Axisymmetric instabilities of propagating relativistic electron beams

We have used a particle simulation code SIMMO to study the axisymmetric resistive macro-instabilities of an intense pinched electron beam propagating in a plasma of high density but low initial conductivity. The (m 0, n = 1) sausage mode is found to be stable as predicted by theory, but the (m = 0, n= 2) hollowing mode is violently unstable under certain conditions, namely when there is strong avalanche ionization near the beam head and the avalanche coefficient (as a function of r) is strongly peaked on axis. The instability grows quickly into the nonlinear regime and disrupts the beam. We present results of a wide-ranging simulation study which elucidates the instability mechanism and specifies the unstable parameter range in uniform density gas.