UC Irvine

Electron beams can be unstable to transverse modes which form small pinch structures, as first pointed out by Weibel. Beams which are not totally self-pinched are liable to this instability, so current neutralized regions near the beam head should display it. If the background response is nonresistive, filamentation is very rapid; if an axial magnetic field is present, interchange instability is competitive and the two may not be distinguishable. Beam motion is usually dominated by the resistive region, where ( omega a/c) 2>>1, which is treated in detail. Using helical particle orbits in a uniform beam of radius a, the dispersion relation and growth rates in a number of differing cylindrical configurations are found. Because all particles have a common betatron frequency a sharp particle resonance appears, which may be broadened by energy spread in the beam. This model is most useful for beams in external axial magnetic fields, which are destabilised by electron drifts.