NONLINEAR QUANTUM-THEORY OF INTERACTION OF CHARGED-PARTICLES AND MONOCHROMATIC RADIATION IN A MEDIUM

We study the quantum theory of nonlinear interaction of charged partic les and a given field of plane-transverse electromagnetic radiation in a medium. Using the exact solution of the generalized Lame equation, we find the nonlinear solution of the Mathieu equation to which the re lativistic quantum equation of particle motion in the field of a monoc hromatic wave in the medium reduces if one ignores the spin-spin inter action (the Klein-Gordon equation). We study the stability of solution s of the generalized Lame equation and find a class of bounded solutio ns corresponding to the wave function of the particle. On the basis of this solution we establish that the particle states in a stimulated C herenkov process form bands. Depending on the wave intensity and polar ization, such a band structure describes both bound particle-wave stat es (capture) and states in the continuous spectrum. It is obvious that in a plasma there can be no such bands, since bound states of a parti cle with a transverse wave whose phase velocity upsilon(ph) is higher than c are impossible in this case. The method developed in the paper can be applied to a broad class of problems reducible to the solution of the Mathieu equation. (C) 1998 American Institute of Physics.