Proof of a quasi linear equation for a bounded beam

A theoretical investigation is made of the problem of quasilinear relaxation of a bounded plane - parallel beam. A derivation is given of a quasilinear transport equation for a bounded beam allowing for specular reflection of electrons by the confining walls; this equation is solved explicitly for a monoenergetic beam. It is shown that at the hydrodynamic stage the quasilinear relaxation of abounded beam is of the same nature as the relaxation of an unbounded beam. A characteristic feature of the relaxation is an inhomogeneity of the electron temperature distribution across the direction of motion.