Abstract
Stability conditions of high-current thin beams of relativistic electrons against excitation of long-wave oscillations in a stellatron and modified betatron have been investigated theoretically. The influence of self electric and magnetic fields obtained from electron beam delayed potentials has been taken into consideration. The correspondent dispersion relation has been found. The electron beam of the modified betatron has been shown to be always unstable against excitation of the oscillations considered. Necessary and sufficient conditions for the elec-tron beam confinement in a stellatron have been found.
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