Effect of a longitudinal wave on the self-resonant motion of electrons

The effect of the longitudinal component of an electromagnetic wave on the self-resonant motion of electrons in waveguides is considered. The equation of motion for electrons in a plane, longitudinal-transverse, circularly polarized wave has been solved by the method of successive approximations with allowance for the longitudinal integral of motion present in such a wave. The expansion parameter is the ratio of the amplitudes of the longitudinal and transverse components of the wave. For the case n < 1 the longitudinal field of the wave does not change the nature of the electron motion, but only induces weak oscillations about a solution that does not include the longitudinal field. For n > 1 with spontaneous phasing of the electrons a criterion is obtained for neglecting the effect of the longitudinal field, and numerical estimates are given.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 66–71, September, 1978.