Model equations from gyrokinetic theory for a non-neutral plasma to include temperature effects and applications to a plasma of infinite length

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Abstract
Gyrokinetic equations are derived for applications to non-neutral plasmas in constant, straight magnetic fields wherein E×B drift velocities are of the same order as thermal velocities. The ratio of the E×B rotation frequency to the cyclotron frequency and the ratio of the gyroradius to a plasma scale length are assumed to be of order ε and terms are retained in the gyrokinetic expansion to second order to include finite-Larmor-radius (FLR) effects. A mode equation is obtained for a non-neutral plasma in the infinite-length approximation. The singularities of this equation are compared and contrasted with the familiar mode equation from the cold-fluid approximation. A numerical investigation of m=1 perturbations for a pure electron plasma with parameters chosen to closely approximate those in the report by Driscoll [Phys. Rev. Lett. 64, 645 (1990)] reveals no exponentially unstable modes with significant growth rates and strongly suggests that finite temperature is not the source of the exponential growth seen in the experiments.