Method for solving the electron-wave interaction problem

We examine a solution to the equations of motion of an electron in a plane electromagnetic wave in the presence of a constant magnetic field. The problem reduces to the solution of a parametric system of equations by the Lagrange and Byurman-Lagrange methods. This approach allows us to write out the solution to the equations of motion both for the forward motion of the electron along magnetic field force lines and for its reflection by the plane wave — a multivalued solution.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 76–83, September, 1989.In conclusion, the authors wish to thank I. M. Ternov for valuable critical comments that assisted in the presented paper.