Numerical studies on the linear and nonlinear evolutions of infernal modes

The present paper numerically investigates the linear and nonlinear evolution of infernal modes through a three-dimensional, toroidal geometric, nonlinear, and full-MHD code CLT. For equilibria with q_min ≈ 2.0, the development of the infernal modes leads to an elongated high-pressure region. We find that the nonlinear behaviors of the infernal modes can be totally different when the parallel thermal conductivity exceeds a threshold. Below this threshold, the infernal modes experience explosive growth in the nonlinear stage; above this threshold, they finally saturate in the nonlinear phase. For the cases with nonlinearly explosive growth, the patterns of the perturbed pressure are ‘ballooning-like’ and the dominant modes are with n > 1, where n is the toroidal mode number. When the parallel thermal conductivity exceeds the threshold, the parallel diffusion along the magnetic field lines is quick enough. Then the nonlinearly explosive growth is suppressed, and the infernal modes will saturate in the nonlinear stage. A two-dimensional (2D) parameter map is provided to illustrate the transition between these distinct nonlinear regimes.