Vlasov-Fokker-Planck description of plasma stability

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Abstract
In two previous papers,1,2 the question of collisional restabilization of a linearly unstable collisionless plasma was studied using a simplified version of the collision term, namely one in which only first derivatives (with respect to the electron velocity) were retained. In the present paper, the results of references 1 and 2 are extended to the full (linearized) Fokker-Planck collision model originally introduced by Chandrasekhar.3 As in the previous papers, we study longitudinal oscillations of an infinite, one-dimensional plasma described by the equations4 where φ is the electron distribution function, EA the applied electric field and E the self-consistent field produced by the space charge density ρ. The positive ions are assumed to form an immobile background, and the entire plasma is taken to be charge neutral.

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