The Hose Instability Dispersion Relation

Abstract

The dispersion relation is obtained for the ``hose'' instability in a modulated beam of charged particles traveling through a finite ohmic plasma channel. For a relativistic beam, the low‐frequency mode obeys a dispersion relation of the same form as for the unmodulated beam, but it involves a constant which will have to be obtained by machine computation. For large enough modulation frequency the dispersion relation is identical to that for an unmodulated beam.