Ion-hose instability in a long-pulse accelerator

The ion-hose instability is a transverse electrostatic instability which occurs on electron beams in the presence of a low-density ion channel. In the DARHT-2 accelerator, the 2 kA, 2 microsecond beam pulse produces an ion channel through impact ionization of the residual background gas (≈1.5×10^-7 torr average). A calculation of the linear growth by R. J. Briggs indicated that the instability could be strong enough to affect the radiographic application of DARHT, which requires that transverse oscillations be small compared to the beam radius. We present semianalytical theory and 3-D particle-in-cell simulations (using the LSP code) of the linear and nonlinear growth of the instability, including the effects of the temporal change in the ion density, spatially decreasing beam radius etc. We find that the number of e-foldings for a particular beam slice is given approximately by the analytic expression for a uniform channel using an average value for the channel density. Hence, in the linear regime, the number of e-foldings increases linearly from head to tail of the beam pulse. We also find that growth is suppressed by nonlinear effects at relatively small amplitudes of the electron beam. This is because the ion oscillation amplitude is several times larger than that of the beam, allowing nonlinear effects to come into play