Finite-Larmor-radius stabilization in a sharp-boundary Vlasov-fluid screw pinch

Abstract

Starting from the basic equations of the Vlasov-fluid model, assuming small ion Larmor radii, and assuming unstable, long-wavelength perturbations in a sharp-boundary screw pinch whose equilibrium distribution of ion velocities is isotropic, a derivation is presented of the dependence upon ξ⊥(r) and its derivatives of the dominant terms in perturbations of the ion distribution, the ion number density, the ion fluid velocity, the pressure tensor, and the heat flux vector. A differential equation governing ξ⊥(r) is derived and solved. A dispersion relation for a perturbation with arbitrary azimuthal mode number is derived by application of boundary conditions appropriate for a sharp-boundary screw pinch. It is found that ideal magnetohydrodynamics and the Vlasov-fluid model yield identical dispersion relations only for an m=1 mode. For m⩾2, the Vlasov-fluid model yields a damping of the ideal magnetohydrodynamic growth rate with increasing ion temperature. The m=2 instability is extinguished at an ion temperature equal to one-fourth of that given by Freidberg’s analysis. This result allows greater leeway for wall stabilization of m=1 modes while maintaining finite-Larmor-radius stabilization of m=2 modes in theta-pinch machines, such as scyllac.