The instability of an electron beam with a finite radius in a boundless plasma

Abstract. Within the framework of a linear theory, the instability of an electron beam with a finite radius in a cold magnetised boundless plasma is considered. It is shown that a finite beam dimension influences the generation of quasi-potential waves in two aspects: the perpendicular wave number is quantised so that the frequencies of the waves are subjected to strong selection; a new kind of instability appears due to wave energy losses by emission into surrounding space. Growth rate dependence of wave numbers and frequencies is investigated for typical parameters of experiments with electron beams in space.