Quasi-neutral Vlasov stability

Abstract

The Vlasov stability principle of Schindler–Pfirsch–Wobig operates with an implicitly defined functional V(a) = W(a, φ[a]), where W(a, φ) is given explicitly, but φ[a] is the solution of a perturbed Poisson equation that relates the perturbation of the electric potential, φ, to that of the flux function, a. Furthermore, in W the stationary and perturbed quantities are interwoven in a complicated manner. Here, using an operator formalism, we separate stationary and perturbed quantities. Then, in the quasi-neutral approximation, we construct the general solution φqn[a] of the quasi-neutrality condition and arrive at an explicit formula for Vqn(a).