Three-Dimensional Normal Modes of a Magnetized Vlasov Plasma

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Abstract
The three‐dimensional velocity‐space eigenmodes of the linearized Vlasov equation for an electronic plasma, imbedded in a uniform applied magnetic field, are derived in the electrostatic limit and are shown to be complete. In general, a continuum of modes exists (except for k · B0 = 0) and, if the plasma is unstable, an additional set of discrete modes appears. It is found that a particular functional of the undisturbed distribution function plays a role (for k · B0 ≠ 0) analogous to Case's η(v) in establishing the properties of the modes. For the case k · B0 = 0, which must be treated separately, two discrete sets of modes exist, only one of which contributes to the density and field fluctuations in the electrostatic approximation.