Theoretical investigations of absolute and convective instabilities in beam-plasma systems

The Cherenkov interaction of a mono-energetic electron beam with the upper branch plasma wave of a cylindrical, homogeneous, Maxwellian magnetoplasma is investigated in the linear and nonlinear regimes. From linear theory the appropriate dispersion relation is derived and solved numerically to obtain conditions for the existence of the absolute and convective instabiities. The instability is shown to be convective when the group velocity of the plasma wave is positive, and is absolute when the group velocity is negative and the beam density exceeds a threshold density. Expressions for this are derived from a simplified form of the dispersion relation valid in the weak beam limit. A computer simulation is used to study the nonlinear regime. When a single mode dominates the instability, beam trapping is shown to be the limiting mechanism for further growth. In the case of the absolute instability a second nonlinear limit is obtained, where long term temporal oscillations are observed. This occurs at relatively high beam densities, at lower densities, following saturation a steady state results. The predictions of this theoretical study agree closely with experimental observations