Dissipative instability of overlimiting electron beam

Summary form only given, as follows. The phenomenon of dissipative instability in systems with an electron beam is well known. The presence of dissipation in these systems (particle collision in plasma, energy radiation, heating of metallic surfaces etc.) leads not to suppression of the well-known beam instability, but to the instability of another type caused by dissipation. The physical nature of this phenomenon is in that the dissipation serves as an additional channel of energy withdrawal and it leads to excitation of beam wave with negative energy. If beam current in the plasma-filled systems exceeds the limiting vacuum current traditional concepts of beam plasma instability cease to be valid. Even in the absence of dissipation the instability is due either to excitation of the beam wave with negative energy or to aperiodical modulation of beam density in medium with negative dielectric constant. In such systems dissipative beam instability has more critical dependence on the parameter characterizing dissipation. In the present report the dissipative instability of the overlimiting electron beam in a plasma-filled waveguide is investigated and the growth rate is obtained. As expected it has more critical (as compared with sublimiting beams) dependence on the effective collision frequency. Namely it is inverse proportional. An equation describing the influence of dissipation on space-time development of the fields is derived and solved. An analytical expression for the fields´ development dynamics and space structure are obtained. It is shown that dissipation suppresses the slowest perturbations and the wave train shortens. Results are compared with the case of a sublimiting beam. An approach is presented that allow the dissipative instability of the overlimiting beams in plasma-filled systems of arbitrary geometry to be considered.