Stabilization of sausage and kink instability modes of a plasma pinch by radial oscillations

The growth of the global sausage (m=0) and kink (m=1) perturbations of a Z-pinch subject to radial oscillations is considered. It is demonstrated that the oscillations result in significant reduction of the growth rate of both kink and sausage instability modes with wavelengths long compared to the pinch radius. The analysis of stability is carried out in two ways. The first method is based on the averaging magnetohydrodynamic equations over the period of radial oscillations. The second one consists in the analysis of the growth of Fourier-components of perturbations. Numerical simulation demonstrates that even moderate radial oscillations cause reduction of the growth rate of long-wavelength sausage instabilities and complete stabilization of long kinks. This can be understood as a result of the effective gravitational field produced in the pinch by the oscillations. The effect in question can explain the anomalous stability of pinches with respect to the kink perturbations observed in experiments. copyright 1995 American Institute of Physics