B.A. Carreras

K. Ichiguchi

National Institute for Fusion Science (NIFS-Repository)

Fig. 1: Time evolution of kinetic energy and beta values.Fig. 2: Profiles of average pressure and rotational trans-form.1.0<0.50.80.62/31/23/70.42/5800000.040000 60000t20000- 1.0I- - - t=82600'tA I/// -I-/-----------<P>1.02) K.Ichiguchi, B.A.Carreras, J. Plasma Fusion Res. SE-RIES 8 (2009) 1171.00 0.2 0.4 0.6 0.8Pis considered to be the stabilizing mechanism of the LHDplasma.Furthermore, both the continuous heating and thebackground pressure diffusion have an effect to smoothout the local flat structure and also influence the interac-tion between the modes. Under the situation, the plasmais continuously self-organized as the beta increases sothat the vortices of all of the modes should not overlap asa whole. Such self-organization can be obtained only inthe analysis including the beta-increasing effect. The re-sult obtained here indicates the existence of a stable pathto the high beta regime obtained in the experiments.1) Ichiguchi , K. et al. , Nucl. Fusion 43 , 1101-1109(2003).Multi-Scale MHD Simulation of LHDPlasma Including Continuous Heating andBackground Pressure DiffusionIchiguchi, K., Carreras, B. A. (BACV SolutionsInc.)In experiments in the Large Helical Device (LHD),high beta plasmas have been successfully obtained. Par-ticularly, average beta of ((3) = was achieved in theconfiguration with the vacuum magnetic axis located atRax = 3.6m. On the contrary, in this configuration,equilibria calculated under the assumption of a parabolicpressure profile that is close to the profile observed in theexperiments are unstable against linear ideal interchangemodes at much lower beta values than 5%. We investi-gate the mechanism from the point of nonlinear MHDdynamics of the plasmal). Since the stability propertystrongly depends on the beta value, we develop a multi-scale simulation scheme including beta-increasing effectsbased on the reduced MHD equations. In the scheme, ef-fects of continuous heating and diffusion of backgroundpressure are incorporated in the equation for the averagepressure. Particularly in the present work, we control theheat source term in the equation so that the beta valueshould increase in a constant rate. This control makesit possible to avoid the saturation of the beta value dueto the diffusion of the total pressure, which is observedin the original work2) under the assumption of a fixedheat source, and to examine the time trace of the plasmabehavior up to any high beta value in principle. By ap-plying the scheme to the LHD plasma, we obtain a timeevolution up to a beta value much higher than that inthe calculation with the fixed heat source.In the analysis of the LHD plasma, we follow thenonlinear evolution by using the heating source termQ given by Q = Qo(l - p2)(1 - p8) , where p denotesthe square root of the normalized toroidal magnetic flux .The amount of Qo is controlled so that the increasingrate of ((3) should be fixed to 0.5 x 1O-5%/TA as shownin Fig.1, where A denotes the Alfven time. In this cal-culation, we treat time evolution of equilibrium and per-turbed quantities with different time scales simultane-ously by iterating the calculations of the equilibrium andthe nonlinear dynamics.As is also shown in Fig. 1, unstable modes areexcited weakly and saturated immediately during thetime evolution of the plasma. A mode-overlapping whichcauses a disruptive phenomenon is suppressed during theevolution. The suppression is attributed to deforma-tion of the background pressure profile. As shown inFig.2, the weak excitations generate local flat structurearound the resonant surfaces. Such structure decreasesthe driving force of the modes and reduces the growth athigher beta. Therefore, the local reduction of the back-ground pressure gradient due to the nonlinear dynamics196§1. lti- c l  MHD Simulation of LHD Plas a Including Continuous Heating and Background Pressure DiffusionIchiguchi, K., Carreras, B.A. ( ACV Solutions Inc.)

Multi-Scale MHD Simulation of LHD Plasma Including Continuous Heating and Background Pressure Diffusion

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