Download Neutral beam plasma heating

Seminar Ib – 1st year, 2nd cycle program
Neutral beam plasma heating
Author: Gabrijela Ikovic
Advisor: prof.dr. Tomaž Gyergyek
Ljubljana, May 2014
Abstract
For plasma to be ignited, external heating is needed. Several ways of heating are known and
studied. In the seminar the neutral beam plasma heating is discussed in details. High-energy
neutral particles that are injected into the plasma can be produced from positive or negative
ion source. For future fusion reactors neutral beams, produced by negative ion source, seem
to be an effective method for plasma heating and therefore this is an important field of
fusion technology research.
CONTENTS
1. INTRODUCTION...................................................................................................................... 2
2. PLASMA HEATING .................................................................................................................. 4
2.1. Ohmic heating.................................................................................................................. 5
2.2. Neutral beam injection .................................................................................................... 5
2.3. Radio frequency waves .................................................................................................... 6
3. NEUTRAL BEAM HEATING ..................................................................................................... 6
3.1 Generating neutral beam ................................................................................................. 7
3.2 Optimal beam energy ...................................................................................................... 8
3.3 Negative versus positive ion source ............................................................................... 10
CONCLUSION ............................................................................................................................ 11
REFERENCES ............................................................................................................................. 12
1. INTRODUCTION
Energy production is theoretically possible by both fission and fusion nuclear reactions. Since
binding energy per nucleus is the largest for nuclei with mass number around 56 (Fig. 1), the
energy is released when heavier atom splits into two or more smaller atoms, or when lighter
atoms collide and fuse into one heavier atom. While fission reactors are commonly used
worldwide, there are no commercial fusion reactors operating yet.
Fig. 1: Binding energy per nucleus. [1]
2
To induce the fusion of two nuclei it is necessary to overcome Columbic force due to their
positive charges and the most efficient way to supply energy is heating the fuel. At those
temperatures atoms become fully ionized and the fuel is in the form of plasma. The cross
section for fusion is small at low energies and it increases with increasing energy. The cross
section for different reactions can vary significantly, as well as the energy at which maximum
cross section is reached.
Table 1 shows possible fusion reactions. Parameter E represents the energy released in
specific reaction,
is the largest cross section for fusion of two nuclei and
is the
temperature of plasma at which the
is achieved. According to the table D-T reactions
seem to be the most promising for future fusion reactors.
Table 1: Some of the fusion reactions that can be considered for energy production. [2]
Reaction
E [MeV]
[b]
[keV]
17.59
5.0
64
3.27
0.11
1750
4.04
0.096
1250
11.33
0.16
1000
18.35
0.9
250
A high density and high temperature environment is required for fusion of two light atoms
to happen and magnetic confinement is one of a very few possibilities to confine plasma,
since the high temperatures would melt any material wall.
First fusion experiments took place back in 1930, but it was not until 1968 that the first big
break was accomplished. A group of experts in the Soviet Union developed a successful
magnetic confinement – tokamak, which is still the most promising type of confinement.
Next important achievement was the tokamak JET. In 1997 it produced 16 MW of fusion
power using deuterium and tritium, which is more than 60 % of input power. The next step
in fusion research will be much larger fusion reactor ITER, followed by the first power plant
DEMO. [3]
For ions D and T to be fused, the ions must achieve high enough kinetic energy, therefore
plasma must be heated. The main goal of fusion reactors is to produce more power from
fusion than used for heating and confinement in order to be competitive with other power
systems.
2. PLASMA HEATING
For a plasma to be ignited, the released fusion power must overcome the power losses from
Bremsstrahlung radiation and diffusion.
2.1
In eq. (2.1)
means fusion power density and since neutrons are uncharged and therefore
the magnetic field cannot confine them, only alpha particles contribute to plasma heating.
The alpha particles that are produced in D-T reactions have 3.5 MeV of kinetic energy. By
colliding with other particles they transfer that energy to the plasma. Therefore so called
alpha power depends on the energy of alpha particles
and the rate of collisions. The rate
of collisions is a function of number density of ions and electrons in the plasma (
3
, mean relative velocity of particles and the cross section for collisions. The number
density can be expressed as
and the fusion power density is given as
〈
〉
〈
〉
2.2
Losses from Bremsstrahlung radiation are given as
2.3
where
√
2.4
⁄
⁄
and
represents an effective ion charge in case where several different ions are present in
a plasma. [3] Diffusion losses are power density loss because of heat flux, which leaks from a
surface of plasma. It is defined as
2.5
where
stands for energy confinement time.
The ignition condition can be calculated from eq. (2.1) and expressed as
2.6
〈
⁄
〉
⁄
Losses from Bremsstrahlung are usually neglected and eq. (2.6) is simplified.
2.7
〈
Fig. 2: Critical
〉
for ignition as a function of temperature [4].
4
As seen in Fig. 2, the eq. (2.7) reaches the minimum at temperature 15 keV, which minimize the
demands on pressure and confinement time.
The external heating is needed to raise plasma temperature to about 5 – 7 keV. Above that alpha
power becomes dominant and able to heat plasma to ignition temperature of 15 keV.
External plasma heating is a complicated field that covers a broad range of types and
methods. The types of plasma heating that are relevant for ITER and future fusion reactors
are ohmic heating, neutral beam heating and electron and ion cyclotron heating. Further on
in the seminar a neutral beam heating is discussed in details. [3]
2.1.
Ohmic heating
The changing magnetic fields that are used to control fully ionized plasma within the
tokamak create a high – intensity electrical current through induction. The current produces
ohmic heating, but the resistivity of a plasma decreases with
. Thus, as the plasma
temperature increases, the effectiveness of ohmic heating diminishes. In typical tokamak the
maximum temperature achievable by ohmic heating is about 3 keV, which is not high
enough for the alpha power to dominate and sort of additional heating is required to
supplement the ohmic heating. [1]
2.2.
Neutral beam heating
Outside of the tokamak, charged particles are accelerated with high voltage to the required
energy level. Beam energy must be much higher than required plasma temperature of 15
keV. Since the charged particles cannot penetrate the magnetic field around the plasma,
accelerated ions pass through an ion beam neutralizer where their electrical charge is
removed. High–energy beams of either neutral deuterium or neutral tritium atoms are then
injected into the core of the plasma, where they are ionized and trapped by the magnetic
field. The high–energy ions transfer their energy as they collide with the plasma ions,
increasing the plasma temperature. A disadvantage of this process is the large scale of the
equipment. [5]
2.3.
Radio frequency waves
The energy carried by high–frequency waves injected into the plasma is transferred to the
charged particles, increasing their velocity. The plasma particles have different resonance
frequencies (typically in the radio – frequency region of the electromagnetic spectrum),
depending on their mass, charge and the magnetic field strength at their location. Injecting
the right frequency, a defined group of particles in a defined location can be heated
selectively. The appropriate frequencies are the cyclotron frequencies of electrons (electron
cyclotron heating - ECH) and ions (ion cyclotron heating - ICH), and their cyclotron
harmonics. Although ECH and ICH can produce a strong absorption of energy at the center of
the plasma, both methods still face technological problems. [5]
5
Fig. 3: Types of plasma heating. [1]
3. NEUTRAL BEAM HEATING
Neutral beam plasma heating seems to be a promising method to achieve ignition in future
fusion reactors. However, there are several problems involving both physics and
technology, which must be studied before the method could be effectively used in
tokamaks.
One of the issues is the optimum value of the beam energy. If the beam energy is too low, it
deposits most of the energy on the outside of the plasma and therefore heating will not be
effective. On the contrary, if the energy of a beam is too high, the beam deposits its energy
on the opposite wall, passing through the plasma with very few interactions.
In current experiments beams capable of penetrating to the center of the plasma can be
produced and their energy is on the order of 100 keV. However, in current experiments the
density and minor radius are both much smaller than those required in a reactor. In a
reactor the beam energies on the order of 1 MeV will be required to effectively heat the
plasma.
Neutral beams can be generated from an initial source of positive or negative ions. Present
experiments mostly generate beams using positive ion sources, since the technology for
producing such sources is less complicated. Efficiency is defined as ratio between beam
power and input power and in the present positive ion technology it rapidly decreases with
increasing beam energy, making this technology useless for future reactors. On the contrary,
according to the theory the overall efficiency using negative ion sources will remain high as
the beam energy increases. [4]
3.1.
Generating neutral beam
A neutral beam source works in in four stages (Fig. 4). In the first stage a source of lowtemperature ions are produced (usually deuterium). In the second, these ions are
accelerated to high-energy by means of a high voltage. A highly directed, nearly monoenergetic beam of high-energy ions exits this stage.
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The third stage is a neutralizer, which is a long tube filled with neutral particles of the same
species as the source ions. In the neutralizer ions undergo charge exchange with the neutral
particles. Positive ions undergo an inelastic collision, where a high-energy positive ion
acquires an electron from low-energy neutral particle. If the high-energy ion is negative, an
inelastic collision strips the excess electron from the atom. The outcome consists of highenergy neutral particles mixed with some of high-energy ions, which escaped the
neutralization, and of low-energy charged particles. The final stage is a magnetic deflector
that separates high-energy ions from neutral particles by magnetic field produced in the
deflector region. Their energy is then collected on the beam dump.
Fig. 4: Schematic diagram of neutral beam system: ion source, acceleration region, neutralizer,
charged particle deflector. [5]
The high-energy neutral beam can be then injected into the plasma perpendicular or parallel
to the plasma axis. The first option is simpler, but particles with a large perpendicular
velocity component are likely to escape the magnetic field. Parallel injection requires more
beam energy because of the longer path and more complicated geometry, therefore an
optimal angle of beam injection is chosen. The overall efficiency of this process can be up to
70 %, meaning that most of the energy used to produce the beam is transferred to the beam
energy. [6]
3.2.
Optimal beam energy
Since too strong absorption leads to heating of the plasma edge and too weak absorption
allows transmission of the beam through the plasma to produce heating and particle
sputtering at material surfaces, the optimal beam energy is required to achieve maximum
deposition of energy in the central region of the plasma.
The optimal beam energy depends primarily on cross sections of various ionization
mechanisms. The mechanisms of ionizing high-energy neutral particles in plasma are charge
exchange, ionization by ions and ionization by electrons.
In charge exchange collisions the neutral particle loses an electron to a plasma ion.
3.1
7
The subscript b in eq. 3.1 refers to high-energy beam particle and p refers to lower-energy
plasma particle. The particles can be deuterium ions/neutrals as well as tritium
ions/neutrals.
Ionization by ions occurs when a high-energy beam particle undergoes a strong collision with
a plasma. The neutral particle splits into a high-energy ion and an electron. Most of the
initial energy is carried by the ion.
3.2
Compared to previous two, the electron ionization has the smallest effect and therefore
does not contribute much to ionization of neutral beam.
(a)
(b)
Fig 5: Cross section for charge exchange
and ionization by ions
depths for a typical JET discharge with plasma density
simple reactor with
(
) (b). [4]
(a) and beam penetration
(
), and a
To determine the penetration depth of the neutral beam, cross sections for ionization
processes need to be known. According to Fig. 5 (a) cross section for the charge exchange
starts to decrease rapidly at 50-100 keV. At high-energies the ionization by ions is the
dominant ionization mechanism and below 90 keV the charge exchange is the dominant one.
Neutral beam flux is defined as
plasma, the neutral beam decays as
. When penetrating and being absorbed into the
3.3
The parameter
represents the plasma density and is in general a function of distance.
However, in the first approximation it is assumed to be constant.
Since the loss of neutral particles means production of the same number of charged
particles, the solution of eq. 3.3 is
(
)
(
)
3.4
8
and the decay length is given by
3.5
The decay length λ and penetration depth are supposed to be of the same order to heat
plasma with most efficiency. In the case of perpendicular heating the beam traverses a
distance of 2a (two minor radius of a tokamak) before leaving the plasma and three decay
lengths are needed to reduce beam losses to an acceptably low level. The equation can
therefore be written as
3.6
and the optimal energy
can be determined from
.
In case of parallel injection the beam must propagate a longer distance and eq. 3.6 is now
written as
3.7
where the parameter depends on plasma geometry.
In Fig.5 (b) the eq. 3.6 is plotted for two different cases. In a reactor plasma with n = 1.5 the
required penetration depth for perpendicular injection is 2 m and 6 m for parallel injection.
The energies needed to achieve this penetration depths are 0.8 MeV and 3 MeV. Those
energies are well beyond the range where positive ions can be used effectively and
therefore negative ion sources must be developed for ITER and future fusion reactors. [4]
3.3.
Negative versus positive ion source
The main difference between efficiency of negative and positive ion sources at high energies
is in the process of neutralization.
In the case of neutralization of positive ion beams two processes need to be considered. A
high-energy positive ion can exchange charge inside of neutralizer, but then it can also reionize again by colliding with a low-energy neutral particle. The number of outcoming highenergy neutral particles is therefore the number of incoming particles that only once
collided with neutrals inside of neutralizer. The reactions are
,
3.8
3.9
where subscript b stands for high-energy particle and n for low-energy particle. The cross
sections for reactions 3.8 and 3.9 are previously mentioned
and . The number of
charged high-energy particles can be determined as combination of both reactions
3.10
9
If
3.11
and if assumed that energy loss of high-energy beam progressing along the neutralizer is
negligible, the results of eq. 3.10 are
3.12
3.13
3.14
The length of the neutralizer is typically much greater than and therefore the exponential
part in eq. 3.13 can be neglected. The fraction of neutralization is defined as
3.15
In case of the negative ion beams, the analysis seems to be very similar. Negative ions can
have their excess electron striped away by colliding with low-energy neutrals. Another
collision can result in re-ionizing high-energy neutral particle. While the second process is
exactly the same as for the positive beams, the cross section for stripping away an electron
is much larger than
for charge exchange because of the weak bonding of the extra
electron. The reactions can be written as
3.16
3.17
The fluxes of high-energy particles can be determined similar as for positive beams
3.18
3.19
In this case, after the second collision a high-energy positive ion is produced. As progressing
along the neutralizer both
and decay towards zero. The optimum length of neutralizer
can be determined corresponding to maximum neutralization. The results of eq. 3.18 and
3.19 are
3.20
3.21
where
and
The neutralization fraction is
10
3.22
and the optimal length of the neutralizer is
( )
3.23
The neutralization fraction at the output of neutralizer is therefore
3.24
Fig. 6: The neutralization fraction as function of energy for positive and negative ion beam. [4]
As seen in Fig. 6, the neutralization factor for positive ion beams decreases rapidly for
energies above 100 keV because of the rapid decrease of the charge exchange cross section.
The optimal neutralization factor remains in order of 60 % at high energies and negative ion
beams are therefore much more appropriate choice for future reactors. [4]
The main reason why the negative ion sources are not in use jet is the production of negative ions.
Relativelly low energy is needed to strip an electron of an atom. However, adding an additional
electron to an atom is much more complicated proces and therefore much more energy is used to
produce negative ions. The efficient method of producing negative is jet to be developed.
CONCLUSION
In an ignited plasma the -particles that are produced in D-T reactions compensate the
energy losses. The fusion reaction rate strongly depends on plasma temperature. Therefore,
plasma must be heated to reach the temperature of ignition. The initial heating in all
tokamaks comes from the ohmic heating, caused by the torodial current.
The ignition temperature cannot be reached only by ohmic heating, since the plasma
resistivity decreases with increasing temperature. Therefore, some other type of external
heating must be used. Neutral beam heating and radiofrequency wave heating are currently
in development for future reactors. They both seem equally promising and they can be used
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at the same time. In case of neutral beam injection, neutral particles injected into a plasma
travel in straight lines, being unaffected by the magnetic field. The atoms become ionized
through collisions with the plasma particles and the resulting high-energy charged particles
are then held by magnetic field. Neutral beams can be generated using positive or negative
ion sources.
High-efficiency positive ion systems have already been developed and are used in present
day research facilities. They are successful in heating experimental tokamaks, but much
higher energies will be needed for future reactors and beams of those energies cannot be
reached with high efficiency by this method.
The high-energy neutral beam produced by technologically more complicated negative ion
source seems to be an effective method to heat the plasma in a future reactor. However, the
procedure is not yet fully developed and the development of this negative-ion-driven neutral
beam source is an important area of fusion technology research.
The first studies of neutral beam heating took place in 1973. Injections were then in order of
tens of keV. Typically plasmas with temperatures of 200 eV were heated to 250 eV. By 1979
beam achieved power in order of megawatt and plasma temperature increased for several
keV. Later on available beam power increased to tens of megawatt and the plasma
temperatures reached tens of keV, which are in the range of reactor relevant temperatures.
In the present additional studies are carried out in JET. [6]
REFERENCES
[1] ITER - plasma heating, http://iter.rma.ac.be/en/physics/plasmaheating/
[2] S. Atzeni, Nuclear fusion reactions, University of Oxford Press, 2004
[3] Euratom, http://ec.europa.eu/research/energy/euratom/index_en.cfm
[4] Friedberg J., Plasma Physics and Fusion Energy, Cambridge university press, New York,
2007
[5] G. McCracken, P. Statt, Fusion The energy of the Universe, Elsevier Academic Press, 2005.
[6] Wesson J., Tokamaks, Clarendon press – Oxford, 2004
[7] EFDA – European Fusion Development Agreement, http://www.efda.org/
[8] Fusion for energy, http://fusionforenergy.europa.eu/understandingfusion/
[9] World nuclear association, http://www.world-nuclear.org/
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