Privileged equilibria of a collisionless homogeneous or inhomogeneous plasma

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Abstract
A statistical method for describing the collisionless (in general non‐Maxwellian) equilibria and the stability of inhomogeneous Vlasov plasmas is proposed and applied to various electrostatic cases. By means of this method the entropy and the other thermodynamic potentials can be calculated. The entropy principle allows the calculation of the electrostatic equilibria which are preferably chosen by the plasma. It is shown that the Bernstein‐Greene‐Kruskal sinusoidal wave is a maximum of the entropy provided dissipative processes are neglected. Examples are given of the general property of a collisionless system to evolve toward the marginal stability point. In one example the evolution of a bump‐in‐tail distribution toward a plateau is easily shown. It also follows from the theory that the collisionless dissipative processes always imply the excitation of short wavelength modes.

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