Numerical study of non-resonant mode in a heliotron plasma

Full text: In the LHD configuration with the vacuum magnetic axis located at 3.6m, sawtooth-like oscillations were observed in the soft X-ray camera system in fairly high density plasmas produced by pellet injection. The mode was localized around the magnetic axis and had m=3 mode structure. In the vacuum configuration, the rotational transform has the value of 0.35 at the axis and increases monotonously in the radial direction. Therefore, the resonant surface for (m,n)=(3,1) mode does not exist in this profile. The resonant surfaces for (m,n)=(3,2) and (3,3) exist, however, they are apart from the axis. Thus, the possibility of an unstable non-resonant mode in such configuration and the relation with the experimental result are studied numerically. In this study, we utilize the VMEC code for the calculation on of the 3D MHD equilibrium and the NORM code for the analyses of the linear stability and the nonlinear dynamics of the mode. In the linear stability analysis, we obtain an unstable non-resonant mode with (m,n)=(3,1) for a substantially peaked pressure profile. The stability results indicate that three conditions for the equilibrium are necessary for the destabilization of the non-resonant mode: steep pressure gradient around the magnetic axis, the central value of the rotational transport close to 1/3, and the existence of low shear region around the axis. To simulate the experimental results, we examine the nonlinear dynamics of the non-resonant mode in the beta increasing phase. We utilize a multi-scale numerical scheme for this analysis. We increase the average beta value continuously by adding a small pressure increment with the peaked profile used in the linear analysis. The non-resonant (m,n)=(3,1) mode grows dominantly when the destabilization conditions are satisfied in the time evolution of the plasma. Reduction of axis beta occurs repeatedly synchronizing the growth of the mode, which may correspond to the sawtooth-like oscillations in the experiment. This work is supported by NIFS cooperation programs NIFS08KLDD015 and NIFS08KNXN129 and by the Grant-in-Aid for Scientific Research (C) 17560736 of the Japan Society for the Promotion of Science. (author)