Abstract
Linear plasma fluid theory is used to study the stability of a cold electron beam in Brillouin equilibrium which passes through a stationary cold ion background, with particular interest in stability for parameters relevant to EBIS devices. Dispersion is studied both analytically and numerically. For l = 0, the usual infinite medium two stream instability condition is shown to correspond to a requirement that beam perveance exceed a minimum value, P > 33 μperv; hence, this mode is stable for EBIS ( P ≈ 1 μperv). The Brillouin equilibrium rotation is shown to cause an electron-ion rotating stream instability, which is convectively unstable. The l = 1 mode is also found to be unstable. Higher modes numbers, l > 1, are unstable, but have reduced growth. Instability is only weakly affected by finite beam radius and boundary conditions.
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