Vlasov fluid stability of a skin current Z pinch with finite electron pressure

Abstract

The linear stability of a Z-pinch confined by a skin current has been studied in the collisionless regime using the Vlasov fluid model for arbitrary m number. The trajectory integrals that 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, an analytic solution is found in the short-wavelength limit for the growth rate, which saturates for all m at a value of π1/2vT/2a, where vT is the ion thermal velocity and a is the pinch radius. This should be compared with the ideal magnetohydrodynamic (MHD) growth rate for the same equilibrium that increases without limit as k1/2, where k is the axial wave number. The solution with finite electron temperature is achieved by a Neumann series expansion, which is shown to converge for all finite values of Γ, the ratio of specific heats. In the short-wavelength limit with Te=Ti, the growth rates are double those for cold electrons. The deviation from this factor of two increase is always less than 10% for longer wavelengths.