On Bursian and Pierce Instabilities of Electron Beams Propagating in Weakly Irregular Channels

Summary form only given. The stability of stationary states of dense electron beams propagating in weakly irregular channels, in particular, in channels with non-deep periodically corrugated walls, is investigated using the method of coupled waves. We show that Bursian´s instability can develop, leading to the formation of virtual cathodes or their disruption. In unlimited channels, separate zones of absolute and convective instabilities on the omega-k plane (Brillouin´s diagram) are possible. In a channel of finite length, these zones are merged forming the well-known Bursian´s instability in a vacuum channel or Pierce´s instability when a space charge of electrons is neutralized by immobile ions. In addition, we investigate the influences of limited conductivity of channel walls, joined elements and other irregularities.