Abstract
Slow cyclotron and Cherenkov instabilities are analyzed self-consistently for unbounded and cylindrical slow wave systems considering electron beam propagating along the direction of a guiding magnetic field. There are two electromagnetic modes present in the beam that are self-consistent solutions of Maxwell's equations. The wave equation in the beam becomes the Altar-Appelton-Hartree equation in the limit of zero beam velocity. For the unbounded system, the beam couples with the electromagnetic modes corresponding to the X and O modes, resulting in the slow cyclotron and Cherenkov instabilities, respectively. For the cylindrical system, axisymmetric electromagnetic modes in the beam are obtained by superposing the plane normal modes of the unbounded system. Since self-consistent boundary conditions require all field components, axisymmetric electromagnetic modes of cylindrical system are hybrid modes, which are classified as axisymmetric EH and HE modes. The slow cyclotron and Cherenkov instabilities occur for both axisymmetric modes. The temporal growth rate is calculated for each of the instabilities and compared.
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