J. Plasma Fusion Res. SERIES, Vol.7 (2006) 118-122

Behavior of Atomic and Molecular Hydrogen by Using the Measurementsof Hα Line Emission in the GAMMA 10 Tandem Mirror
KUBOTA Yuusuke, YOSHIKAWA Masayuki, NAKASHIMA Yousuke, SAWADA Keiji1 , KOBAYASHI Takayuki,SAITO Masashi, HIGASHIZONO Yuta, ITAKURA Akiyosi and CHO Teruji
Plasma Research Center, University of Tsukuba, Tsukuba 305-8577, Japan
1 Faculty of Engineering, Shinshu University, Nagano 380-8553, Japan（Received: 4 October 2004 / Accepted: 24 May 2005）

Abstract
The eﬀective rate coeﬃcients for atomic and molecular hydrogen are calculated based on collisionalradiative model and the rate coeﬃcients of several atomic and molecular processes. The results indicate thatthe eﬀect of atomic hydrogen is dominant for Hα line emission and the eﬀect of molecular hydrogen for
the ionization rate is larger than that of atomic hydrogen at the parameter range of the GAMMA 10 centralcell. Moreover the atomic and molecular hydrogen densities are estimated by H α line emission. From theevaluation of the ionization rate by using the estimated neutral hydrogen densities, it is necessary to consider
the behavior of molecular hydrogen for analysis of the particle balance in GAMMA 10.
Keywords:
neutral hydrogen, ionization rate, Hα line emission, particle balance, GAMMA 101．Introduction
In magnetically confined plasmas, a neutral hydrogen behavior is an important subject to clarify the particle balance. Measurements of Hα line emission fromthe plasmas are also important to evaluate particle andenergy confinement. In the GAMMA 10 tandem mirror, the ionization rate is estimated experimentally by
the measurements of an electron density and Hα lineemission. The ionization rate and Hα line emission depend on the atomic hydrogen and molecular hydrogen.
However it is diﬃcult to separate the contributions fromthe atomic hydrogen and the molecular hydrogen on
the measurement of Hα line emission. Then we calculated an eﬀective rate coeﬃcient of atomic and molecular hydrogen for Hα line emission by using collisionalradiative model (CR-model) [1] and evaluated an ionization rate based on the rate coeﬃcients of several
atomic and molecular processes. From these calculation results and the measurements of Hα line emission,
atomic and molecular hydrogen densities and the ionization rate in the mid-plane of the GAMMA 10 central cell are estimated. In this article, we show the calculation results of the eﬀects of atomic and molecularhydrogen and discuss the particle balance near the midplane of the central cell.

Fig. 1 The schematic view of the GAMMA 10 tandem
mirror.

confinement device with a thermal barrier. It consistsof a 5.6 m long axisymmetric central cell, two anchor
cells for suppressing magnetohydorodynamic (MHD)
instabilities which are located in both ends of the centralcell. Two plug/barrier cells are connected to the anchor
cells for forming the plug and thermal barrier potentials.
Figure 1 shows the schematic view of the GAMMA 10tandem mirror. In the GAMMA 10 plasma, the confinement is achieved by not only a magnetic mirror configuration but also high potentials at the both plug/barriercells. The potentials are produced by means of theelectron cyclotron resonance heating (ECRH) at theplug/barrier cells. The main plasma is produced andheated by the ion cyclotron range of frequency (ICRF)
waves. In plasmas produced in the core region of the2．Experimental apparatuses
GAMMA 10 is a 27 m long tandem mirror plasma

C 2006 by The Japan Society of Plasma

Science and Nuclear Fusion Research

Corresponding author’s e-mail: kubotay@prc.tsukuba.ac.jp118

Behavior of Atomic and Molecular Hydrogen by Using the Measurements of Hα Line Emission in the GAMMA 10 Tandem Mirror

central cell, typical electron density, electron temperature and ion temperature are about 2 × 1012 cm−3 , 100
eV and 5 keV, respectively.
The line-integrated electron density of the plasma ismeasured with the microwave interferometer. The interferometer mounted on the mid-plane of the central cell
can be scanned along the Y-axis of GAMMA 10. The
radial profile of electron density is obtained by using
the Abel inversion.
Hα line emissions are measured with detectors which
consist of Hα interference filters, focusing lenses, apertures, optical fibers and photomultiplier tubes (PMTs).
Near the mid-plane of the central cell, vertical and horizontal arrays of Hα detectors are installed to measure
the spatial profiles of Hα brightness [2,3]. Each array has 12 channel detectors. The output signals fromthe PMTs are amplified and led to a CAMAC system.
This system is absolutely calibrated by a standard lamp.
From the measurement results of these arrays, the spatial profile of Hα emissivity is obtained by using Algebraic Reconstruction Technique (ART) [4].

Fig. 2 The calculation results of R1 (3) and R2 (3) by using CR-model.
3.2 Effective rate coefficients for the ionization rate

The ionization rate is determined by atom-electron,atom-ion, molecule-electron and molecule-ion collisions. These collisions include several reactions, which
are ionization, ionization of molecule, dissociation, etc.
[5,6]. Considered processes are shown below.
e + H → e + H+ + e(3.a)

p + H → p + H+ + e(3.b)

e + H2 → e + H + H+ + e(3.c)

e + H 2 → e + H2 + + e(3.d)

p + H 2 → p + H2 + + e(3.e)

p + H2 → H + H2 +(3.f)

e + H+2 → H + H(3.g)

e + H+2 → e + H+ + H(3.h)

e + H+2 → e + H+ + H+ + e(3.i)(2)

e + H+2 → e + H+ + H∗

(3.j)

where ne , nH , nH2 , R1 (3), R2 (3) are the electron density,
the atomic hydrogen density, the molecular hydrogendensity, the eﬀective rate coeﬃcient of atomic hydrogen, the eﬀective rate coeﬃcient of molecular hydrogen, respectively. R1 (3) and R2 (3) can be obtained byusing CR-model. R1 (3) and R2 (3) indicate the eﬀectof atomic and molecular hydrogen for Hα emissivity.
The calculation results of R1 (3) and R2 (3) are shown inFig. 2. In Fig. 2, it is found that R2 (3) that originates
a dissociative-excitation is about one tenth on the R 1 (3)at the plasma parameter of the GAMMA 10 central cell.
In the central cell, electron density and electron temperature are 3 × 1012 cm−3 (core region) −5 × 1011 cm−3
(peripheral region), 100 eV (core) −20 eV (peripheral)in this case without ECRH, respectively. For Hα lineemission, the eﬀect of atomic hydrogen is dominant tothat of molecular hydrogen.

p + H 2 + → p + H+ + H(3.k)

3．Calculation results
3.1 Effective rate coefficient for Hα line emission

Hα emissivity is shown as below.
E(Hα ) =Ha A32n(3),4π(1)where A32 , Hα , n(3) are the transition probability of Hα ,the energy of Hα line emission and the population density of n = 3 of hydrogen atoms, respectively. Moreovern(3) is shown asn(3) = ne nH R1 (3) + ne nH2 R2 (3),The ionization rate equation is shown as follows,s = ne nH σveH + ni nH σvHp+ ne nH2 σveH2 + ni nH2 σvHp 2= ne nH [σveH + σvHp ] + ne nH2 [σveH2 + σvHp 2 ]H2H+ ne nH2 σvtotal,= ne nH σvtotal(4)

where the subscript e and p represent electron and proton, respectively. The eﬀective rate coeﬃcients in Eq. 4
can be rewritten as follows by using the rate coeﬃcientsof the reactions 3.a-3.k [5].
σveH = σv3.aσvHp = σv3.bσveH2 = σv3.c + ησv3.d119

Behavior of Atomic and Molecular Hydrogen by Using the Measurements of Hα Line Emission in the GAMMA 10 Tandem Mirror

Temporal behavior of line-integrated electron density and the diamagnetism (a), the radial profiles of electron density and ion temperature (b) and the profile ofHα emissivity (c) at 125 ms are shown in Fig. 4. The
typical electron temperature profile [7] is used for calculation. The plasma of this experiment is ICRF-heatedplasma with ECRH (130 ms to 180 ms). The plasma isheated only ICRF-heating at the analyzed time of 125
ms.
4.1 Estimation of the radial profiles of atomic andmolecular hydrogenFig. 3 The effective rate coefﬁcients for the ionization.
ex. e-H : electron - atomic hydrogen collision.

As the preparation for the estimation of the radialmax
profiles, nmax
H and nH2 are defined as below,
nH max ≡σvHp 2 = η(σv)3.e + σv3. f )η=σv3.h + 2σv3.i + σv3. j + σv3.kσv3.g + σv3.h + σv3.i + σv3. j + σv3.k(5)E(Hα ),
αne R1 (3)nH2 max ≡E(Hα )αne R2 (3)Hα A32(6)4πThe nH max and nH2 max indicate maximum density ofatomic and molecular hydrogen obtained by the Hαemissivity. From eq. 1, eq. 2 and eq. 6, the relationshipbetween nH , nH2 and nH2 max is expressed as
α=The calculation results of rate coeﬃcients are shown inFig. 3. In figure, it is found that the eﬀect of molecularhydrogen for the ionization rate is several times larger
than that of atomic hydrogen at the parameter range ofthe central cell. The ion temperature is 6 keV (core) −500 eV (peripheral) in the central cell. In particular,
the contribution from molecular hydrogen for ionization
rate is dominant in the peripheral region, because bothdensity and rate coeﬃcient of molecular hydrogen arelarger than those of atomic hydrogen.

nH2 max =R1 (3)n H + n H2 .
R2 (3)(7)

Because the radial profile of n H is flat compared withthat of nH2 [8] and the profile of R1 (3)/R2 (3) is also flat,
it is supposed that the profile shape of n H2 max is determined by that of nH2 . Assuming that no molecular hydrogen exist in the center of the plasma, n H (r = 0) is
equal to nH max (r = 0). Then nH max (r = 0) is substituted
for nH in eq. 7, nH2 is shown asR1 (3)maxmax(r)nH (r = 0) , (8)nH2 (r) = C nH2 (r) −R2 (3)4．Experimental results and discussion

where C is a constant to evaluate the absolute value ofFig. 4 Temporal behavior of line-integrated electron density and the diamagnetism (a), the radial proﬁles ofelectron density and ion temperature (b) and theproﬁle of Hα emissivity (c) at 125 ms.

Fig. 5 The radial proﬁles of atomic and molecular hydrogen estimated by the new method and those obtained by DEGAS code.
120Behavior of Atomic and Molecular Hydrogen by Using the Measurements of Hα Line Emission in the GAMMA 10 Tandem Mirror

nH2 . It is assumed to determine the C that all neutralhydrogen is molecular hydrogen in the boundary of theplasma (r = 20 cm). However, there is no data at r = 20cm. Then assuming again that n H2 (r = 10 cm) is equal
to the half of nH2 max (r = 10 cm), C is determined asC=0.5nH2 max (r = 10)
max (r = 0)
nH2 max (r = 10) − RR12 (3)(3) (r = 10)nH(9)Therefore nH2 (r) is obtained. nH (r) is also obtained
from eq. 7 as below,
nH (r) =R2 (3)(nH max (r) − nH2 (r)).
R1 (3) 2(10)Fig. 6 The radial proﬁles of the total ionization rate s andthe ionization rate from atomic and molecular hydrogen sH and sH2 .

The radial profiles of atomic and molecular hydrogen estimated by the above method and those obtainedby DEGAS simulation code [9] in which the moleculardissociation eﬀects are taken into account [10] areshown in Fig. 5. From the figure, the profiles estimatedby the above method almost agree with those obtainedby DEGAS code. Therefore the rough estimation of theradial profiles of atomic and molecular hydrogen canbe obtained by the above method. However, the above
method has some points of notice. First, the molecular hydrogen density estimated by the above method islarger than the results of DEGAS code in the core region. Next, the above method has very weak sensibility
to the electron temperature and no sensibility to the ion
temperature because R1 (3) and R2 (3) only have weaksensibility to the electron temperature in the central cellparameter range.

molecular hydrogen for the ionization rate is larger thanthat of atomic hydrogen in the central cell parameter
range. Moreover, we estimated the radial profiles ofatomic and molecular hydrogen densities based on themeasured results of Hα line emission together with theabove-obtained eﬀective rate coeﬃcients. Those profiles almost agree with the profiles obtained by DEGAS
code. As the result of the evaluation of the ionization
rate based on the estimated neutral hydrogen density
profiles, the contribution from molecular hydrogen havea dominant role in the ionization rate near the mid-planeof the central cell. Therefore it is necessary to consider
the behavior of molecular hydrogen for analysis of theparticle balance of GAMMA 10.

4.2 The contributions from atomic and molecular hy-Acknowledgements
The authors would like to thank members of theGAMMA 10 group of the University of Tsukuba.

drogen for ionization rate

The ionization rate (s [1/cm3 s]) is obtained by using
nH and nH2 estimated in last section and Eq. 3. The ionization rate s, the ionization rate from atomic hydrogensH = ne nH σvH total and the ionization rate from molecular hydrogen sH2 = ne nH2 σvH2 total are shown in Fig.
6.
From Fig. 6, it is found that s is nearly equal to s H2
excluding core region. In particular, s H2 is about one
hundred times larger than sH in the peripheral region.
The contribution from molecular hydrogen for ionization rate is dominant to that of atomic hydrogen. The
total ionization rate near the mid-plane of the centralcell is determined by the ionization rate from molecularhydrogen in this experiment.

[1]
[2]
[3]
[4]
[5]
[6]

5．Summary
We calculated the eﬀective rate coeﬃcients for Hαline emission and the ionization rate. The calculation results indicate that the eﬀect of atomic hydrogen is dominant for Hα line emission and the eﬀect of

[7]
[8]

121

References
K. Sawada et al., Phys. Rev. E 49, 5565 (1994).
M. Yoshikawa et al., Trans. Fusion Technol. 35,273 (1999).
Y. Kubota et al., to be printed in J. Plasma Fusion
Res. SERIES 6 (2004).
A. Macovski, Medical Imaging Systems(PRENTICE-HALL, INC.).
S. Kobayashi, Ph. D. Thesis Tsukuba Univ.
(2001).
R.K. Janev, W.D. Langer, K. Evans, Jr. and D.
E. Post, Jr., Elementary Processes in HydrogenHelium Plasmas (Springer-Verlag, Berlin, 1987).
R. Minami et al., Plasma Phys. Control. Fusion
44, 1363 (2002).
Y. Nakashima et al., J. Nucl. Mater. 313-316, 553(2003).

Behavior of Atomic and Molecular Hydrogen by Using the Measurements of Hα Line Emission in the GAMMA 10 Tandem Mirror[9]

D. Heifetz, D. Post, M. Petravic et al., J. Comput.
Phys. 46, 309 (1982).

[10] Y. Nakashima et al., J. Nucl. Mater. 196-198, 493(1992).

122