Instabilities in compensated electron ring beams

An analysis is performed of the coherent instabilities which can develop in electron ring beams when an ion component is present in the beam. Increments of the instabilities are introduced, and it is shown that the compensation of an electron beam by ions results in a weakening of the instabilities characteristic of purely electron beams. The most rapidly growing coherent instabilities are determined, and possible methods are pointed out for their stabilization.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 37–53, January, 1978.