23P050-P
Dependence of Thermal Diffusivity on Plasma Parameters in Perturbed
Magnetic Field in Toroidal Plasma
トロイダルプラズマの摂動磁場領域での熱輸送シミュレーション
Ryutaro Kanno, Masanori Nunami, Shinsuke Satake
菅野龍太郎, 沼波政倫, 佐竹真介
National Institute for Fusion Science,Toki 509-5292, Japan
核融合科学研究所 〒509-5292 土岐市下石町322-6
We consider the modeling of radial heat transport under effects of both the Coulomb collision and resonant
magnetic perturbations (RMPs) in toroidal plasma. It is found in the previous study that the radial thermal
diffusivityχr in the perturbed region is represented asχr =χr(0){1+c|δBr/Bt|2}, where |δBr| is the strengthof RMPs in the radial directions, |Bt| is the strength of toroidal magnetic field at the magnetic axis,χr(0) is
the diffusivity when δB=0, and c is an unknown coefficient. In the present study, dependence of thecoefficient c on plasma parameters is investigated by a Monte-Carlo simulation code KEATS. We find thatthe dependence of c is given as c∝ωb/νin the banana regime, whereωb is the bounce frequency andνisthe collision frequency.

1. Introduction
Essentially, energy transport phenomenon inperturbed magnetic field under conditions of
n=constant, V=0 and E=0 in the radial directions(i.e., the radial heat transport in the perturbedregion) is one of diffusive phenomena caused by
the Coulomb collision [1], where n is the density,
V is the mean velocity, and E is an electric field.
The radial heat flux after a sufficient time isrepresented by using the following model ofradial thermal diffusivity: χ r= χ r(0){1+c|δBr/Bt|2};see [1].
The present study is devoted to investigate
dependence of the unknown coefficient c inχr on
collision frequencies and particle species by usinga δf simulation code KEATS [2].
2. δf simulation for estimating radial thermal
diffusivity
We investigate dependence of the coefficient con plasma parameters in the modeling of radial
thermal diffusion, where the radial heat flux isestimated by using a guiding center distributionfunction. The radial thermal diffusivity can beevaluated by the δf simulation code KEATS [1, 2].
In the simulation, a toroidal magnetic
configuration is formed by adding RMPs to asimple tokamak field having concentric circular
flux surfaces and an ergodic region is boundedradially on both sides, where the major radius of themagnetic axis is set as Rax=3.6 m, the minor radiusof the plasma is a=1 m, and the magnetic fieldstrength on the axis is Bax=4 T. The Poincare plot ofmagnetic field lines with RMPs on a poloidal crosssection is shown in Fig.1. Details of magnetic field
including RMPs used in the simulations aredescribed in [1]. The temperature profile is fixed asT(r) = Tax - (Tax-Tedge)(r/a) with Tax=1.137 keV and
Tedge=0.8Tax, and the density n is assumed to be aconstant, where r={(R-Rax)2+Z2}1/2 is the label ofmagnetic flux surfaces if neglecting the RMPs incylindrical coordinates (R, φ, Z). Comparison
between the results of the δf simulation of KEATS
and previous studies including the field-line
diffusion theory is discussed in detail in [1].

Fig.1. Poincare plot of the magnetic field lines on apoloidal cross section in coordinate space.

As shown in Fig.2, the radial thermal diffusivity
is proportional to the square of the strength ofRMPs in the radial directions, |δBr|2, and also
depends on the collision frequency,ν, where thecollision frequency is proportional to the density n.

Fig.2. The radial thermal diffusivity of ion (proton) at
r/a=0.6 depends on both the strength of RMPs in theradial directions and the density n, where n(0)=1×1019
m-3, |δBr| = <||δBr||2>1/2 is given as the averaged value ofδBr on a reference surface of r/a=0.6, and |δBr(0)| is thestrength of δBr at r/a=0.6 in Fig.1.

The dependence ofχr on the collision frequency
in the configurations with and without RMPs isshown in Fig.3, where the radial thermal diffusivity
in the plateau regime is close to the one given by
the neoclassical theory in the plateau regime, i.e.,χr= 0.3 m2/s [3]. We see that difference between thediffusivities with and without RMPs is negligibly
small in the plateau regime, and that one of the key
parameters is ω b/ ν , where ω b is the bounce
frequency. As shown in Fig.4, the dependence ofχronνis represented as c∝ 1 /ν from the results
calculated by using data in Fig.3. Therefore, thediffusivity in the perturbed magnetic field isformulated as χ r=χ r(0){1+c’(ω b/ν)|δBr/Bt|2}, whereFig.4. The radial thermal diffusivity of ion (proton) at
r/a=0.6 depends on the collision frequencyν, where|δBr| = <||δBr||2>1/2 is given as the averaged value of δBr
on a reference surface of r/a=0.6 and |δBr(0)| is thestrength of δBr at r/a=0.6 in Fig.1.

As shown in Fig.5, the radial thermal diffusivityalso depends on the particle mass, i.e., c’ should bea function of the particle mass. We are investigating
the dependence of c’ on particle species in detail,and will report on it in the near future.

c’ is a coefficient.
Fig.5. The radial thermal diffusivities of electron andion (proton) at r/a=0.6.

Acknowledgments
This work was performed with the support andunder the auspices of the NIFS Collaborative
Research Program NIFS11KNST019.

Fig.3. The radial thermal diffusivity of ion (proton) at
r/a=0.6 in the configuration with and without RMPs.

References[1] R. Kanno et al., Plasma Phys. Control. Fusion 52(2010) 115004.
[2] M. Nunami et al., Research Report NIFS Series
No.NIFS-871 (2007).
[3] P. Helander and D.J. Sigmar, Collisional Transportin Magnetized Plasmas (Cambridge University Press,Cambridge, 2002).