Nonlinear development of absolute and convective instabilities

The instability resulting from the interaction of a weak, monoenergetic electron beam with a magnetoplasma (ω>ω/subC//subE/) has been studied experimentally. A calculation, using the dispersion relation appropriate to the experiment, shows that the interaction may take the form of convective or absolute instability, depending on plasma temperature. This is in qualitative and quantitative agreement with the experiment. The convective mode has spatially amplified waves which are steady state in time. Saturation is due to beam trapping, and agrees quantitatively with a trapping calculation which includes cyclotron damping. After saturation the wave damps, which is attributed to untrapping of the beam by relatively low-level amplified plasma noise. The absolute instability is a feedback oscillation due to the negative group velocity in the plasma. It rises suddenly to large amplitude near the electron gun and has a short over-all length. There are two nonlinear states: one is steady state in time, and agrees with a beam trapping calculation for absolute instability; the second has temporal quenching, or relaxation oscillations. This is attributed to the interaction of several oscillation modes strongly coupled by the nonlinear beam dynamics. This effect may limit wave amplitudes below the value predicted by trapping theory