Ion-hose instability in a long-pulse linear induction accelerator

Abstract

The ion-hose instability is a transverse electrostatic instability which occurs on electron beams in the presence of a low-density ion channel. It is a phenomenon quite similar to the interaction between electron clouds and proton or positron beams in high-energy accelerators and storage rings. In the DARHT-2 accelerator, the 2-kA, $2\mathrm{\text{\ensuremath{-}}}\ensuremath{\mu}\mathrm{s}$ beam pulse produces an ion channel through impact ionization of the residual background gas (${10}^{\ensuremath{-}7}--{10}^{\ensuremath{-}6}\text{ }\mathrm{torr}$). A calculation of the linear growth by Briggs indicates 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 3D 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 and spatially decreasing beam radius. We find that the number of $e$-foldings experienced by a given beam slice is given approximately by an analytic expression using the local channel density at the beam slice. Hence, in the linear regime, the number of $e$-foldings increases linearly from head to tail of the beam pulse since it is proportional to the ion density. We also find that growth is strongly suppressed by nonlinear effects at relatively small oscillation 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. An analogous effect has recently been noted in electron-proton instabilities in high-energy accelerators and storage rings. For DARHT-2 parameters, we find that a pressure of $\ensuremath{\le}1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}\text{ }\mathrm{torr}$ is needed to keep the transverse beam oscillation amplitude less than about 20% of the rms beam radius.