23P042-P
Study of isotope effects on transport phenomena in LHD by TASK3DTASK3Dを用いたLHDにおける輸送現象に対する同位体効果の研究	 
Masahiko Sato, Masayuki Yokoyama, Ryosuke Seki, Arimitsu Wakasa1), Sadayoshi Murakami1),
Atsushi Fukuyama1), Yuji Nakamura2),
Kiyomasa Watanabe, Hisamichi Funaba and Noriyoshi Nakajima
佐藤雅彦, 横山雅之，關良輔，若狭有光1)，村上定義1)，福山淳1)，中村祐司2)，
渡邊清政，舟場久芳，中島徳嘉
National Institute for Fusion Science322-6 Oroshi, Toki 509-5292, Japan
核融合科学研究所	  〒509-5292 土岐市下石町322-61)
Graduate School of Engineering, Kyoto University
Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, Japan
京都大学大学院工学研究科	  〒606-8501 京都市左京区吉田本町2)
Graduate School of Energy Science, Kyoto University
Gokasho, Uji 611-0011, Japan
京都大学大学院エネルギー科学研究科	  〒611-0011 宇治市五ケ庄
An integrated simulation code for helical plasmas, TASK3D, is applied to transport simulation forhydrogen/deuterium/helium plasmas in order to clarify isotope effects on transport phenomena. In thisanalysis, 3D MHD equilibrium module VMEC, 1D diffusive transport module TR, ambipolar radial
electric field module ER and NBI heating module FIT3D are used. Dependence of the stationary state onmain ion’s mass number is reported.

1. Introduction
For systematic analysis of confinement physics
in helical plasmas, an integrated transport codefor three-dimensional configurations (TASK3D[1])is being developed on the basis of an integrated
modeling code for tokamak plasmas, TASK [2].
In order to extend the TASK code to beapplicable to three-dimensional configurations,the transport equations for the rotationaltransform and the radial electric field have beenreformulated by taking the three-dimensional
nature of configurations into account. With thenew formulation, new modules for the rotationaltransform (EI module)[3] and radial electric field(ER module) [1] have been developed andimplemented. For the neutral beam injection(NBI) heating, FIT3D module[4] has added to theTASK3D and the demonstration of simulation
was shown by combining FIT3D, VMEC and TR
modules, in order to check the consistency of theinterface among modules[5]. In the previousstudies, the transport phenomena for a hydrogenplasma have been analyzed by TASK3D. In thisstudy, TASK3D is applied to a deuterium plasma
and a helium plasma as well as a hydrogenplasma, in order to clarify isotope effects ontransport phenomena.

2. Numerical ModelTASK3D has a modular structure, allowing us to
conduct simulations using an individual module orcombination of some modules according to theuser’s objective. In this study, 3D MHD
equilibrium module VMEC, 1D diffusive transportmodule TR, radial electric field module ER andNBI heating module FIT3D are used. Numerical
scheme used in this study is shown in Fig.1. In theTR module, the following particle and heattransport equations are solved;

where, ns is the density, Ts is the temperature and sexpresses the particle species. VEs=VKs+(3/2)Vs,
where VKs is the heat pinch velocity and DS, χs,and Vs are the particle diffusion coneffcient, thermal
diffusion coefficient, and particle pinch velocity,respectively, which consists of a neoclassical partand an anomalous part. Ss is the particle source andPs is the energy source (or sink). t, r, V are the time,minor radius variable of magnetic surface, andvolume enclosed by the magnetic surface,respectively. The prime denotes the derivative withrespect to r, and〈〉represents the magnetic surface
average. The geometry factors V ′ ,〈|∇ρ|〉,〈|∇ρ|2〉
in eq.(1) are calculated by the VMEC module.
Since the ambipolar condition is not satisfied
intrinsically due to the non-axisymmetry of helicalplasmas, radial electric field Er is determined byneoclassical transport. The time scale of the time
evolution of Er is much shorted than that for thedensity and temperature. Therefore, the time step inthe calculation of Er has to be smaller than that forthe density and temperature. In this study, Er is
determined from the ambipolar condition byassuming the stationary state of the equation of thetemporal evolution of Er. Estimation of neoclassicalparticle fluxes is required for obtaining theambipolar Er in the ER module. For the neoclassicaltransport model, two models are implemented inTASK3D. One is analytic single helicity model[6]and the other is the database of neoclassicaldiffusioncoeffcients,
DGN/LHD[7],beingconstructed using DCOM and GSRAKE.
3. Test Simulation
Figure 2 shows one of test simulation results for
H-He plasmas. Here, for simplicity, the plasma
density is fixed in the transport module TR. It isalso assumed that the plasma is heated by ECH andanomalous transport coefficient is set to be 1 m2/s.
For neoclassical transport model, the analytic single
helicity model is used. The stationary state depends
on the density ratio of ions. As the density ratio of
H to He increases, positive radial electric field
becomes negative at some critical density ratio. The
transition of the structure of the radial electric field
is sensitive to the ratio of ions.
4. Concluding Remarks
TASK3D has been applied to analysis of isotope
effects on transport phenomena. Test simulation
results show that there is a clear difference in thestationary state. The detail analysis using DGN/LHD
and FIT3D will be reported in this conference.

Fig.1. Numerical scheme for transport simulation byTASK3D.

Fig.2. Structure of radial electric field at the stationarystate calculated by TASK3D.
References[1] M.Sato et al., Plasma Fusion Res., 3 (2008) S1063.
[2] A.Fukuyama et al., Proc. Of 20th IAEA Fusion
Energy Conf. (Villamoura, Portugal, 2004)
IAEA-CSP-25/CD/TH/P2-3.
[3] Y.Nakamura et al., FusionSci.Technol. 50 (2006)
457.
[4] S.Murakami et al., Trans. Fusion Technol. 27 (1995)
256.
[5] M.Sato et al., Proc. of 18th Int. Toki Conf. (2008)
P1-05.
[6] K.C.Shaing, Phys. Fluids 27 (1984) 1567.
[7] A.Wakasa et al., Contributions to Plasma Phys. 50(2010) 582.