Vlasov Equilibria and Stability of an Electron Gas

Self-consistent Vlasov equilibria with space charge are constructed for a pure electron gas radially confined in a uniform external magnetic field. A sufficient condition is obtained for the stability of these nonuniform equilibria to electrostatic perturbations. For the case in which the electron density is constant in the column interior, the dispersion relations for small-amplitude interior perturbations, electrostatic and electromagnetic, are shown to be similar in structure to the corresponding results for a neutral plasma. Algorithms are given for obtaining electron gas stability information from the neutral plasma literature.