Stability of a partially compensated electron beam

The author discusses the conditions for stability of a partially compensated electron beam in relation to deflection (“snaking”). It is shown that, with a continuous spectrum of perturbation wave vectors, there is always a region of strong instability (with relatively large increments). With a discrete spectrum (e.g., with a beam of finite length in an accelerator), instability occurs only at beam currents greater than a certain critical value. Landau damping and radiation friction do not eliminate the instability. A weak dissipative instability is discovered, caused by radiation friction. In some cases Landau damping stabilizes this instability, but can also increase it.The investigation is based on a model beam in the form of two pinches, electron and ion, with constant dimensions and uniform densities.