Theoretical studies of the ion-hose instability in a plasma-focused free-electron laser

An `ion-focused´ relativistic electron beam traversing a magnetic wiggler is subject to a transverse two-steam or `in-hose´ instability, resulting from the coupling of transverse displacements of the beam centroid to the `slosh´ motion of the (beam-focused) nonneutral ion plasma, and driven by the `V×B´ deflection in the wiggler field. The equations of motion are resolved into an inhomogeneous `beam breakup´ equation, and asymptotic growth is computed in the limit of linear focusing. The effect of nonlinearities is assessed numerically with a `distributed-mass´ model. As examples, ion-hose growth is considered in a UV FEL and a microwave FEL two-beam accelerator