A generalization of the equations governing the evolution of a particle distribution in a random force field

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Abstract
The problem of a system of charged particles moving in a random force field and its application to the study of turbulent plasmas are discussed. We point out the inapplicability of existing formalisms to many cases of astrophysical interest. A generalization of this formalism is developed from two different points of view—a Fokker‐Planck approach and a quasilinear approach. Both approaches lead to the same equation for the evolution of the particle distribution; this equation has the form of a Fokker‐Planck equation, but the terms describing the effects of the random field do not retain the interpretation which they have in usual Fokker‐Planck development. It is shown that this equation reduces to a quasilinear diffusion equation when the random field is electromagnetic.