Space charge instabilities in gyrotron electron beams are studied via both the solution of the linear dispersion equation and by nonlinear particle simulation. The linear analysis addresses the stabilizing effects of energy spread in the beam and the inhomogeneity of the external magnetic field. The nonlinear multifrequency simulation demonstrates that for a uniform magnetic field, the energy spread induced by many unstable waves will be larger than the corresponding spread induced by a single unstable wave. This emphasizes the need to design electron guns that are stable to this mode.
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Li et al. (1994) studied this question.
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