Electron-hose instability in an annular plasma sheath

A relativistic electron beam propagating through an annular plasma sheath is subject to a transverse plasma - electron coupled electrostatic instability. From the linearized fluid equations, the beam - sheath interaction is resolved into three coupled equations. The corresponding wakefield is computed and the asymptotic linear evolution is noted. For illustration, numerical examples are given for a plasma accelerator employing such a sheath. While the coasting beam scalings are quite severe at low energy, single-bunch instability growth can in fact be reduced to nil for a very high-gradient accelerator.