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Fine-Structure Resolved C-R Model for the Diagnostic of hydrogen-cesium
Plasma Relevant to ITER Negative Ion Based NBI Systems Priti1, Dipti2, R K Gangwar3, and R. Srivastava1 1Indian Institute of Technology Roorkee, Roorkee-247667, India
2Atomic Spectroscopy Group, National Institute of Standards and Technology, Gaithersburg, MD 20899-8422, USA 3Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot -7610001, Israel
Introduction
In ITER, the prime requirement to initiate the
nuclear fusion reaction between the two hydrogen
isotopes is the heating of fusion plasma (up to
temperature hundreds of millions degrees
centigrade [1].
To achieve such a high temperature some external
heating systems are required as high performance
neutral beam injection (NBI) systems.
Cs-seeded negative ion source is expected to
fulfill the requirement of ITER project [2].
To characterize the hydrogen-cesium plasma an
accurate numerical population collisional radiative
(CR) model has been developed [3].
The detailed required electron impact cross section
data for various fine-structure excitations are
calculated by using our relativistic distorted wave
(RDW) theory [3].
Results obtained from present CR model for
different plasma parameters are compared with the
theoretical and experimental results of Wünderlich
et al. [4].
RDW Theory
T-matrix for excitation (i → f)
Cross sections and Rate coefficients
The accuracy of cross-section fitting is within 5%.
2002
0 1 2
ni
i
i
b E
ac c E c E
Work is supported by R.S. DAE-BRNS, Mumbai, CSIR and MHRD, New Delhi India.
Conclusions
References
Electron impact excitation cross sections for 82
fine structure transitions have been calculated.
Fitting to the cross section are provided for the
plasma diagnostics.
Since we used complete set of reliable input cross-
section data for the dominant production channel,
the various results obtained from the present CR
model should approach to the real plasma.
1. (https://www.iter.org/).
2. U Fantz, et al., Rev. Sci. Instrum. 2016 87 02B307.
3. Priti, Dipti, R K Gangwar, R Srivastava, J. Quant. Spectrosc. Radiat.
Transf. (2017) 187 426.
4. D Wünderlich, C Wimmer and R Friedl, J. Quant. Spectrosc. Radiat.
Transf. 2014 149 360.
5. P Jonsson, X He, C F Fischer and I P Grant, Comput. Phys.Commun.
2007 177 597.
CR Model for H-Cs Plasma
I. Collisional Processes :
f,
i,
( , , ..., )F ( , ) ( 1)
{ ( , , ..., )F ( , )}
j
i
RDW rel DW
i j j j j
rel DW
i i
T V U N
1 2 N k N 1
1 2 N k N 1A
i i ij je E X eX
Ionization and recombination
Excitation and de-excitation
i iX e E X e e
iX e X h
Mutual neutralization
Cs CsH H
II. Radiative Processes :
ijA
i jX hX
Particle Balance Equation
,
( ( ) )
( )
( ) ( ) 0
ij e i e ij i e e j e j m jHi i
i j i j
ji e j e ji j j e j ei i
i j i j
n n k T A n n kk T n n A n n
k T n n A n n n k T
Multi-configurational Dirac-Fock wave functions
for the target atom have been obtained using
GRASP2K [5] program.
Relativistic distorted wave functions for the
scatted electron is obtained by solving the Dirac
equation numerically.
2Eij
ij ijk E E f E dE
10 100 100010
-24
10-23
10-22
10-21
10-20
10-19
10-18
Cro
ss-s
ect
ion
(m
2)
Energy (eV)
(a)
From 6 2S1/2
0 10 20 30 40 50
10-17
10-16
10-15
10-14
10-13
10-12
62
P1/2 62P3/2
72
P1/2 72
P3/2
82
P1/2 8 2P3/2
Rate
coff
icie
nt (m
3/s
)
Electron temperature (eV)
(b)
10 100 100010
-24
10-23
10-22
10-21
10-20
10-19
Cro
ss-s
ect
ion
(m
2)
Energy (eV)
(a)
From 6 2S1/2
0 10 20 30 40 50
10-17
10-16
10-15
10-14
10-13
52
D3/2 52
D5/2
72
S1/2 62
D3/2
62
D5/2 82
S1/2
72
D3/2 72
D5/2
R
ate
coff
icie
nt (
m3/s
)
Electron temperature (eV)
(b)
From 6 2P solid line j=1/2 dashed line j=3/2
0 10 20 30 40 50
10-16
10-15
10-14
10-13
72P
1/2 7
2P
3/2
72P
1/2 7
2P
3/2
82P
1/2 8
2P
3/2
82P
1/2 8
2P
3/2
Electron temperature (eV)
Ra
te c
offic
ien
t (m
3/s
)
(b)
1 10 100 1000
10-23
10-22
10-21
10-20
10-19
Cro
ss-s
ect
ion
(m
2)
Energy (eV)
(a)
1 10 100 1000
10-22
10-21
10-20
10-19
10-18
10-17
Cro
ss-s
ect
ion
(m
2)
Energy (eV)
(a)
From 6 2P solid line j=1/2 dashed line j=3/2
0 10 20 30 40 50
10-15
10-14
10-13
10-12
52D
3/2 5
2D
5/2
52D
3/2 5
2D
5/2
62D
3/2 6
2D
5/2
62D
3/2 6
2D
5/2
Electron temperature (eV)
R
ate
co
ffic
ien
t (m
3/s
)
(b)
Cross section Fittings
Population density Vs electron temperature and electron density
2 4 6 8 1010
10
1011
1012
1013
1014
ne=10
17 m
-3, n(6
2S)=10
15 m
-3, n(Cs
+)=9*10
15 m
-3, n(H
-)=0
72D
72P
n [m
-3]
Te [eV]
62P
1016
1017
1018
1010
1011
1012
1013
1014
72D
72P
62P
n [m
-3]
ne [m
-3]
Te=2eV, n (6
2S)=10
15 m
-3, n(Cs
+)=9*10
15 m
-3, n(H
-)=0
with bias without bias10
10
1011
1012
1013
72D
72P
Upper LOS (XR1)
n [
m-3]
62P
with bias without bias10
8
109
1010
1011
1012
6 2P
7 2P
n [
m-3]
Lower LOS (XL1)
7 2D
Parameter Measurements [21 and
references there in]
Present calculations Previous calculations
[21]
Te with bias [eV]
Lower (XL1) 2.0 2.0 2.0
Upper (XR1) 2.0 2.0 2.5
Te without bias [eV]
Lower (XL1) 2.1 2.1 2.0
Upper (XR1) 2.1 2.1 2.2
ne [m-3] 2.8x1016-1017 2.6x1016 - 1017 2.8x1016 - 1017
ne, upper/ ne, lower (without bias) 2.1 2.37 2.07
ne, upper/ ne, lower (with bias) 3.6 3.85 3.57
n(62S) [m-3] 6x1014– 7x1014 2x1014–3.2x1015 2.4x1014–4.5x1015
n(62S)upper/ n(62S)lower 1-2 with bias=16
without bias= 4.5
with bias= 18.7
without bias= 6.2
n+/ n(62S) 9 9 9
nH- [m-3] ~1017 1-4x1016 1-3x1016
Effect of Mutual Neutralization
Extracted Parameters from present CR Model
1014
1015
1016
1017
1018
1010
1011
1012
1013
1014
72D
72P
62P
Te=2eV, n
e=10
17 m
-3, n(6
2S)=10
15 m
-3, n(Cs
+)=9*10
15 m
-3
n [m
-3]
n (H-) [m
-3]
Acknowledgement
**For all results of cross sections and rate coefficients see Ref. [3].
*Solid line presents the represent CR model calculations while the dashed lines are the results from CR model calculations of Wünderlich et al. [4].
Rate Coefficient: