B.A. Carreras

K. Ichiguchi

National Institute for Fusion Science (NIFS-Repository)

HereW(p) = l P(P)(p)(y'g)dp, Sp(p) = l P Q(p) (y'g)dp,(2)where p is a radial coordinate and V9 is the Jacobian.As shown in Fig.3, the coefficient also locally enhancesaround the resonant surfaces and increases as beta. Thisproperty reflects the enhanced diffusion due to the inter-change dynamics.Fig.1 : Time evolutions of kinetic energy (Ek ), axis ((30)and average (((3)) and amount of heat source.Fig.2 : Birds eye view of pressure and mode pattern att == 166800TA.In the LHD experiments, high beta plasmas havebeen successfully obtained beyond ((3) == 5% in the con-figuration where linear ideal interchange modes are un-stable even for ((3) < 1%. We investigate the stabi-lizing mechanism utilizing a nonlinear simulation codeNORM1), which is based on the reduced MHD equations.Since the stability property strongly depends on the betavalue, we develop a multi-scale simulation scheme in-cluding beta-increasing effects. We can treat both timeevolutions of perturbed and equilibrium quantities withdifferent time scales simultaneously with this scheme. Inthe scheme, the equation for the average pressure is re-garded as a pressure transport equation, which consistsof nonlinear convection, diffusion of background pressureand continuous heating source. The heating source Q(p)is adjusted so that the beta value should increase in aconstant rate.We apply the scheme to the LHD plasma to analyzethe nonlinear dynamics in the beta increasing phase2).We have followed the dynamics up to ((3) == 1.05%. Thenumerical result shows a stable evolution of the LHDplasma with weak fluctuations as shown in Fig.1. At alow beta just larger than the marginal value, an inter-change mode is weakly excited and saturates immedi-ately because the driving force is small. The weak ex-citation generates local flat regions around the resonantsurface in the background pressure profile. Such struc-ture decreases the driving forces of the mode at higherbeta. Similar weak activity occurs for multiple modeswith different helicities simultaneously. As a result, asshown in Fig.2, each mode is localized around its reso-nant surface and the profile of the background pressurebecomes staircase-like. Thus, the local reduction of thebackground pressure gradient due to the nonlinear dy-namics is considered to be the stabilizing mechanism ofthe LHD plasma. That is, the plasma is continuouslyself-organized as a whole in the increases of beta so thatno disruptive phenomenon occurs.By utilizing the evolution of the background pres-sure profile (P) (p), we evaluate an effective diffusion co-efficient Deff , which is defined as(1)Fig.3 : Profiles of Deff .1) Ichiguchi, K. et aI., NucI. Fusion 43, 1101 (2003).2) Ichiguchi, K. et aI., NucI. Fusion 51, 053021 (2011).340§1. Multi-Scale MHD Analysis of  Beta-Increasing LHD PlasmaIchiguchi, K., Carreras, B.A. (BACV Solutions Inc.)3-1.  Fusion Plasma Simulation

Multi-Scale MHD Analysis of Beta-Increasing LHD Plasma

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