J. Plasma
J.
Plasma Fusion
Fusion Res.
Res. SERIES,SERIES,Vol.
Vol.6 6(2004)(2004)512–515
000–000

Fully Three-Dimensional Simulation of Neutral Particle Transport
in the Plasma Periphery on the Large Helical Device
SHOJI Mamoru, MORISAKI Tomohiro, MASUZAKI Suguru, GOTO Motoshi
and LHD Experimental Groups
National Institute for Fusion Science, Toki 509-5292, Japan(Received: 9 December 2003 / Accepted: 8 June 2004)

Abstract
Fully three-dimensional simulation of neutral particle transport is applied to analyses of the density profiles ofneutral hydrogen in the plasma periphery and in the divertor region on the large helical device (LHD). For considering
the three-dimensionally complicated geometry of the LHD plasma and the vacuum vessel, a detailed three-dimensional
grid model is formed. In order to simulate the effect of the full toroidal geometry of the plasma, a new wall ‘warp
wall’ is introduced. The calculations of three-dimensional profile of neutral densities in the grid model prove theavailability of the warp walls for detailed analyses of neutral transport. The simulation strongly suggests that baffle
plates installed in the inner region located between two helical coils in the vacuum vessel are cost-effective in achieving
divertor detachment and efficient particle removal and control in the plasma periphery.
Keywords:
neutral particle transport simulation, Large Helical Device, divertor

1. Introduction

effect of the full toroidal geometry of the LHD plasma into
the code.

One of the experimental objects in the Large HelicalDevice (LHD) is to demonstrate the effect of helical divertor
configurations for reduction of heat load on divertor plates
due to divertor detachment, and suppression of impurities in
the main plasma, etc. In the next experimental phase (PhaseII), modification of the divertor configuration (change fromthe present open divertor configuration to a closed one) isplanned [1]. An LHD vacuum vessel has larger space for thedivertor compared to that in modular coil configurations suchas W7-X and W7-AS, etc [2,3]. It enables more flexible
design of the closed divertor (e.g. the shape and size of baffle
plates and the position for vacuum pumps, etc.).
In Tokamaks, the density of neutral particles (molecules)in the divertor region is one of the most essential parameters
for achieving divertor detachment and efficient particle/
impurity removal in the plasma periphery [4]. Conventionally,
two-dimensional neutral transport simulation codes have been
widely applied to analyses of neutral particles, which isreasonable because of the almost toroidal symmetry ofTokamak systems. However, fully three-dimensional codes areindispensable in non-axial symmetric systems such as LHD.
For this purpose, we have applied a fully three-dimensional
neutral transport simulation code (DEGAS ver. 63) to theanalyses of the neutral particles in the divertor region [5]. In
this paper, the effect of the closed divertor configuration on
neutral particle transport will be investigated by including the2. Neutral particle transport simulation in
LHD plasmas
For neutral particle transport analyses, several simulation
codes have been developed and widely used for toroidally
symmetric plasma confinement systems [6,7]. In these codes,
test particles that represent neutral particles such as hydrogenatoms and molecules are launched from neutral gas sources(gas puffers and divertor plates, etc.) into a grid model which
simulates the shape of vacuum vessels and plasmas. The
trajectories of these particles are determined by the MonteCarlo method based on experimental or theoretical databasesof neutral-plasma/plasma-wall interactions [8,9]. The
application of the simulation code to the toroidal symmetricsystems has lead to development of the two-dimensional
simulation code assuming the symmetry for simple and fastcalculation algorism to trace test particle trajectories.
We have successfully developed a three-dimensional
simulation code for the analyses of neutral particle density inthe LHD plasma during local gas puffing [6]. The LHDvacuum vessel and plasma in our three-dimensional code
consist of triangles and tetrahedrons, respectively. Plasma
parameters (electron density (ne), ion density (ni), ion andelectron temperature (Ti, and Te)) and rate coefficients of©2004 by The Japan Society of Plasma
Science and Nuclear Fusion Research

Corresponding author’s e-mail: shoji@LHD.nifs.ac.jp1512

Shoji M. et al., Fully Three-Dimensional Simulation of Neutral Particle Transport in the Plasma Periphery on the Large Helical Device

plasma-neutral interactions inside of each tetrahedron areassumed to be constant. The profile of the plasma parametersin the grid model is defined on the bases of experimental datameasured with LHD plasma diagnostic systems [10]. The rate
coefficient of the interactions and the velocity components of
the reactants are dependent on the plasma parameters at thelocation of the test particles. The correlation of a test particle
position with a vacuum wall or a plasma grid in the threedimensional model is investigated by using a database ofplasma and vacuum wall geometries. The shape of thevacuum vessel and plasma are complicated, which restrains
the fabrication of the full toroidal model (0 < φ < 360 degrees;
φ is a toroidal angle) due to the finite memory sources andCPU power in our computer. To overcome this restriction, weintroduce a new wall ‘warp wall’ into the grid model. Whena test particle reach the warp wall located at both toroidal
ends in the grid model, the position and the direction of thetest particle are changed on the bases of the geometry of theend wall. The change of the above two parameters are
determined such that the test particle escaping from a toroidal
end wall returns from another end wall with keeping theabsolute velocity and the injection angle against the wall.
Setting the warp wall at both toroidal ends in the grid model,
we can effectively consider the effect of the full toroidal
geometry on neutral particle transport by using a grid modelfor only one toroidal pitch angle (0 < φ < 36 deg.) except fortoroidally local gas fueling cases.

densities (hydrogen atoms and molecules) in the LHD vacuum
vessel for typical neutral beam injection (NBI) heatedhydrogen plasma in an inward magnetic axis configuration (amagnetic axis position Rax of 3.60 m). Figure 1 shows a threedimensional grid model for simulating the vacuum vessel andplasma for one toroidal pitch angle. We defined the profile ofthe plasma parameters inside the LCMS as the measurements.
The parameters outside the LCMS are estimated on the basisof a typical experimental result locally measured with a fastmoving Langmuir probe and Thomson scattering by assuming
no poloidal variations. With regard to the three-dimensional
profile of the plasma parameters on divertor legs, we assume
that the electron temperature equals to the ion temperature,and the plasma density linearly depends on the calculated
density of particle deposition pattern on the divertor plates.
The absolute plasma density on the divertor legs is determinedby normalizing the density to experimental data measured
with the electro-static probes at a divertor plate.
Thin lines in the grid model shown in Fig. 1 represent
the trajectory of the test particles released from the strike
point on the divertor plates. Conventionally, a mirror wall,
which reflects the test particles on the basis of the principleof specular reflection, has been widely used to simulate thefull toroidal geometry in the grid model. For confirming theavailability of the new warp walls on the calculation, thedensity profile of neutral hydrogen molecules is compared in

3. Calculations of neutral particle
densities in the divertor region
A particle trajectory analysis by tracing magnetic fieldlines from just inside of the last closed magnetic surface(LCMS) with a random walk process predicts a threedimensionally complicated particle deposition pattern on
divertor plates installed in the vacuum vessel [11]. In oursimulation code, we assumed that the release rate of hydrogenmolecules from divertor plates is proportionally dependent on
the density of the calculated particle deposition on the divertor
plates. The calculation of the above particle tracing shows thatthe particle deposition is periodically distributed at one
toroidal pitch angle interval, which enables to analyze theneutral density profile by using the grid model for one
toroidal pitch angle with the warp walls. Experimental resultsmeasured with thermocouples and ion saturation currents
detected with electro-static probes embedded in divertor plates
support the calculation of the above particle trajectory analysis[12]. High neutral density is expected near divertor plates
installed in high particle deposition areas. A tangentially
viewing Charge Coupled Device (CCD) camera with aninterference filter for observing an Ha emission near divertor
plates detected high Ha intensity near the high particle
deposition area. The above three experimental results
qualitatively support our assumption that the neutral particle(hydrogen molecules) release rate from divertor plates
depends on the calculation of the particle deposition pattern.
We calculated the three-dimensional profile of neutral

Fig. 12513

Three-dimensional grid model for neutral transport
simulation in the LHD plasma and the vacuum vesselfor one toroidal pitch angle. Thin lines in the gridmodel are trajectories of a test particle emitted from thestrike point on a divertor plate.

Shoji M. et al., Fully Three-Dimensional Simulation of Neutral Particle Transport in the Plasma Periphery on the Large Helical Device

Fig. 2Fig. 3

Five toroidal cross sections of the density profile ofneutral hydrogen molecules when the mirror walls areused at both toroidal ends of the grid model.

the case where both toroidal ends of the grid model are themirror walls and the warp walls, respectively. Figure 2
illustrates the five toroidal cross sections of the density
profiles of neutral hydrogen molecules between one toroidal
pitch angle (φ = 36 deg.) in the case of mirror walls. The
high density of molecular hydrogen in the inner region in thevacuum vessel (φ = 18 deg.) can be explained by the facts
that the density of the particle deposition on the divertor plates
is significantly high in this region, and the released neutralhydrogen is confined in the small space between two helicalcoils. In these calculations, the inconsistency of the density
profile of molecular hydrogen between at toroidal angles of
φ = 0 and 34 deg. (nearly one toroidal pitch angle) isobservable. Specifically, the high density region is located in
the upper outer and the lower outer side for φ = 0 and 34
deg., respectively, which clearly shows the toroidaldiscontinuity of the neutral density profile. This is caused by
the three-dimensionally complicated distribution of the neutral
release rate from the divertor plates near the mirror walls(both toroidal ends), and by the complicated shape of theLHD vacuum vessel and plasma.
Figure 3 gives the five toroidal cross sections of thedensity profiles of neutral hydrogen molecules in the gridmodel with the warp walls. Hydrogen molecules are localized
in the inner region as well as these in the model with mirror
walls. The density profiles near the both toroidal ends (at φ =0 and 34 deg.) are fairly consistent, showing no observable

Five toroidal cross sections of the density profiles ofneutral hydrogen molecules when the warp walls areused at both toroidal ends of the grid model. Upperright illustration shows the enlarged contour plot of thedensity profile in inner divertor region.

toroidal discontinuity. These calculations indicate that the newwarp walls can be successfully applied to the detailed
simulation of neutral particle transport in the threedimensionally complicated geometry such as LHD.

4. Analyses of neutral particle transport ina closed divertor configuration
For a preliminary study of the closed divertor
configuration in LHD, we constructed a three-dimensional
grid model with the warp walls including baffle plates which
are fully helically installed along the space between the twohelical coils. The distance between an X-point of the plasma
and the head of the baffle plates is set to be 150 mm (the gap
between the two baffles is about 300 mm). Figure 4 illustrates
the five toroidal cross sections of the density profile of neutralhydrogen molecules. The distribution and quantity of therelease rate of hydrogen molecules from the divertor plates
are identical with these in the model without the baffle plate(Figs. 2 and 3). The neutral density between two helical coils
is higher than that without the baffle plates, which indicatesthe effective confinement of neutrals in the divertor region
due to suppression of the outflow of neutral particles fromthe divertor plates to the main plasma region. The figure
shows that the baffle plates significantly increase molecularhydrogen density in inner divertor region. The insets in Figs.
3514

Shoji M. et al., Fully Three-Dimensional Simulation of Neutral Particle Transport in the Plasma Periphery on the Large Helical Device

main plasma is indispensable for plasma heating anddiagnostic systems. The calculation in Fig. 4 strongly suggeststhat the cost-effective particle removal and control can berealized by installing the baffle plates only in inner divertor
region because of effective confinement of the high density
neutral hydrogen molecules in this region. It can almost keep
accessibility to the main plasma from vacuum ports (exceptfor from inner ports). Measurements of a fast ion gauge
suggest that the vacuum pressure in the present LHD divertor
region is about one-order of magnitude lower than that in
Tokamak open divertor cases [13]. That is, the present vacuum
pressure in the LHD divertor is not enough for achieving
divertor detachment. An optimized closed divertor
configuration is a possible candidate to achieve divertor
detachment in LHD plasmas, because actual neutral density
in the divertor region can be further increased by the enhanced
release rate of neutral hydrogen molecules on the divertor
plates due to the plasma flow on the divertor leg produced by
the ionization of recycled hydrogen from the divertor plates.
For quantitative prediction of the vacuum pressure in thedivertor region, detailed analyses of neutral particle transport
coupling with a fully three-dimensional plasma transport
simulation will be necessary in the future.
Fig. 4

Five toroidal cross sections of the profiles of neutralhydrogen molecules in the grid model including a fully
helically baffle plates with the warp walls. Upper rightillustration shows the enlarged contour plot of thedensity profile in inner divertor region.

References[1] O. Motojima et al., Nucl. Fusion, 40, 599 (2000).
[2] M. Borchardt et al., J. Nucl. Mater. 290, 546 (2001).
[3] E. Strumberger, J. Nucl. Mater. 266, 1207 (1999).
[4] G.M. MacCracken et al., J. Nucl. Mater. 266, 37 (1999).
[5] M. Shoji et al., J. Nucl. Mater. 313, 614 (2003).
[6] D. Reiter et al., J. Nucl. Mater. 313, 845 (2003).
[7] Y. Nakashima et al., J. Nucl. Mater. 241, 1011 (1997).
[8] D.B. Heifetz et al., J. Comp. Phys. 46, 309 (1982).
[9] D.P. Stotler et al., J. Nucl. Mater. 196, 894 (1992).
[10] S.Sudo et al., Plasma Phys. Control. Fusion 45, 1127(2003).
[11] T. Morisaki et al., 2000 Proc. 27th Eur. Conf. On
Controlled Fusion and Plasma Physics 23J, 1345 (2000).
[12] S. Masuzaki et al., Nucl. Fusion 42, 750 (2002).
[13] N. Noda et al., Nucl. Fusion 41, 779 (2001).

3 and 4 are the enlarged contour plots of the density profile
of molecular hydrogen in inner region, showing that thedensity of molecular hydrogen around a divertor leg in thecase without and with the baffle plates ranges from 4.0 × 106
to 8.0 × 106 , and from 4.0 × 10 6 to 1.6 × 10 6 (A.U.),
respectively. It indicates that the molecular hydrogen density
in this region with the baffle plates increases about twice asmuch as that without the baffle plates, which is favorable forachieving divertor detachment and efficient particle control
in the LHD plasma periphery.
Fully helical installation of the baffle plates is actually
impossible because the accessibility from vacuum ports to the4515