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: