Abstract
A discussion is given of the stability conditions for a partially compensated electron beam with respect to wriggling (snaking). It is shown that in the case where the wave vectors of the perturbations have a continuous spectrum a region of strong instability (with a relatively large increment) always exists. In the case of a discrete spectrum (for example, when the beam in the accelerator has a finite length), the instability appears only for beam currents above some critical value. Neither Landau damping nor radiation friction are able to stabilize the instability. A weak dissipative instability caused by radiation friction is revealed which, in certain cases, is stabilized by Landau damping although, in other cases, it is reinforced by it. For the purpose of these investigations a model of the beam in the form of two pinches (electron and ion) having fixed dimensions and uniform densities was taken.
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