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A Brief tutorial to
Thomson Scattering
With a focus on LIDAR
By Mark Kempenaars
For the EFTS/EODI training, 12th June 2009 at Culham Science centre
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Outline of Talk
1. Introduction
2. Thomson scattering theory – the highlights
3. Conventional TS
4. LIDAR TS
5. Towards ITER
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Introduction
 Thomson scattering was first described in
1903 by J.J. Thomson, many years before
lasers existed. Thomson discovered electrons
in 1897.
 First application to a laboratory plasma in
1963 by Fünfer (First ruby laser in 1960)
 First measurements in hot plasmas by
Peacock et al., in 1969 at the Russian T3
Tokamak
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Thomson scattering theory
Thomson scattering is nothing more than the interaction of
EM radiation with an electron any light will do. We can use
Maxwell’s equations (1873) to describe the forces on and
movements of the electrons. The highlights…
Let’s consider this
experimental setup:
dW
Incident EM wave with
amplitude E0, propagation
vector k0, and angular
frequency w0, so electric
field at the electron is
given by:
E  E0 cos k0  rj  w0t

Scattering
Electron
E0

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ks
k
j
R
q
k0
rj
Origin
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Theory cont’d - 1
This electric field will then apply a force
dW
on the electron (with mass m and charge e
at position rj) and following Maxwell’s
k
k R
E
j
equations, we get the acceleration of the
q
k
r
electron:
e
rj  E0 cosk0  rj  w0t 
m
This equation clearly shows us that the electron will be
oscillating up and down, together with the electric field of the
light wave.
Scattering
Electron
s
0
0
j
Origin
Since this electron is now a moving charged particle it will
create an EM field of its own, with the same wavelength as the
incoming light!
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Theory cont’d - 2
When a moving electron like this is
observed from a large distance (R>>l) its
radiation can be described as dipole
radiation:
r02 E0 sin j
E s  R, t  
cosk  rj  w0t 
R
This equation shows us that the radiation
from ions is negligible compared to that
of electrons, since r0 ~ 1/m:
dW
2
 me 
   2.966 10 7
 mi 
Where k is the differential vector (ks-k0).
and r0 is the classical electron radius:
r0 
e
2
40 mc2
Scattering
Electron
E0
ks
k
j
q
rj
k0
Origin
 2.82 1015 m
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R
Theory cont’d - 3
In this lay-out dW is the solid collection angle, it basically
describes the fraction of scattered radiation we collect. If we then
divide the total scattered power by this solid collection angle we
get the differential scattering cross section:
dW
c 0 ES R
d T
2
2


r
sin
j
0
2
1
dW
2 c 0 E0
1
2
2
Scattering
Electron
2
E0
ks
k
j
R
q
rj
k0
Which tells us that the re-radiation is
maximum perpendicular to E0; dT/dW=r02.
30
2
8

10
m
And that the scattering cross section is very small
Origin
This makes it clear that every photon is important! And we want
as big a window as possible.
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Theory cont’d - 4
Obviously the scattered power depends on the number of
electrons caught by the laser, but also on the interaction between
them. This interaction start to happen above the Debye length.
So this depends on the density and
3 Te
lD  7.4 10
temperature of the electrons
ne
For Te = 10 keV, ne = 5×1019 m-3: lD ~ 100 mm (typical for JET)
The so-called Salpeter-parameter tells us whether the scattering we are
l0
observing is coherent or not:
a  klD 1 
4lD sin
q
2
If a << 1 : then the scattering is from individual electron: Incoherent TS
If a ≥ 1
: then scattering by electrons surrounding ions;
(Ion) Coherent Thomson Scattering
If a ~ 5-20 : Scattering by electron density fluctuations, or Bragg-scattering
Coherent Thomson scattering
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Theory cont’d - 5
The total scattered power is given by:
With P0
:
ne
:
L
:
S(k,w) :
d T
Ps  P0
ne LWS k , w sin 2 j
dW
Incident (laser) power
Electron density in the plasma
Length of scattering volume
Scattering form factor
describes frequency shifts from electron motion as
well as correlation between electrons.
The scattered light is clearly proportional
to the density.


The form function is given by: S k , w    f vk  w0  wS v dvk
where f(n) is the velocity distribution 
In this equation the delta function tells you about the Doppler
shift: wS v   w0  k  v
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Theory cont’d - 6
If the velocity distribution f(v) is Maxwellian (i.e. low
density, no interaction between particles) then:
  vk  2 
f vk  
exp    
a 
  a  
1
with ‘a’ the thermal velocity: a  2k BT2
me
One then finally finds an equation that contains wavelengths:
  lS  l0  2 
S lS  
exp  
 
l 
  l  
1
With l0 the incident wavelength and ls the scattered wavelength
Where we then find the spectral width of the scattered light,
which has a Gaussian shape:
a
q 2l0
q 2k BTe
l  2l0
c
sin
2

c
sin
2
me
If we were to take a Ruby laser (694.3nm) and 90º scattering
then this would give: l nm  1.94 Te eV 
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Theory cont’d - 6
Once the electrons get really hot (i.e. really fast) we have to start
including relativistic effects, which effectively change the
scattering cross section of the electrons, by a factor 1/g 2 where g
c
is the Lorentz factor g 
, which shows that for a 1%
2
2
c a
deviation we need an electron temperature of 2.56 keV.
Also there is a “search light” effect or relativistic aberration,
which means that the electrons radiate preferentially in their
forward direction. E.g. moving at 10% of c, then power in
forward direction increases by 36%, it decreases by 26% in
backwards direction. This leads to a blue shift of the spectrum…
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TS spectra
So, what does this look like?
7
Scattered Spectra
Spectral Intensity
6
Selden-Matoba, q=180o
5
0.5keV
5keV
10keV
20keV
40keV
4
3
2
1
0
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Normalised Wavelength
l/llaser
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TS Spectrometer
What does a spectrometer look like?
If we cut our scattered light “broadband” light into sections:
Incoming
collected light
4
3
2
Spectral Intensity
1
3
4
3
2
1
2
1
0
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Normalised Wavelength
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1.6
1.8
2
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So, what do we need?
 A powerful pulsed laser
– Typically one would get 1 photon in every 1×1014 back,
e.g. if we use a 3GW laser pulse we get 30 mW back on a
high density plasma (1020m-3) and 100% transmission.
 Fire this laser into the plasma
– A window on the machine that can stand the high laser
power and does not get dirty
– plus the optics to deliver it there.
 Collect as much light as possible
– A large window is needed that can see the laser line
– This window can’t get dirty, or if it does we must be able
to clean it.
– The other optics need to be aligned and stable (also during
disruptions etc.)
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90º TS - Single point
In the early days of TS on Fusion devices all TS systems were
“single point” diagnostics, i.e. the optics were only looking at
one point. This seems archaic but it was still one of the better
and more reliable diagnostics.
Laser
This was also the case on JET,
where a ruby laser was fired
vertically into the plasma. A
large set of windows and
mirrors was used to relay the
light to a spectrometer.
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Plasma
Collection
optics
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90º TS - Multi point
More modern systems have a range of points. Where each
spatial point is imaged onto an optical fibre.
Each fibre then represents a spatial point in
the plasma, a high spatial resolution can be
achieved by using a lot of fibres. Keep in
mind however that a smaller volume will
scatter fewer photons.
Laser
Plasma
And this setup means one
needs a spectrometer for each
spatial position, so can get
very expensive
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Collection
optics
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90º TS on JET – HRTS
A new system was installed on JET in
2004. High Resolution Thomson
20 m
Scattering.
20 + 10 m (50 ns)
+ 20 m(5J,
(100 ns)
- High 20
power
15ns) Nd:YAG
laser.
Fiber bundle into each polychromator
- Fire at 20Hz, horizontally
- Scattered light is then collected from
a window at the top of the machine.
In order to collect as many photons as
possible we need a big
window, largest
Signal reconstruction with 50 ns delay
on JET 20cm diameter.
63 spatial points on the LFS, at
approximately 1.5cm resolution
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ns
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90º TS on JET – HRTS cont’d 1
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MAST 90º TS
A set of lasers can be fired in
sequence or in a burst, giving a
high temporal resolution ~1ms
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LIDAR – 180º TS
Now we go to q = 180º, or back scattering
Light detection and ranging, we fire a laser pulse and count the
elapsed time before we get a signal back, like in radar.
Plasma
Of course we have to count very
quickly, since light travels at
~3×106 m/s (or 1m every 3ns)
Major advantages: ‘Point and
shoot’ method, which requires
minimum access
Mirror
labyrinth
Very short laser pulse ~250ps
Only one spectrometer needed,
but it has to be fast!
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LIDAR – 2
The main advantages of LIDAR:
 The alignment is relatively easy
 Only one spectrometer
Because of the previous two, much easier to calibrate and
maintain
The main disadvantage of LIDAR:
 Time is of the essence!
If anything is slow it will contribute to the spatial resolution.
HOWEVER! Time is on our side:
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LIDAR – 3
Laser
Pulse
Plasma,
Length L
Scattered
Light
Scattered
Light
Note that the profile length in time is dt=2L/c.
Effectively 15cm/ns! Instead of normal 30cm/ns
Detector and laser response defines spatial resolution
7cm (ITER requirement) is equivalent to ~460ps combined laser
and detector response time (so det/laser response ~300ps FWHM)
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LIDAR on JET - 1
JET is the only fusion machine in the world that has LIDAR.
LIDAR only really works on big machines due to its limitations
in spatial resolution.
Two LIDAR systems on JET, the Core LIDAR and the Edge
LIDAR. The edge LIDAR has recently been upgraded with new
detectors and digitiser, so it has better resolution.
Core LIDAR
Edge LIDAR
Laser pulse length
~ 300ps
~ 300ps
Laser power
3J/pulse = 10GW
1J/pulse = 3GW
Detector response
~ 300ps
~ 650ps
Digitiser response
8GHz, 20GSa/s
1GHz, 4GSa/s
Spatial resolution
~ 6.5cm
~ 12cm
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LIDAR on JET - 2
The total distance the laser
beam has to travel is about
50m, important to keep the
beam “nice”.
Light is collected through a
set of 6 windows
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LIDAR on JET - 3
Collected light is relayed via a set of mirrors and lenses to the
spectrometer. The Core LIDAR spectrometer has 6 detectors in a
3D layout.
Each detector generates its own trace, these are then combined to
form a temperature and density profile
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NEXT: ITER LIDAR
Core LIDAR (C.01 group 1b – advanced plasma control)
Target
requirements
35
Te 0.5 – 40 keV (10%)
ne 3x1019-3x1020m-3(5%)
r/a < 0.9
10 ms
~7см (a/30) (100 Hz)
Scenario 5n
Te-keV
ne x10^19/m3
Approx sample width
30
25
Short line indicates the required
measurement resolution of a/30.
This is equivalent to
approximately 7cm in real space.
20
15
Note: the full profile from -0.9r/a
to 0.9r/a is required
10
5
~2m
0
0
0.2
0.8
1.2
Thomson
Scattering0.4
Tutorial 0.6
for EFTS/EODI,
12th1 June 2009,
Normalised
Radius
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ITER LIDAR - 1
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ITER LIDAR - 6
Low impact diagnostic access required
In vacuum mirror protection (passive/active)
Detectors (sensitivity, response time, wavelength)
Materials (neutrons/radiation)--fit purpose
Long term, low maintenance reliability
Laser development
~2m
Beam dump
Lasers
Mirrors
Large mirrors
collect
suitable
amount of
light
Exposed to
plasma
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enter machine
Mirrors
boundary
Access to
anywhere inside
this area is similar
to accessing a
satellite-very
infrequent
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ITER LIDAR - 2
Need to have radiation
below 100uS/Hr
ITER
Port Plug
F/18
F/12
14 days after a
shutdown in area behind
plug
Bio Shield
F/6
First Laser Mirror (ML1)
(Vacuum connections
not shown)
M1
Detector ø18mm
M2
Schematic straight through
optical path shown for clarity
Vacuum window ø110mm
4.2m
6.2m
8.2m
11.2m
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ITER LIDAR - 3
From Attila code
 Influence of optical labyrinth
 Minimising activation of
components just outside the
tokamak will be key to easier
maintenance in the future
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ITER LIDAR - 4
7
0.5keV
5keV
10keV
20keV
40keV
Spectral Intensity
6
5
4
Scattered Spectra
q=180o
Several
options, but
none good
enough yet.
GaAsP
GaAs
NIR
S-20
3
2
1
0
0
0.2
0.4
0.6
0.8
1
1.2
Wavelength(microns)
Photocathode
Response time, ns
Wavelength coverage
S-20
0.2 ns(below)
UV, visible up to 500 nm
GaAsP
0.3 ns (as above)
visible up to 750 nm
GaAs
0.35ns (estimated)
visible up to 850 nm
InGaAs
?
NIR
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ITER LIDAR - 5
 Needs reasonable energy and short pulse simultaneously
 Options to chose from:
– Nd:YAG (1064nm)
– Ruby (694nm)
– Ti:Sapphire (~800nm)
– Nd:YLF (1056nm)
Wide temperature range
Time repetition expected from laser(s) – 100Hz
Also need to consider
– Space envelope/ Maintainability/ Power consumption/ Data
quality
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ITER LIDAR - 6
 Laser specifications
wavelength~ ~1.06microns (1ω +2ω +cal )
laser energy ~5J/pulse
laser pulse ~250-300ps (20GW)
 Proposing 7 lasers at ~15Hz
More achievable technology
Compact footprint
Measurement capability maintained even if 1,2,3... lasers
malfunction
Burst mode available to exploit plasma physics e.g. very
fast MHD events
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Epilogue
At the end…
 This tutorial is intended as a first introduction in
to Thomson scattering and not as an exhaustive
review
 Only some typical examples were given (mostly
JET), every fusion machine has TS
 I’ve only focused on incoherent TS
 The aim was mainly on demonstrating how it
works and how powerful a technique it can be
Thank you for your attention
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Any extras… ?
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Space time domain
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