Linear simulation of magnetohydrodynamic plasma response to three-dimensional magnetic perturbations in high-beta (P) plasmas

We report the numerical analyses of the linear magnetohydrodynamics (MHD) plasma response to applied three-dimensional magnetic perturbations (MPs) in a joint DIII-D/EAST collaboration on high-beta (P) (poloidal beta) plasmas, utilizing the extended-MHD code M3D-C1, with the purpose of gaining a better understanding of the existing experiment in which n = 3 MPs were applied to such high-beta (P) plasmas attempting to control large-amplitude type-I edge-localized modes (ELMs). These high-beta (P) plasmas obtained at the DIII-D tokamak feature an upper-biased double-null configuration, a high edge safety factor q (95) similar to 6.4, and a stable internal transport barrier (ITB), leading to relatively high core pressures. Single-fluid simulations show that the plasma response to n = 3 MPs, including both non-resonant/kinking and resonant components, is significantly weaker than that to n = 1 or 2 MPs. To survey the impact of q (95) on the plasma response to applied MPs, the self-consistent equilibrium-generating workflow for analysis module, developed in the OMFIT integrated modeling framework, is employed to generate a series of equilibria with a wide range of q (95), while other key parameters, including the normalized beta, electron density at the pedestal top, and plasma shape, are kept fixed. Compared to the vacuum response, single-fluid M3D-C1 simulations predict a much more significant decrease in resonant plasma response to the applied n = 3 MPs at the maximum penetration radii as q (95) increases. In contrast to single-fluid simulation results, showing that resonant penetration occurs only near the pedestal top where the E x B toroidal rotation frequency is zero, two-fluid simulations show two comparable resonant penetrations located near the pedestal top and the ITB foot, where the perpendicular electron rotation frequency is zero. Such resonant field penetration near the ITB foot may be responsible for the observed formation of a staircase structure in both the electron density and temperature profiles, and thereby a considerable deterioration in the global plasma performance, when MPs are applied in high-beta (P) plasmas. Motivated by this numerical work, we provide some ideas for future research, with the purpose of realizing effective ELM control in such high-beta (P) plasmas in the DIII-D and EAST devices.