The axisymmetric instability of a self-pinched beam with rounded radial density profile

The axisymmetric perturbations (sausage and hollowing modes) of an intense relativistic self-pinched electron beam propagating in a resistive plasma background are studied, especially for a beam with rounded radial density profile. The Bennett profiles are assumed for both the equilibrium beam current Jb(r)=Jb(0) (1+r2/R2b)−2 and plasma return current Jp(r)=−fJb(0) (1+r2/R2p)−2, where Rb and Rp are the characteristic radii of the beam and plasma return currents, respectively. It is further assumed that the electric conductivity σ(r) of the plasma channel is proportional to the return current. For a paraxial electron beam with complete space-charge neutralization by the ambient plasma, the axisymmetric modes can be destabilized by the phase lag between the magnetic field and beam current, even without the plasma return current. The plasma return current significantly modifies the growth rate of the instability such that the ratio of plasma current to beam current (−Ip/Ib=fR2p/ iR2b) largely determines the stability character of the beam. Furthermore, for the same fractional current neutralization f, the modes are highly unstable for a smaller ratio of plasma to beam radius Rp/Rb. As compared to the resistive hose instability, the growth rates for the hollowing mode can be larger than those of the hose mode, while the sausage mode is much stabler than the hose mode. Stability properties are illustrated in detail for various system parameters.