Non-local theory of the resistive hose instability of beams with the Bennett profile

The resistive hose instability of nonrelativistic counter-streaming electron and ion beams propagating through a background plasma with finite conductivity is analyzed by a non-local kinetic theory. The beam as well as the plasma have the Bennett profile and the dominant orbit of the beam particles is taken to be betatron orbits. The eigenmodes are expressed in terms of the zeroes of a Bessel function, and the non-local effects are taken into account by this integral formulation of the stability analysis. In general the eigenvalues of the resistive hose mode are numerically computed from a matrix dispersion relation. A reduced dispersion relation is derived from the general case and this may be solved analytically in the long wavelength limit. The new physical effect considered in this paper is the Landau damping due to the spread in the axial velocity. Thi effect has significant stabilizing influence on the hose eigenmode