Instability of a thin field-aligned electron beam in a plasma

Mathematics

Scientific paper

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Cold Plasmas, Electron Beams, Magnetohydrodynamic Stability, Plasma-Particle Interactions, Frequency Response, Mathematical Models, Modal Response, Phase Velocity

Scientific paper

Elliott's (1975) model and basic equations are recapitulated for a top-hat model in which the electron beam and plasma properties are uniform in the beam region, while outside the beam region there is a background plasma which is also uniform and the same on both sides. The purpose is to investigate the effect of the thinness of the beam on the mode which varies most slowly in the x-direction. For frequencies just above the plasma frequency, even a very small amount of negative Landau damping causes instability, with radiated waves propagating at a small angle to the beam. Between the electron gyrofrequency and the plasma frequency ducted modes are found. Radiative solutions are also found and plotted for the range below the gyrofrequency.

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