Ideal magnetohydrodynamics stability spectrum with a resistive wall

The eigenvalue equations describing a cylindrical ideal magnetohydrodynamics plasma interacting with a thin resistive wall are presented in the standard mathematical form, A · x=λB · x, without discretizing the vacuum regions surrounding the plasma. This is accomplished by using a finite-element basis for the plasma perturbations, and by coupling the plasma surface perturbations to the perturbed electrical current in the wall using a Green's-function approach. The perturbed wall current introduces a single additional degree of freedom into the system, which, together with an auxiliary variable, u=ωξ, allows the system to take the standard linear form. The standard form allows the use of linear eigenvalue solvers, without additional iterations, to compute the complete spectrum of plasma modes in the presence of a surrounding resistive wall at arbitrary separation. Standard results are recovered in the limits of (i) an infinitely resistive wall (no wall), and (ii) a zero resistance wall (ideal wall).