Radiation and energy loss of an electron in an infinitely long wave-guide filled with a linear medium

摘要

This chapter deals with the electromagnetic fields excited by a single electron with prescribed motion in an infinitely long cylindrical space surrounded by perfectly conducting walls, and filled with a uniform linear medium. The medium is assumed to be lossy in order to avoid complexities arising from the radiation condition.nThe problem is attacked by first obtaining a general expression for the electric Hertz vector. From this Hertz vector the electric fields are calculated for (1) uniform motion of the electron parallel to the axis of a wave-guide of arbitrary cross section (2) uniform but longitudinally oscillatory motion and (3) undulating notion with constant velocity parallel to the axis of a rectangular wave-guide.