A collisional-radiative (CR) model that extracts the electron temperature, Te, of hydrogen plasmas from Balmer-line-ratio measurements is examined for the plasma electron density, ne, and Te ranges of 1010–1015 cm−3 and 5–500 eV, respectively. The CR code, developed and implemented in Python, has a forward component that computes the densities of excited states up to n = 15 as functions of Te, ne, and the molecular-to-atomic neutral ratio r(H2/H). The backward component provides ne and r(H2/H) as functions of the Balmer ratios to predict the Te. The model assumes Maxwellian electrons. The density profiles of the electrons and of the molecular and atomic hydrogen neutrals are shown to be of great importance, as is the accuracy of the line-ratio measurement method.

1.
I. H.
Hutchinson
, “
Principles of plasma diagnostics
,”
Plasma Phys. Controlled Fusion
44
,
2603
(
2002
).
2.
T.
Fujimoto
,
K.
Sawada
, and
K.
Takahata
, “
Ratio of Balmer line intensities resulting from dissociative excitation of molecular hydrogen in an ionizing plasma
,”
J. Appl. Phys.
66
,
2315
2319
(
1989
).
3.
S.
Iordanova
and
T.
Paunska
, “
A collisional radiative model of hydrogen plasmas developed for diagnostic purposes of negative ion sources
,”
Rev. Sci. Instrum.
87
,
02B110
(
2016
).
4.
M. A.
Lieberman
and
A. J.
Lichtenberg
,
Principles of Plasma Discharges and Materials Processing
(
John Wiley & Sons
,
2005
).
5.
S.
Sasaki
,
S.
Takamura
,
S.
Watanabe
,
S.
Masuzaki
,
T.
Kato
, and
K.
Kadota
, “
Helium I line intensity ratios in a plasma for the diagnostics of fusion edge plasmas
,”
Rev. Sci. Instrum.
67
,
3521
3529
(
1996
).
6.
A.
Bogaerts
,
R.
Gijbels
, and
J.
Vlcek
, “
Collisional-radiative model for an argon glow discharge
,”
J. Appl. Phys.
84
,
121
136
(
1998
).
7.
K.
Verhaegh
,
B.
Lipschultz
,
B. P.
Duval
,
A.
Fil
,
M.
Wensing
,
C.
Bowman
, and
D. S.
Gahle
, “
Novel inferences of ionisation and recombination for particle/power balance during detached discharges using deuterium Balmer line spectroscopy
,”
Plasma Phys. Controlled Fusion
61
,
125018
(
2019
).
8.
R.
Prakash
,
T.
Pütterich
,
R.
Dux
,
A.
Kallenbach
,
R.
Fischer
, and
K.
Behringer
, “
Spectroscopic divertor characterization and impurity influx measurements in ASDEX upgrade tokamak
,” IPP Report No. 10/31,
2006
.
9.
L. C.
Johnson
and
E.
Hinnov
, “
Ionization, recombination, and population of excited levels in hydrogen plasmas
,”
J. Quant. Spectrosc. Radiat. Transfer
13
,
333
358
(
1973
).
10.
D.
Wünderlich
,
S.
Dietrich
, and
U.
Fantz
, “
Application of a collisional radiative model to atomic hydrogen for diagnostic purposes
,”
J. Quant. Spectrosc. Radiat. Transfer
110
,
62
71
(
2009
).
11.
F.
Guzmán
,
M.
O’Mullane
, and
H. P.
Summers
, “
ADAS tools for collisional–radiative modelling of molecules
,”
J. Nucl. Mater.
438
,
S585
S588
(
2013
).
12.
H.
Summers
, The ADAS User Manual, version 2.6, http://www.adas.ac.uk/,
2004
.
13.
S. P.
Vinoth
 et al., “
Electron temperature measurement using spectroscopic measurements of Balmer’s ratio in PFRC-II pulsed hydrogen plasmas using collisional radiative model
,” in
62nd Annual Meeting of the APS Division of Plasma Physics,
2020
, https://meetings.aps.org/Meeting/DPP20/Session/VP13.2.
14.
A.
Dogariu
,
S.
Cohen
,
E.
Evans
,
S.
Vinoth
, and
C.
Swanson
, “
A diagnostic to measure neutral atom density in RF-heated PFRC-2 plasmas
,”
Rev. Sci. Instrum.
(these proceedings) (
2022
).
15.
L. C.
Johnson
, “
Approximations for collisional and radiative transition rates in atomic hydrogen
,”
Astrophys. J.
174
,
227
(
1972
).
16.
L.
Vriens
and
A. H. M.
Smeets
, “
Cross-section and rate formulas for electron-impact ionization, excitation, deexcitation, and total depopulation of excited atoms
,”
Phys. Rev. A
22
,
940
(
1980
).
17.
K.
Sawada
,
K.
Eriguchi
, and
T.
Fujimoto
, “
Hydrogen-atom spectroscopy of the ionizing plasma containing molecular hydrogen: Line intensities and ionization rate
,”
J. Appl. Phys.
73
,
8122
8125
(
1993
).
18.
See https://dataspace.princeton.edu/handle/88435/dsp01x920g025r
for example for the following paper “Electron heating in 2-D: combining Fermi-Ulam acceleration and magnetic-moment non-adiabaticity in a mirror-configuration plasma
the MATLAB codes used in this paper are found on the same website
.
You do not currently have access to this content.