S-P4-4Physics of Isotope Effect on Turbulent Transport in LHD Plasmas
LHDプラズマの乱流輸送に生ずる同位体効果の物理
Tomo-Hiko Watanabe, Hideo Sugama, and Masanori Nunami
渡邉智彦, 洲鎌英雄，沼波政倫
National Institute for Fusion Science / The Graduate University for Advanced Studies (Sokendai)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 〒509-5292 岐阜県土岐市下石町322-6
A possible isotope effect on turbulent transport in the Large Helical Device (LHD) plasma is discussed.
Zonal flow response enhancement by an equilibrium-scale radial electric field is predicted by thegyrokinetic theory and simulation. Coupling of the neoclassical transport, the zonal flow enhancement, andthe turbulence regulation brings the ion-mass dependence of the turbulent transport in the LHD plasma.
The isotope effect on turbulent transport is expected to appear as a more favorable ion mass dependence ofthe transport than the conventional gyro-Bohm scaling.

1. Introduction
Isotope effects on turbulent transport inmagnetically confined fusion plasmas areimportant but still remain to be resolved forreliable prediction of plasma performance infusion reactors [1]. The conventional gyro-Bohm
scaling,! ! " 2 vt / L ! mTi 3/2 LB 2 ,(1)suggests that the transport coefficient increases inproportion to the square root of the ion atomic
mass number for the same ion temperature Ti(where ρ, vt, L, m, and B denote the ion thermal
gyroradius, the thermal speed, the equilibrium
scale-length, the ion mass, and the magnetic fieldstrength, respectively). Equation (1) implies thatthe confinement may degrade in the deuterium
discharge with respect to the hydrogen plasma.
However, the various tokamak experiments reporta more favorable ion mass scaling of the energy
confinement time than the gyro-Bohm one andthe lower power threshold of the H-mode
transition.
The isotope effect on the plasma transport isone of the main issues in non-axisymmetricsystems, such as the Large Helical Device (LHD)[2]. The LHD deuterium experiment project aims
“to clarify the mass dependence (isotope effect)in the plasma confinement, leading toestablishment of a model for the burning
experiment using deuterium and tritium” [3].
The theoretical understanding on the isotope
effects is still not mature, while the gyrokinetic
simulation of the plasma turbulent transport madea tremendous progress in the last two decades.
The conventional local transport model leads tothe gyro-Bohm scaling by construction, even witha numerical coefficient for Eq. (1) involving
dependences on various plasma parameters.
In the transport analysis of tokamak plasmas,thus, a sheared poloidal E x B rotation isincorporated causing an additional ion massdependence of the turbulent transport to thegyro-Bohm through difference of the Machnumber.
In contrast, in non-axisymmetric systems, anequilibrium-scale radial electric field (Er) isgenerated by the neoclassical transport, andimproves the collisionless orbits of helical ripple
trapped particles. Recent theory and simulations ofzonal flows in helical systems have opened a newroute to possibly suggest the isotope effects on theplasma turbulent transport, where the zonal flow
response turns out to be enhanced by theequilibrium scale Er. [4-6].
In this article, we briefly describe possible
physics mechanisms of the isotope effect on theturbulent transport expected in the deuterium
experiments in LHD.
2. Theory of Zonal Flow Enhancement in HelicalSystems
Zonal flows with the constant electrostatic
potential on flux surfaces in a torus are generated
by the Reynolds stress of turbulence, and regulate
the turbulent transport. Effective generation of thezonal flow is thought to be a key for lowering theanomalous transport. In helical systems, the zonal
flow generation is enhanced by optimization of theconfinement field structure with slower radial driftof helical-ripple trapped particles [7-8]. The
theoretical prediction is verified by gyrokinetic
simulations of the ion temperature gradient (ITG)
turbulence [9].

The idea of the zonal flow enhancement isextended to helical configurations with theequilibrium radial electric field Er which isgeneratedby
theneoclassicaltransport.
Improvement of the collisionless particle orbits by
Er leads to enhancement of the zonal flow response
kernel, where the residual zonal flow [10]amplitude increases as the poloidal Mach number(Mp) of the E x B rotation [4,5].
The neoclassical transport analysis for thehydrogen and deuterium plasmas in LHD showsthat magnitude of the equilibrium-scale Er is
insensitive to the ion mass. It means that thepoloidal flow with higher Mp is expected forlarger ion mass, if the same ion temperature isachieved. Therefore, the Mp-dependence of thezonal flow enhancement is translated into theion-mass dependence. This could be an origin of theisotope effects on the turbulent transport in LHD
plasmas.
3. Simulation of Zonal Flow Enhancement inLHD
The zonal flow enhancement by Er has recently
been confirmed by means of the gyrokinetic
simulations using GKV code [6]. The residual zonalflow amplitudes given by the GKV simulation for amodel LHD configuration with the inward-shiftedmagnetic axis position are summarized in Fig. 1 asa function of Mp. The dashed line indicates thetheoretical prediction of the residual zonal flowlevel in the long wavelength limit in the radial
direction (kr=0). A quantitatively good agreement isfound between the theory and simulation. One findsthat the residual zonal flow amplitude rapidlyincreases in the Mp-range relevant to the LHD
Inward-Shifted Model

Residual Zonal Flow

0.10.08kr = 0.065
Theory (kr=0)

0.06
0.04
0.02
00 0.05 0.1 0.15 0.2 0.25 0.3
Poloidal Mach Number (Mp)

Fig.1. Poloidal Mach number dependence of the residual
zonal flow obtained by gyrokinetic simulation for theLHD model configuration with the inward-shiftedmagnetic axis position [6].

experiments. For example, the residual level isamplified more than two times when Mp is changed
from 0.1 to 0.15. Thus, the increase of the ion massfrom the hydrogen to the deuterium results in thestronger response of zonal flows to a source givenby the turbulence. The nonlinear gyrokinetic
simulations of the ITG turbulence for the LHD
model configuration with Er also suggest effective
zonal flow generation in case with finite Mp [6].
4. Summary
In this article, we have described a possible
isotope effect on turbulent transport expected in thedeuterium experiment in LHD. The zonal flow
response enhancement by the equilibrium-scale
radial electric field is confirmed by both thegyrokientic theory and simulation. Coupling of theneoclassical transport, the zonal flow enhancement,
and the resultant turbulent regulation, thus, is
expected to bring the ion-mass dependence of theturbulent transport in helical systems with morefavorable isotope scaling than the gyro-Bohm one.
Acknowledgments
This work is supported in part by grants-in-aid ofthe MEXT (No. 21560861 and 22760660), and inpart by the National Institute for Fusion Science(NIFS)
Collaborative
Research
Program(NIFS10KTAT040,NIFS10KDAT020,andNIFS10KNXN186). Simulations are carried out by
use of the Plasma Simulator system at NIFS.
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