Drift-ideal magnetohydrodynamic simulations of m = 0 modes in Z-pinch plasmas

The effects of m = 0 modes on equilibrium Z-pinch plasmas are studied in this paper using a drift-ideal magnetohydrodynamic (MHD) model. The model equations are an extension of ideal MHD to include finite-ion-inertial-length/cyclotron-frequency (Ωi) effects in Ohm's law and in the electron and ion heat transport equations. The linear modes contained in this model include the ideal interchange (sausage) mode and in the magnetized limit, Ωiτi≫1 with τi the ion collision time, nonideal entropy modes. It is well known that these two modes are decoupled in the kρs≪1 limit, where k is the axial mode number and ρs=cs/Ωi is the gyro-Bohm scale with cs the sound speed [B. Kadomtsev, Sov. Phys. JETP-USSR 10, 780 (1960)]. For Bennett equilibrium profiles, it is shown that the regions of stability for both modes are completely governed by the adiabatic coefficient γ in these limits. Equilibria with Bennett profiles are stable to entropy modes for γ < 2 but unstable to ideal modes and vice versa for γ > 2. However, these modes are no longer decoupled when kρs≳1. The simulation results of the fully nonlinear set of equations in the magnetized limit show that seeded modes with kρs≳1 and γ = 5/3 display the characteristics of both ideal and entropy modes. The general heat flux for both ions and electrons as a function of the species magnetization is retained in the model. Both the linear and nonlinear behaviors of seeded modes for kρs≳1 display a strong dependence on the magnetization of the ions. The growth rate increases linearly with k at large kρs when the ions are magnetized but decreases with increasing k when Ωiτi≲1.