23P122-P
Diffusive Transport Analysis in Low Aspect Ratio Reversed Field Pinch
低アスペクト比逆磁場ピンチプラズマにおける輸送解析
Yasuo Nagamine1, Atsushi Fukuyama2, Shoichi Shiina3 and Masamitsu Aizawa1
長峰康雄1, 福山 淳2，椎名庄一3，相澤正満1
1

Institute of Quantum Science, Nihon University
1-8-14 Kanda-Surugadai,Chiyoda-ku,Tokyo 101-8308, Japan
日本大学量子科学研究所 〒101-8308 東京都千代田区神田駿河台1-8-14
2
Department of Nuclear Engineering, Kyoto University
Yoshida-Honcho, 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
3
National Institute of Advanced Industrial Science and Technology
Umezono, Tsukuba, Ibaraki 305-8568, Japan
産業技術総合研究所 〒305-8568 つくば市梅園
For the evaluation of confinement property of the low aspect ratio reversed field pinch (RFP) plasma,diffusive transport analysis including the neoclassical and turbulent transport models is studied. To analyze
such transport phenomena, the applicability of TASK (Transport Analysing System for TokamaK)simulation code is considered. Several turbulent transport models are implemented, but this code has beendeveloped for the tokamak and (recently) helical magnetic configurations. For the analysis of RFP, becauseof the different nature of the magnetic configuration, some modifications and validation analysis of thephysical models in TASK code are required.

1. Introduction
In order to evaluate the confinement propertiesof a low aspect ratio (A) reversed field pinch(RFP) plasma, diffusive transport analysis isstudied theoretically. For the conventional RFP
plasma with laeger aspect ratio, transport
analyses by using the theoretical model orthree-dimensional numerical simulations basedon the cylindrical approximation have beenshown to be nearly consistent with experimental
results such as the confinement scaling in thestandard ohmically driven RFP [1,2]. On theother hand, confinement performance in a low
aspect ratio RFP is not well understood, but it isconsiderd to be important to introduce thetransport model including the effect of toroidal
geometry. Numerical analysis based on theneoclassical transport model in a low aspect ratio
RFP shows that a considerable bootstrap current
contibution can be expected in the RFP
configuration, when incorporating the effects of
non-circular cross-section and low aspect ratio [3].
However, of transport phenomena in an RFP, theenergy confinement time τE might be determinedby anomalous transport due to micro-instabilities.
Therefore, it must be considered to introduce anappropriate model for the turbulent transport inthe RFP configuration.
2. TASK code

TASK (Transport Analysing System for
TokamaK) code is an open source code which has
been developed at Kyoto University [4,5]. This
code consists of some modules calculating eachphysical process such as equilibrium, transport,wave propagation, etc. and analyzes the transport
process of the whole nuclear burning plasma byintegrating them. A part of the modules are listed inTable I.
Table I. A part of modules of TASK code [5]In this study, we use EQ and TR modules mainly
for the diffusive transport analysis. In the TRmodule, some diffusive transport models based on
the neoclassical transport theory and turbulent
transport theory are implemented. Applied for the
first time to the RFP configuration, the code isexploited for steady state calculations with theneoclassical and basic turbulent transport models.
In order to include the description of the RFP
geometry, some parts of the code need to beimproved. The most fundamental improvement isrelated to the existence of 0 points of the toroidal
magnetic field at the reversal surface [6].
3. Preliminary Results of TASK/EQ calculation
As preliminary calculations of TASK code,
equilibrium analysis of low A RFP is performed by
the modified EQ module. Figure 1 shows the resultof calculations: (a) toroidal and poloidal current
density profiles on the midplane, (b) safety factor
profile, in the case of parameters A=2.0, ellipticity
κ=1.4, triangularity δ=0.4, plasma current
Iφ=0.15MA and parabolic pressure profile.
(a)(b)

Fig. 1. Basic equilibrium profiles calculated by themodified EQ module: (a) toroidal and poloidal current
density profiles on the midplane, (b) safety factor
profile.

4. Considerations for turbulent transport
analysis
In tokamaks, so many transport analyses havebeen performed, and developed some turbulent
transport models, such as gyro-kinetic or gyro-fluid
simulations of ITG (Ion Temperature Gradient)instability and turbulence. Comparisons and physics
basis of tokamak transport models and turbulencesimulations are summarized in Ref. [7].
As major turbulent transport models, CDBM(Current Diffusive Ballooning Mode), GLF23,
IFS/PPPL and Weiland models are employed inTASK code. In these models, it is considered thatthe CDBM model has difficulty in application tothe RFP configuration. Three of the remainder are
all models based on the gyro-fluid description.
More basic models such as Bohm or Gyro-Bohm
model are also implemented in this code. For thefirst application to RFP, it is expected that thesemodels are passable as a model of the anomaloustransport.
Recently, linear gyro-kinetic calculations areapplied to the RFP configuration to investigate theoccurrence of ITG instabilities [8]. In Ref. [8],linear electrostatic calculations of ITG instability
are performed by exploiting the GS2 numericalcode, which is a widely known gyro-kinetic code
based on the electromagnetic nonlinear gyro-kinetic
equation and the flux tube geometry. This analysis
shows ITG modes are in general stable in RFP
plasmas in the area of experimental parameters, andthis type of instability to be only marginallyresponsible for particle and energy transport. The
required gradients could be reached only incorrespondence to the temperature slopes arising at
the boundary of the helical structure in QSH states.
Numerical calculations in Ref. [8], however, arebased on geometry and parameters of the RFX
experimental device. Also some geometricsimplifications such as circular surfaces with noshift and so on are imposed, for the code is basedon the flux tube domain.
As for a low aspect ratio RFP with shaped
magnetic surface and neoclassocal effects,
understanding the mechanism of transport isconsidered to be an interesting subject, for its
configuratin has some different characters from thestandard high aspect ratio RFP plasma.
5. Summary
In analysis of a low A RFP using TASK code,
because of the different nature of the magnetic
configuration from tokamaks, some modificationsand validation analysis of the applicability of thephysical models in this code are required.
References[1] Bruno A, et al., Physics of Plasmas 10, 2330 (2003).
[2] Scheffel J and Schnack D D, Nuclear Fusion 40,
1885 (2000).
[3] Shiina S, et al., Physics of Plasmas 12, 080702(2005).
[4] Fukuyama A, et al., J. Plasma Fusion Res. 81, 747(2005).
[5] http://bpsi.nucleng.kyoto-u.ac.jp/bpsi/en/[6] Nagamine Y, et al., Journal of Physics Conference
Series (to be published).
[7] Dimits A, et al., Physics of Plasmas 7, 969 (2000).
[8] Predebon I, et al., Physics of Plasmas 17, 012304(2010).