Bounds on Plasma Instability Growth Rates

Abstract

A method is presented for obtaining upper bounds on the growth rate of plasma instabilities predicted by the linearized Vlasov equation. The technique is applicable to spatially nonuniform equilibria not amenable to conventional analysis. As examples, radially confined arc columns and mirror machine configurations are discussed. The fastest growth in these systems corresponds to that of known electrostatic instabilities in uniform, infinite plasmas. For arbitrary equilibria, it is shown that growth is always slower than some exponential, the plasma frequency being a typical maximum growth constant. Growth is strongly limited for equilibria ``near'' a stable state. For example, the streaming instability growth rate vanishes at least linearly with the streaming speed.