Self-excitation in a radially bounded beam-plasma system in a strong longitudinal magnetic field

Gvozdetskii et al. have shown that self-excited oscillations, which are usually necessary in steady injection of an electron beam into a plasma, can result from the 'Pierce' feedback mechanism which arises in longitudinally bounded systems. Numerical solution of the correspondingg nonlinear equations for cold plasma permits the possible oscillation frequency and the amplitudes and spatial dependence of the eigenmodes to be calculated self-consistently as a function of the densities of the beam and plasma and the system length L. Feedback can arise when there are oppositely direct beams, and if the plasma temperature is finite, also in the case of reflected waves, but again only in a system of finite length. The condition that the longitudinal dimension L be finite is necessary for the existence of these types of feedback. Oscillations in a beam-plasma system are observed even when the beam collector is at a considerable distance, in which case it appears to have essentially no effect on them. It is shown that in principle self-excitation can occur in beam-plasma systems by virture of the finite radial extent of the electron beam and plasma. The frequencies and spatial parameters of the self-excited waves are found self-consistently in the thin-beam approximation in a longitudinal magnetic field