Transcript Kein Folientitel

Diagnostics of Fusion Plasmas
Spectroscopy
Ralph Dux
European Joint PhD Programme, Lisboa, 10.2.2009
The Methods
Passive Spectroscopy (line averaged)
• X-ray, soft X-ray  impurity species , impurity densities,
ion temperature, velocity
• Visible (VUV)  impurity species, impurity influx, hydrogen influx,
electron density
Active Spectroscopy (spatially resolved)
• Charge exchange recombination spectroscopy
 ion temperature,
velocity (radial electric field),
impurity density of fully ionized species
• Motional Stark Effect Polarimetry
 direction of magnetic field
Important reactions for ionisation and excitation balance
Z
A e


 electronimpact ionisation
 photo ionisation

 electronimpact excitation
A

h
 

Z
 photon absorption
A 
e'
e' '

  
 three body recombination
Z
A

h
 

Z
A
e
 Z 1
 Z 1
A
e


 radiative recombination
Z*
A

e'


 electronimpact de -excitation
Z*
A

 spontaneous photon emission
Z
Z
A

h


e

A

e'

 



 photon absorption
 bremsstrahlung
Reaction rates: product of densities x rate coefficient (atomic physics)
Contributions to the plasma radiation
Energy levels of atoms, ions and molecules (dimers)
Energy levels of atoms, ions and molecules (dimers)
Radiative transitions between bound states
Radiative transitions between bound states
Interference on gratings and crystals
Types of spectrometers for different wavelength ranges
Density of emitting ions from spectroscopy
Density of emitting ions from spectroscopy
Corona ionisation balance
In fusion plasmas (and in the solar corona): low electron density
three body recombination rate (ne2) << radiative recombination rate (ne)
Balance of:
electron impact ionisation = radiative recombination
nZ ne SZ ,Z 1 (Te )

ne nZ 1 Z 1,Z (Te )
nZ 1 S Z ,Z 1 (Te )

nZ
 Z 1,Z (Te )
ionisation degree is independent of electron density
• charge state of ion increases with electron temperature
• low-Z impurities are fully ionized in large part of the plasma
( no line emission from light elements)
• medium to high-Z impurities can be dedected
• hydrogen like ions: Eion=13.6eV Z2
Corona ionisation balance
Argon
ions with filled electron shells
are most stable
(He-like, Ne-like …)
He- and H-like ionsation
stages of Ar still present
up to the plasma center
Corona ionisation balance
Tungsten
fractional abundance
1.0
ionisation stages of tungsten
28+
27+
37+ 46+
38+
43+
35+
45+
44+
55+
56+ 61+
64+
63+
62+
0.1
0.01
modified CADW+408
0.001
1000
Te [keV]
10000
Th. Pütterich
Ph.D. thesis
2005
Impurity density determination
X-ray spectroscopy
Impurity density determination
X-ray spectrum of tungsten
spectral radiance [10 5 W m-2 sr -1nm -1]
#16778
Te,cntr = 3.9 keV
1.5
74W
- measurement
This line from W46+ is used
for density evaluation at AUGD.
n=1
n=2
0
ADAS
modelled spectrum
38+
49+
W
W
1.5
0
HULLAC
modelled spectrum
38+
49+
W
W
1.5
0
0.4
0.5
0.6
Th. Pütterich, PhD thesis 2005
0.7
 [nm]
0.8
Impurity density determination
tungsten concentrations
Impurity influx measurements
Visible Spectroscopy
Neutral impurity atoms
(or low ion stages) radiate
sufficiently strong visible
line emission.
 Can be used to determine
the erosion rates at the
plasma walls (impurity influx)
Impurity influx measurements
Visible Spectroscopy
1dim continuity equation for neutrals
(small recombination rates = ionising plasma)
n0

  x  S01ne n0  10 ne n1

 


t
x 
ionisation
recombination0
temporal equilibrium: n0  0
Integrate up to l, where all neutrals are ionised:
x
l
x
l
0 x dx  x (0)  0 S01ne n0 dx
The photons emitted on transition ik per area and time:
l
l
l
l
X 1i n0
ph
ph
ik  4   ik dx   Aik ne n0,i dx   Aik ne
dx   ne Bik X 1i n0 dx
0
0
0
0
A
 in
l
x0
0
n i
Excitation rate and ionisation rate shall have similar temperature dependence
(excitation energy  ionisation energy) around x0 where the excitation and ionisation
mainly occurs:
 S T ( x)n n dx
l
x (0)  
ph
ik
0

l
0
01
e
e 0
X 1i Te ( x) Bik ne n0 dx
S01 Te ( x0 )  f x ne n0 dx
l

ph
ik
0
X 1i Te ( x0 ) Bik  f x ne n0 dx
l
0
 ikph
S01 Te ( x0 ) 
X 1i Te ( x0 ) Bik
Impurity influx measurements
Visible Spectroscopy
x (0)  
ph
ik

L
0

L
0
S 01ne n0 dx
X 1i Bik ne n0 dx
 ikph
S
XB
S/XB-value:
• number of ionisations per emitted photon
• gives impurity influx from photon flux
•  independent of ne
S/XB of W I 400.875 nm
5d5(6S) 6s - 5d5(6S) 6p 7S – 7P°
S/XB
100
10
1
A. Geier et al., Rev. Sci. Instr. (1999)
A. Geier et al., Plasma Phys. Control. Fusion (2002)
Steinbrink et al., 24th EPS 1997
calculations: I Beigman et al., Plasma Phys. Control.
Fusion (2007)
Tw= 0.3 eV
Tw= 1 eV
0.1
5
10
15
20
25
30
Te / eV
Impurity influx measurements
Influx of tungsten from the divertor strike point tiles
Strongest W-erosion in
the divertor (modulation
due to ELMs)
Beyond impurity densities and fluxes
spectroscopy can also deliver information about
• temperatures
• electron density
• B-field
from the line shape or the splitting of spectral lines
Natural line width
Oscillation with decay time 
1


1
m

1
1
n
m
  Amk
k m
Emn  Em  En 
1
n
  Ank
k n
h 

  Amk   Ank 
2  k  m
k n

Spectral emission coefficient:
   mn
 FWHM
1

  mn 
h  FWHM  Emn
2
2

  FWHM 
2

2
Doppler shift and Doppler broadening
 measurement of ion temperature
and drift velocity
Active Spectroscopy on Hydrogen Beam
Charge Exchange Recombination Spectroscopy
Active Spectroscopy on Hydrogen Beam
Charge Exchange Recombination Spectroscopy
Stark broadening (Hydrogen)
Linear Stark Effect
In Hydrogen the electric field leads
to a line splitting linear with the field
strength ( linear Stark effect)
E  nkE0
E0 
k  0,  1, ...., n  1
3
Fea0
2
In the edge plasma
Linear Stark broadening due
to time varying microfields
from electrons and ions can
dominate Doppler broadening
 measurement of ne
Line splitting of the Balmer lines of Hydrogen
(Balmer= transitions between states with
principal quantum number n=3,4,5,6,7  2)
Stark broadening (Hydrogen)
Linear Stark Effect
In Hydrogen the electric field leads
to a line splitting linear with the field
strength ( linear Stark effect)
E  nkE0
E0 
k  0,  1, ...., n  1
3
Fea0
2
In the edge plasma
Linear Stark broadening due
to time varying microfields
from electrons and ions can
dominate Doppler broadening
 measurement of ne
Profile of Balmer- lines of Deuterium
(n=7 2) measured in the ASDEX
Upgrade divertor
Active Spectroscopy on Hydrogen Beam
Motional Stark effect polarimetry
Observe D spectrum of D0 beam
• wavelength shifted due to Doppler effect
• electric field in reference frame of D-atoms
due to movement in magnetic field
 

F  vbeam  B
leads to splitting of energy levels via the linear
Stark effect:
E  nkE0
E0 
k  0,  1, ...., n  1
3
Fea0
2
60kV D0 beam, B=2T:
F  4.8 106 Vm -1 E0  3.8 104 eV
Polarization
-components (m=0): parallel to el. field
-components (m=±1): perpendicular to el. field
D0 (60keV)
Lines-of-sight
Active Spectroscopy on Hydrogen Beam
Motional Stark effect polarimetry
Observe D spectrum of D0 beam
• Wavelength shifted due to Doppler effect
• electric field in reference frame of D-atoms
due to movement in magnetic field
 

F  vbeam  B
leads to splitting of energy levels via the linear
Stark effect:
E  nkE0
E0 
k  0,  1, ...., n  1
3
Fea0
2
60kV D0 beam, B=2T:
F  4.8 106 Vm -1 E0  3.8 104 eV
Polarization
-components (m=0): parallel to el. field
-components (m=±1): perpendicular to el. field
D0 (60keV)
Lines-of-sight
Active Spectroscopy on Hydrogen Beam
Motional Stark effect polarimetry
Observe D spectrum of D0 beam
• Wavelength shifted due to Doppler effect
• electric field in reference frame of D-atoms
due to movement in magn. field
 

F  vbeam  B
leads to splitting of energy levels via the linear
Stark effect:
E  nkE0
E0 
k  0,  1, ...., n  1
3
Fea0
2
60kV D0 beam, B=2T:
F  4.8 106 Vm -1 E0  3.8 104 eV
Polarization
-components (m=0): parallel to el. field
-components (m=±1): perpendicular to el. field
Active Spectroscopy on Hydrogen Beam
Motional Stark effect polarimetry
• unshifted -component is selected
with very narrow interference filter
(just works for one beam voltage)
• polarization direction of light is determined
(accuracy  1/10 degree)
Additional radial electric field changes
polarization direction:
 
 e
F  vbeam  B 
Ψ
Ψ
 measurement of 2 beam energy
components is used to separate
both contributions
Line splitting in the magnetic field
Zeeman Effect
  
H  H0  μB (L  2S).B
Level splitting:
• Zeeman case:
angular momentum
of orbit and spin remain
coupled in ext. B-field
ELSJm J  
e
mJ g J B
2me
J J  1  S S  1  LL  1
gJ  1
2 J J  1
 measurement of B? No!
but can be used to get the
main emission region on the LOS
Line splitting in the magnetic field
Zeeman Effect
  
H  H0  μB (L  2S).B
Level splitting:
• Zeeman case:
angular momentum
of orbit and spin remain
coupled in ext. B-field
ELSJm J  
gJ  1
e
mJ g J B
2me
J J  1  S S  1  LL  1
2 J J  1
 measurement of B? No!
but can be used to get the
main emission region on the LOS
B-field splitting for CII
here more emission from HFS
Line splitting in the magnetic field
Zeeman Effect
  
H  H0  μB (L  2S).B
Level splitting:
• Zeeman case:
angular momentum
of orbit and spin remain
coupled in ext. B-field
ELSJm J  
gJ  1
e
mJ g J B
2me
J J  1  S S  1  LL  1
2 J J  1
 measurement of B? No!
but can be used to get the
main emission region on the LOS
B-field splitting for CII
here more emission from LFS
Line splitting in the magnetic field
Zeeman Effect
  
H  H0  μB (L  2S).B
Level splitting:
• Zeeman case:
angular momentum
of orbit and spin remain
coupled in ext. B-field
ELSJm J  
e
mJ g J B
2me
J J  1  S S  1  LL  1
gJ  1
2 J J  1
 measurement of B? No!
but can be used to get the
main emission region on the LOS
B-field splitting for Balmer- of D
dominated by LFS