A new perturbation theory based on a canonical transformation for solving the Vlasov equation is developed. The theory is designed to cope with time secularities. The method is based on the transformation of orginal system to the new system where the particle is in free motion, that is, the transformed Vlasov equation is of free streaming. Practical calculation is systematic but restricted to the second order approximation in the expansion parameter (wave potential energy/particle kinetic energy). The result is used to obtain Fokker-Planck type equation, and a velocity space diffusion coefficient is obtained.
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Ichiro Kawakami (1970) studied this question.
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