Kinetic Equations for Plasma and Radiation

Abstract

The starting point is the Liouville equation for the density in phase space of a system of charged particles and a denumerably infinite set of field oscillators. By integrating out the coordinates of all but a finite number of particles and oscillators one obtains a chain of equations relating the reduced distribution functions. A complete solution to the chain is obtained by a generalization of the expansion method of Rosenbluth and Rostoker. In lowest order, a coupled set of self-consistent field equations in the one-particle and one-oscillator distributions is obtained. These are partially decoupled to give the usual Vlasov equation and a companion equation for the oscillator distribution. In first order one obtains a similar set of equations for the two-particle and the particle-oscillator correlation functions. An entirely similar pair of equations then relates the first-order distribution functions themselves. It appears that the general solution is obtained by the steady unfolding of higher correlation functions in terms of higher and higher self-consistent field equations. The first-order equations can be regarded as a ``Fokker-Planck'' equation for particles and a ``Fokker-Planck'' equation for radiation.