Magnetohydrodynamic instabilities of radiating Z-pinches

The stability of equilibrium states in Z-pinches is considered in this paper. In the analysis of equilibrium states, as in the study of the dynamics of small perturbations disturbing translational and axial symmetry, account was taken of the process of mutual diffusion of the plasma and the magnetic field, Ohmic heating, radiative losses and heat transfer due to electron heat conductivity. The study was prompted by the experimentally observed enhanced stability of dense Z-pinches. It has been shown that heterogeneous equilibrium states with low weighted mean heat conductivity, just like nearly isothermal Z-pinches with high heat conductivity, are stable against disturbances of heat balance but have inherent magnetohydrodynamic (MHD) instability. The core of a heterogeneous pinch is virtually unaffected by MHD modes. It has been found that the growth rates of large scale MHD instabilities for heterogeneous equilibria fall sharply when the magnetic Reynolds number calculated from the parameters of the main current carrying plasma becomes ≲ 1. On the basis of the results obtained, the authors postulate a possible non-linear stabilization of MHD instabilities in heterogeneous Z-pinches.