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 (Omega(i)) 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, Omega i tau i >> 1 with tau(i) the ion collision time, nonideal entropy modes. It is well known that these two modes are decoupled in the k rho s << 1 limit, where k is the axial mode number and rho s=cs/Omega i is the gyro-Bohm scale with c(s) 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 gamma in these limits. Equilibria with Bennett profiles are stable to entropy modes for gamma < 2 but unstable to ideal modes and vice versa for gamma > 2. However, these modes are no longer decoupled when k rho s greater than or similar to 1. The simulation results of the fully nonlinear set of equations in the magnetized limit show that seeded modes with k rho s greater than or similar to 1 and gamma = 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 k rho s greater than or similar to 1 display a strong dependence on the magnetization of the ions. The growth rate increases linearly with k at large k rho(s) when the ions are magnetized but decreases with increasing k when Omega i tau i less than or similar to 1.