Multistream instabilities of crossed electron beams in a plasma are investi
gated analytically. By using successively more complicated models, the inst
ability of a finite number of crossed monoenergetic beams and the instabili
ty of an infinite number of crossed monoenergetic beams with different dist
ributions in the azimuthal angle are studied. The conclusion is drawn that
an isotropic plasma is unstable against the excitation of longitudinal wave
s. (C) 2001 MAIK "Nauka/Interperiodica" .