Magnetohydrodynamic stability of a resistive fluid limited by a nonideal boundary

Abstract

A new set of boundary conditions for a resistive plasma that takes into account the effect of a nonideal rigid wall of finite conductivity and thickness, is derived. These conditions, in cylindrical geometry, take the form of a system of integrodifferential equations involving the perturbed plasma variables v1, B1, T1, at the inner surface of the rigid wall. This system of integrodifferential equations is numerically solved, using a numerically stable scheme, and is implemented in an existing linear one-dimensional resistive initial value code, the Ripple IVA, developed by Dibiase and Killeen [Comput. Phys. 24, 158 (1977)]. An approximate solution of the problem, valid in a neighborhood of the time origin, is also derived. Attention is then focused on the linear behavior of resistive tearing and interchange modes as a function of the ratio of plasma and wall conductivity as well as the magnetic Lundquist number S, especially for high-beta equilibria of the reversed field pinch (RFP) type.

Stability of tearing and g-modes in high beta plasmas confined by non-ideal walls

“…One must remember that the whole problem is solved as an initial value problem, so that the knowledge of every function near the time origin is essential for finding the solution. To overcome this difficulty a different series expansion for the electric field components appearing in the right-hand side of equations (3), ( 4) and (5) has been derived (NALESSO, 1984) and then an approximate expression has been used which is valid when the elapsed time is shorter than the resistive diffusion time through a plane slab zd = A:,UOO.M for modes with long wavelengths ( A l k + 1) or, less restrictively, for short wavelengths, when t < AlrwpooM.…”

“…(GOEDBLOED, 1972;NALESSO, 1980)], while for the full non-ideal MHD stability (i.e. the stability of a resistive fluid with viscosity and other dissipative effects added) only recently (NALESSO, 1984) the problem has been tackled.…”