Stability analysis of dynamic Z pinches and theta pinches

The stability of diffuse, dynamic Z pinches and theta pinches is analyzed. Spectra of the growth rates of hydromagnetic instabilities of dynamic pinches are calculated. The acceleration of plasma pinches during compression and expansion strongly modifies the growth of bulk instabilities. Also, even a relatively weak axial magnetic field substantially suppresses instabilities in Z pinches, in agreement with recent experiments. The initial axial field Bz 0 needed for a stable implosion of a pinch of initial radius R0 and average current Ī is Bz 0 ≳(10–30 kG) Ī (MA)/R0(cm). The approximate analytic solutions of the linearized equations are shown to agree well with the exact numerical solutions. The stability analysis demonstrated here for dynamic pinches is broadly applicable to the stability of dynamic plasmas in general.