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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 e 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...

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