Vlasov fluid stability of a skin current z-pinch

Abstract

The m=0 linear stability of a z‐pinch confined by a skin current has been studied in the collisionless regime using the Vlasov fluid model. The trajectory integrals which are normally so formidable an aspect of Vlasov fluid analyses are greatly simplified in this equilibrium and the eigenvalue equation reduces to a dispersion relation derived from the plasma edge boundary condition. For the case Te=0 and analytic solution is found in the short wavelength limit for the growth rate, which saturates at a value of π1/2vT/2a where vT is the ion thermal velocity and α is the pinch radius. This should be compared with the ideal MHD growth rate which increases without limit as k1/2 where k is the axial wavenumber. The solution with finite electron temperature is achieved by a Neumann series expansion which is shown to converge for values of Tw/Ti≤1. In the short wavelength limit with @ie=Ti the growth rate is increased from the Te=0 value by factor of 1.94.