Abstract
The perturbative version of the asymptotic expansion method proposed by N. N. Bogoliubov is applied to the derivation of kinetic equations for a system composed of gaseous plasma and radiation field, which is assumed to be non-relativistic and classical. The approximation that ions are uniformly smeared out is used. Bogoliubov’s boundary conditions are generalized so as to be applicable to the system including the radiation field.
As the result, up to the first order with respect to the interactions, the Vlasov equation with the Lorentz-force drift term is obtained as the kinetic equation for electrons. The collision terms appearing as the second-order terms are of the form similar to those for the Kramers-Chandrasekhar type equation, in which the “diffusion coefficients” and the “frictional drag forces” are functionals of the one-body distribution functions. This is a generalization of the Landau equation, and contains the collision terms due to the interaction with the radiation field. A kinetic equation for the field oscillators is also derived. The equilibrium Maxwell-Boltzmann distribution functions for electrons and field oscillators are shown to satisfy these kinetic equations.
