The Vlasov equation with strong mangnetic field and oscillating electric field as a model for isotop resonant separation (Q2778470)

The main object of this work is to study the influence of oscillations generated by external electric and magnetic fields on the distribution function of electrons using the Vlasov equation. In this problem, the distribution function of electrons depends upon slow and fast variables. Physical results of this paper are relevant to the isotope resonant separation problem. The method of solving a Vlasov equation which includes a small parameter (this small parameter is the ratio of the Larmour radius to the characteristic length of the system) is based on an asymptotic expansion of the distribution function. It is shown that the Vlasov equation for the distribution function may be reduced to a kinetic equation which includes a special memory term. The memory term is a pseudo-differential operator. The kernel of this pseudo-differential operator could be found by solving a Volterra equation. Kernels of the pseudo-differential operator were found explicitly for the two particular cases: a) an electric field is perpendicular to the magnetic field, b) an electric field independent of time. The authors have formulated several theorems that were proved by using Fourier transformation.