Abstract
An analysis of the excitation of a space charge wave and a predominantly transverse magnetic mode in a cylindrical metallic waveguide filled with a relativistic electron beam is presented. The beam is guided by a uniform, axial magnetic field of arbitrary magnitude and passes through a spatially periodic, longitudinal electric (wiggler) field. A non-linear wave equation is derived in a form which includes the coupling of TM and TE modes due to the finite axial magnetic field. For the case of a weak and purely axial wiggler field, a solution of this wave equation is developed with each of the two excited waves expressed as a sum of three partial waves. A spatial growth rate formula is derived in a form appropriate for operation infinitesimally above cut-off of the TM mode. Numerical calculations indicate that the axial magnetic field magnitude should be somewhat larger than the value which maximizes the growth rate in order to achieve high efficiency.
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