Hose Instability for Relativistic Particle Beams in a Plasma Background

A macroscopic analysis is given of the low-frequency, long-wavelength instabilities of the relativistic beam-plasma configuration. A two mass approximation is used for the particle dynamics. Plasma effects are accounted for by means of a tensor conductivity whose nondiagonal elements are due to the self-magnetic field of the beam. The analysis is directed toward establishing the effect of the nondiagonal terms on growth rates. Three approximate methods of analysis are discussed. The conclusion is that the nondiagonal terms, even when large, contribute minor modifications to the dispersion law.