Influence of Dissipation on Instability of Overlimiting Electron Beam

Summary form only given. Plasma filling of microwave devices makes possible to pass through the devices e-beams with currents that are several times higher than the limiting vacuum current. This gives possibilities to increase power of output radiation. In addition plasma filling allows gradually change output frequency by changing plasma density. Theory of these devices actually considers waveguide with thin annular e-beam and coaxial thin annular plasma [Barker, R., et al., 2001; Kuzelev, M.V., et al., 1995]. With increase in beam current proper oscillations of the beam and its inner degrees of freedom play more and more important role. Space charge forces change physical character of the beam interaction with plasma. Instability of overlimiting beams can be due to growing of the beam wave with negative energy. Instability of this type comes instead of conventional beam-plasma instability in different cases: in no-uniform-cross-section waveguide with overlimiting beams, weak coupling of underlimiting beam with plasma, when the beam actually is left on its own, and increasing dissipation in the system [Rostomyan, E.V., et al., 2007]. The third case can be realized for both underlimiting and overlimiting e-beams. The growth rate of the instability caused by the growth of the beam negative energy wave attains its maximum in resonance of the beam slow wave with the plasma wave. Present investigation considers waveguide with spatially separated thin annular coaxial e-beam and plasma. Beam current is assumed to be overlimiting. Approach based on equation for polarization potential allows obtain dispersion relation comparatively easily [Rostomyan, E.V., et al., 2007]. In addition the dispersion relation has more obvious form that clearly shows interaction of the beam and plasma waves. It is shown that strong dissipation in the system transforms overlimiting e-beam instability caused by growing of the beam negative energy wave not to conventional dissipative instability w- ith growth rate ~ 1/radicnu , but to dissipative instability of new type with inverse proportional dependence on dissipation. The process of transformation is elaborated in detail and the growth rate is obtained for arbitrary value of dissipation. More critical as compared to conventional, inverse proportional dependence on dissipation nu^-1/2 to nu^-1 is result of superposition of two factors that lead to excitation of the beam wave of negative energy.