time interval
[t0 2ms, t0 0.1ms], where t0 is the time when the NBI was turned on. Figure D.1 is added
to have an idea of how POH looks like for the di↵erent smoothing factors that are used in
these figures.
124
125
Figure D.1: The artificially calculated ohmic heating power POH of shot #5909 for three di↵erent smoothing
factors (SF).
(a) EFIT
(b) Dia
Figure D.2: Results of method 1.
(c) DiaBT
126
APPENDIX D. ESTIMATION OF PN BI FOR SHOT #5909
(a) EFIT, 50
(b) EFIT, 100
(c) EFIT, 1000
(d) Dia, 50
(e) Dia, 100
(f ) Dia, 1000
(g) DiaBT, 50
(h) DiaBT, 100
(i) DiaBT, 1000
Figure D.3: Results of method 2 for t = 1060
factor of POH .
1069ms. The number under the figure denotes the smoothing
127
(a) EFIT, 50
(b) EFIT, 100
(c) EFIT, 1000
(d) Dia, 50
(e) Dia, 100
(f ) Dia, 1000
(g) DiaBT, 50
(h) DiaBT, 100
(i) DiaBT, 1000
Figure D.4: Results of method 2 for t = 1076
factor of POH .
1084ms. The number under the figure denotes the smoothing
128
APPENDIX D. ESTIMATION OF PN BI FOR SHOT #5909
(a) EFIT, 50
(b) EFIT, 100
(c) EFIT, 1000
(d) Dia, 50
(e) Dia, 100
(f ) Dia, 1000
(g) DiaBT, 50
(h) DiaBT, 100
(i) DiaBT, 1000
Figure D.5: Results of method 2 for t = 1091
factor of POH .
1105ms. The number under the figure denotes the smoothing
Appendix E
Current spikes algorithms
E.1
Algorithm 1
Goal: find time and height of D↵ spikes
Algorithm:
1. Estimate the average spike width yourself by looking at the original graph (±0.3ms).
2. Choose between:
(a) Send ID↵ through a bandpass filter with fmin = 200Hz and fmax = 10kHz.
(b) Remove the linear background signal in H-mode.
3. Search for possible spikes1 :
ID↵ > c · std(ID↵ )
(E.1)
with c a tunable parameter implemented as the ‘sensitivity’ and set equal to 1.5. This
results in groups of duplicates.
4. Distinguish the groups from each other by searching consecutive spikes that are farther
from each other than the estimated average spike width. ) dummy spikes
5. Look for the maximum value in each group.
6. Plot the signal and indicate the found spikes with vertical lines.
1
std=standard deviation
129
130
APPENDIX E. CURRENT SPIKES ALGORITHMS
Figure E.1: Illustration of the algorithm for shot #6058. The blue curve is the D↵ radiation modified by
step 2. The red horizontal line is the threshold 1.5 · std(ID↵ ). The red dots are the possible spikes resulting
from step 3. The green dots are the dummy spikes resulting from step 4. The arrow indicates the maximum
between two dummies as described in step 5.
E.2
Algorithm 2
Goal: measure less distinct spikes in for example the plasma current or the plasma energy,
starting from the times when bursts occur in the D↵ radiation.
Algorithm:
1. Send the data through a (widowing) low-pass filter with fc = 10kHz.
2. Search for the time tmax when the maximum occurs around the given time i of the d↵
burst ( t is the sample period of 0.5µs):
for k = 20 ! 1 do
j=k t
while data(i + j) > data(i) do
i = time when data reaches its maximum in the time interval [i, i + j]
end while
while data(i j) > data(i) do
i = time when data reaches its maximum in the time interval [i j, i]
end while
end for
tmax = i
3. Search for the time tmin when the minimum occurs in front of the determined maximum
( t is the sample period of 0.5µs, i = tmax 50 t):
for k = 50 ! 1 do
j=k t
while data(i + j) < data(i) do
i = time when data reaches its minimum in the time interval [i, i + j]
end while
while data(i j) < data(i) do
i = time when data reaches its minimum in the time interval [i j, i]
end while
end for
tmin = i
E.2. ALGORITHM 2
131
4. Calculate the di↵erence between the determined maxima and minima. This is defined
as the spike height.
5. Plot the signal and indicate the maxima and minima by respectively green and red lines.
Now, control manually if the code has done a good job and remove the badly calculated
spike heights.
Figure E.2: Resulting plot of the MeasureSpikes algorithm for shot #6311.
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