23R3-4
Simulation Research of Toroidal Fusion Plasmas Including
Three-Dimensional Effects
3次元効果を含むトロイダル核融合プラズマのシミュレーション研究
Hideo Sugama, Naoki Mizuguchi, Shinsuke Satake, Tomohiko Watanabe, and Masanori Nunami
洲鎌英雄, 水口直紀，佐竹真介，渡邉智彦，沼波政倫
National Institute for Fusion Science / Graduate University for Advanced Studies
322-6 Oroshi-cho, Toki, Gifu 509-5292, Japan
核融合科学研究所・総合研究大学院大学 〒509-5392 岐阜県土岐市下石町322-6

Large-scale computer resources such as the new supercomputer in the IFERC-CSC are highly
necessary to conduct simulation researches in toroidal fusion plasmas especially for investigatingcomplicated systems including three-dimensional magnetic field structures. As examples of simulation
studies of toroidal plasmas including the three-dimenstional effects, recent results from nonlinear MHD
simulation of reversed field pinch plasmas, δ f Monte Carlo simulation of neoclassical toroidal viscosity intokamaks, and gyrokinetic Vlasov simulation of ion temperature gradient turbulence and zonal flows inhelical sytems are presented. It is shown that the three-dimensional structures appear ubiquitously invarious toroidal systems as critical factors of plasma confinement and their effects need to be extensivelypursued.

1. Introduction
In the National Institute for Fusion Science, theNumerical Simulation Research Project is inprogress,
which
promotes
comprehensive
simulation studies of toroidal magnetic
confinement fusion plasmas and aims to realize ahelical numerical test reactor as integrated codesfor predicting whole plasma behaviors over
diverse spatiotemporal scales [1]. Generally, forsimulations of helical plasmas such as heliotronsand stellarators, complicated three-dimensional
magnetic-field structures require larger numbers ofgrid points and longer computational time than forthe case of tokamaks, and effective utilization ofmassive parallel computers like the one of theIFERC-CSC is highly desirable. In addition,
three-dimensional physical phenomena caused bysymmetry breaking have recently been attracting
much attention even in researches of tokamaks andreversal field pinches (RFP) which are originally
axisymmetric. In this paper, examples of recent
simulation studies on such three-dimensional
physics are illustrated.
2. Nonlinear MHD Simulation
Recent experiments have shown structuralchanges of RFP plasmas into self-organized
three-dimensional states with helical magnetic
configurations, which are now examined as acontrol method to avoid confinement degradation
due to intrinsic tearing mode instabilities [2].
Applying the MHD simulatin code, MHD
Infrastructure for Plasma Simulation (MIPS) [3], tothe experimental RFP configurations of the RELAX
device [2], the mechanisms of formation of helicalstructures are clarified [4]. Figure 1 shows thenonlinear MHD simulation result, in which helicalstructures of isopressure surfaces are seen.

Fig.1. Formation of helical structures in the core region of an
RFP plasma obtained from the nonlinear MHD simulation.

3. Simulation of Neoclassical Toroidal Viscosities
The control of the toroidal rotation is an
important issue in tokamaks and the International
Thermonuclear Experimental Reactor (ITER), in
order to improve the stability of the containedplasmas. The significant change of the toroidal
rotation can occur when the axisymmetry is broken.
The δ f Monte Carlo simulation code, FORTEC-3D ,which was originally developed to investigate theneoclassical transport processes in helical systems,
are applied to the evaluations of neoclassicalviscosities(NTVs)
intokamaks
withnonaxisymmetric magnetic perturbations [5,6]. As
shown in Fig.2, the NTVs calculated from theFORTEC-3D simulation agree well with Park’s
analytical formula [7] in wide collisionality range
except the edge region. Also, a difference between

the simulation and analytical results is found in the
shape of the peak profile of NTV around theresonant surface. Thus, the direct kinetic simulation
using FORTEC-3D can reveal the detailed
properties of NTV, which are difficult to treat
analytically.

Fig.2. Dependence of the neoclassical toroidal viscosity (NTV)on the normalized collisionality ν* for several radial positions.
The “F” curves are results from the FORTEC-3D simulations
and the “P” symbols are from the analytic formula, and thenumerals denote the normalized radial position ρ. The "1/ν "and "SB-P" lines represent the values from the asymptotic limit
theoryfor the 1/ν and superbanana-plateau regimes,respectively.

4. Gyrokinetic Simulation
Gyrokinetic simulation is a powerful means toevaluate turbulent transport in magneticallyconfined plasmas from the first principles. Since the
gyrocenter distribution function on the fivedimensional phase space is treated, the gyrokinetic
simulation requires huge computer resources
especially for helical systems. The gyrokinetic
Vlasov (GKV) simulation code [8], which employs
the local flux tube as a simulation domain, wasdeveloped and applied to the investigation of theITG turbulent transport and zonal flows in helicalsystems. It was elucidated that, as predicted by thezonal-flow response theory [9], the zonal-flow
generation is enhanced and accordingly the ITG
turbulent transport is reduced in the neoclassically
optimized helical configuration [8]. An extended
version of the gyrokinetic Vlasov code (GKV-X)
can treat full geometric data of three dimensional
MHD equilibria precisely corresponding to theexperimental conditions [10]. Simulation resultsfrom the GKV-X simulation of the ITG turbulence
are successfully compared with experimental results
for a high ion temperature plasma in the LHD [11].
Potential contours obtained from the simulation are
shown in Fig.3. It is theoretically predicted that, inhelical systems, the macroscopic or backgroundradial electric field can enhance generation of zonal
flows leading to the further reduction of turbulent
transport and the favorable isotope effect of the ionmass [12]. The poloidally global simulations of theITG turbulence are done by a newly-developed
gyrokinetic Vlasov simulation code, from which theincreased background electric field is confirmed tostrengthen the zonal flow generation [13,14].

Fig.3. Potential contours in a high Ti LHD plasma obtained
from the gyrokinetic ITG turbulence simulation using theGKV-X code.

5. Summary
In this paper, recent results from different types(Nonlinear MHD, δf Monte Carlo, and GyrokineticVlasov) of simulations are presented, whichinvestigate effects of three-dimensional magnetic
field structures in various types (RFP, tokamak, andhelical system) of toroidal plasmas. As seen fromthese examples, three-dimensional effects criticallyaffect the performance of the magnetic confinement
fusion and further simulation studies on them are tobe done by maximum utilization of the advanced
supercomputers.
Acknowledgments
This work is supported in part by the Japanese Ministry ofEducation, Culture, Sports, Science, and Technology, Grant
Nos. 21560861, 22760660, and 23760810 and in part by theNIFS Collaborative Research Programs, Grant Nos.
NIFS10KNTT003, NIFS11KNST017, NIFS11KNXN229,
NIFS10KNST006, and NIFS11KNST014.

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