J. Plasma
J.
Plasma Fusion
Fusion Res.
Res. SERIES,SERIES,Vol.
Vol.6 6(2004)(2004)546–549
000–000

Neutral Transport Analysis in Non-axisymmetric Anchor Region ofthe GAMMA 10 Tandem Mirror Using a Monte-Carlo Simulation
NAKASHIMA Yousuke, HIGASHIZONO Yuta, OHKI Toshikazu, SHOJI Mamoru1,
KOBAYASHI Shinji2, KUBOTA Yuusuke, YOSHIKAWA Masayuki, ISLAM Md. Khairul,
FUKASAWA Takahiro, ISHIMOTO Yuki, WATANABE Kazuhiro, OGITA Takeshi,
YAMADA Masaki, MURAKAMI Ryouhei and CHO Teruji
Plasma Research Center, University of Tsukuba, Ibaraki 305-8577, Japan
1
National Institute for Fusion Science, Toki 509-5292, Japan
2
Institute of Advanced Energy, Kyoto University, Uji 611-0011, Japan(Received: 9 December 2003 / Accepted: 25 April 2004)

Abstract
Transport of neutral particles in non-axisymmetric anchor region of the GAMMA 10 tandem mirror is describedin terms of a Monte-Carlo simulation and of Hα line-emission measurements. A three-dimensional neutral transport
simulation has been performed by applying the DEGAS ver.63 code to the anchor region. A detailed mesh structure
was built up for the three-dimensional geometry in this region and the simulation was carried out under a plausible
assumption of particle source on experimental data basis. In standard Hot-Ion-Mode plasmas, a series of Hα lineemission measurements have been carried out and axial distribution of particle source rate over the region from themirror-throat to the anchor-cell is discussed based on both calculation and measurements.
Keywords:
GAMMA 10, tandem mirror, neutral transport, Monte-Carlo simulation, DEGAS code, Hα emission,hydrogen recycling

1. Introduction

In the transition region, the thickness of the plasma is thesame order of the mean free path length of hydrogenmolecules and is much shorter than those of Franck-Condon
neutrals. Under these circumstances, the behavior of neutrals
provides valuable information not only for the tandem mirror
research but also for the edge plasma investigation in divertor
configurations.
In standard ion-cyclotron-range-of-frequency (ICRF)heated hot-ion-mode plasmas, fueling experiments using
neutral beam injectors (NBIs) have been started for achieving
potential confinement of higher density plasmas [9,10]. Inthese experiments, detailed measurements of Hα lineemission were performed from the central-cell midplane tothe outer-transition region of the anchor-cell [11]. In order toevaluate the neutral density profile in non-axisymmetricregion, a three-dimensional neutral transport simulation has
been started by using the DEGAS ver.63 code [12]. In thispaper, we describe the detail of the Monte-Carlo simulationand discuss the location of particle source and its intensity inthe non-axisymmetric anchor-cell based on the measured
results of Hα line-emission.

Analysis of neutral particle transport is an important
issue to understand hydrogen recycling and transportphenomena in the edge plasma regions. It is also importantto analyze particle and energy balance for attaining high β
plasmas in the tandem mirror devices [1,2]. In the GAMMA
10 tandem mirror, neutral hydrogen density in the centralcell has been estimated by measuring spatial-profiles of Hαline-emission together with neutral transport simulation [24]. The neutral density is evaluated from the absolute valueof the Hα emissivity based on the collisional-radiative model[5]. The DEGAS Monte-Carlo code [6] has been used for theneutral transport simulation in the GAMMA 10 plasma. The
code has been modified to take into account of the effect ofdissociative-excitation reaction of molecular hydrogen [2,7].
GAMMA10 is axisymmetric minimum-B anchoredtandem mirror with thermal barrier [8]. The device consistsof an axisymmetric central-mirror cell, anchor-cells withminimum-B configuration, and plug/barrier cells withaxisymmetric mirrors. In the anchor-cell, there exist transition
regions where the shape of the magnetic flux tube becomesflat and the cross section of plasma is elongated elliptically.

©2004 by The Japan Society of Plasma
Science and Nuclear Fusion Research

Corresponding author’s e-mail: nakashma@prc.tsukuba.ac.jp1546

Nakashima Y. et al., Neutral Transport Analysis in Non-axisymmetric Anchor Region of the GAMMA 10 Tandem Mirror

2. Neutral transport simulation using theDEGAS Monte-Carlo code
2.1 Mesh structure in non-axisymmetricanchor-cell
The DEGAS ver.63 Monte-Carlo code, which is applied
to execute the three-dimensional neutral transport simulationin anchor-cell, is modified so as to take the dissociativeexcitation of hydrogen molecules into consideration in theneutral transport process in order to make the simulation adapt
to the lower density range below 1013 cm-3. The mesh modelof the wall-surface of the anchor minimum-B region and thesurface plot of the plasma grid newly constructed for thesimulation are shown in Fig. 1. As shown in the figure, themodel introduces a symmetry in vertical direction and thesimulation space is divided into 11 segments radially and 8segments azimuthally. In the axial direction, 41 segments are
utilized for the simulation. In this simulation, gas desorption
from the movable limiter inserted in the outer-transition
region of the anchor-cell is considered together with theparticle source from the gas puffer near the mirror throat
region.

Fig. 1

Mesh model of the anchor minimum-B region used for
DEGAS ver.63. (a) schematic view of the vacuum
vessel, (b) surface structure of the vessel wall, (c) crosssection (x-y plane) of the plasma and the wall, (d) grid
shape of the plasma surface.

Fig. 2

Spatial profiles (on y-z plane) of the electron density
used for the simulation. (a) Collision-less plasma flow
model, (b) uniform density model.

2.2 Modeling of plasma parameter
Since the obtained plasma parameters from theexperiments are practically insufficient for the simulation, anappropriate assumption is required for taking an input dataset
into the simulation code. The following two typical models
are adopted as electron density profile. The spatial profiles(on y-z plane) of the plasma electron density used for thesimulation are shown in Fig. 2. One, as shown in Fig. 2(a), is
the density model assuming the flux conservation withcollision-less plasma flow in the region where the intensityof magnetic field varies in the axial direction. The other isthe uniform density model from the central-mirror throat tothe periphery of the anchor midplane, considering the particle
trapping effect in the local mirror configuration of anchor
transition region as shown in Fig. 2(b). In both models, thedensity profiles are determined on the basis of the measured
data at the central-cell, the mirror throat and the anchor
midplane, considering the shape of the magnetic flux tube
from the central-cell to the anchor-cell.

3. Simulation results and discussion

In contrast to the molecular density, atomic hydrogendensity shown in Fig. 3 (b) has a tendency to concentrate in
the plasma core region. The atomic density also shows therather uniform density over the plasma cross section in innerand outer transition regions where the plasma cross section
becomes much elongated elliptically. Although thesemechanisms are not clarified in detail, longer mean free pathof Franck-Condon neutrals compared with the plasma
thickness may enhance the production of atomic hydrogen
inner region of the plasma column and form such density
profiles in the anchor-cell.

3.1 Neutral density profiles in the anchor-cell
Figure 3 shows the 3-D simulation results of neutralhydrogen density profiles. In the anchor midplane, as shownin Fig. 3(a), it is recognized that the molecular hydrogendensity radially decreases toward the core region of theplasma and further reduces along with the magnetic field linefrom the mirror throat (z = – 300 cm) to the anchor midplane(z = – 520 cm). Penetration of neutrals is taking place in theedge region where the plasma thickness becomes thin. The
result implies that injected hydrogen molecules from themirror-throat gas puffer are transported to the anchor
transition region with significant attenuation and only a small
amount of them reaches the anchor midplane.

3.2 Comparison to the experimental results
Figure 4 shows the comparison between the simulation
2547

Nakashima Y. et al., Neutral Transport Analysis in Non-axisymmetric Anchor Region of the GAMMA 10 Tandem MirrorFig. 3

Results of the 3D-DEGAS simulation in the case that the gas puffing at the mirror throat and gas desorption from the movable
limiter in the outer-transition region is applied as the particles source. (a) molecular hydrogen, (b) atomic hydrogen.

discrepancy is observed at the anchor midplane in the case of
the uniform density model. The hydrogen recycling near themovable limiter plays an important roll on the behavior ofneutral particles in the non-axisymmetric anchor region.
By accumulating the information of neutral density
obtained above and the data of plasma parameters, total
particle source rate from the central-cell to the anchor-cell isevaluated. An example of the results is shown in Fig. 5. In
the figure, axial profiles of the particle source rate radiallyintegrated up to rcc = 20 cm are plotted in cases of given two
density models. Here, rcc represents the plasma radius reduced
to that at the central-cell midplane along the line of magneticforce. There is no significant difference observed between
both cases. The dissociative-excitation reactions of hydrogenmolecules are presumably less effective on the Hα intensity
than the dependence of the plasma density profile. As shownin the figure, it is found that the particle source rate in themirror throat is dominant compared with those in the regionsof the anchor midplane and of the movable limiter.

Fig. 4 Axial intensity profile of Hα line-emission.

results and measured one. Calculated results of Hα intensity
obtained with two typical density models are normalized so
as to fit to the measured results at each source location. The
simulation assuming both particle sources from the gas puffer
and from the movable limiter successfully reproduces theaxial profile of measured H α intensity. While, a small

4. Summary
Using three-dimensional Monte-Carlo code DEGAS
3548

Nakashima Y. et al., Neutral Transport Analysis in Non-axisymmetric Anchor Region of the GAMMA 10 Tandem Mirror

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Calculated axial profiles of the particle source rate
integrated within rcc = 20 cm.

ver.63, a modeling of neutral transport was successfully
performed in the GAMMA 10 anchor-cell with nonaxisymmetric configuration of the magnetic field, and thebehavior of neutrals in this region was investigated on thebasis of the experimental data of H α line-emission
measurements. From the simulation results, it was found thatboth particle sources from gas puffing at the central mirrorthroat region and the hydrogen recycling from the movable
limiter located in the outer-transition region predict theexperimental results well. The estimation of ionization rate
based on the simulation shows that ionization in the mirrorthroat region is dominant in the total particle source inGAMMA 10. Comparison between the two typical density
models in the anchor region indicates that the total ionization
amount is not affected strongly by this difference. Above theseresults give an important subject on the investigation of theparticle source-rate in the non-axisymmetric regions.

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