A relativistic electron beam magnetically self-focused in a plasma is
subject to an electrostatic hose instability. A linear theory of hose
growth is formulated, taking into account nonlinear focusing of the be
am and collisionless damping due to a plasma gradient. Theory is compa
red to particle-in-cell simulations of three-dimensional transport of
a beam with a Bennett profile, through a broad uniform plasma, as well
as a plasma channel matched to the beam. (C) 1997 American Institute
of Physics.