Transverse dynamics of a relativistic electron beam in an underdense plasma channel

The transverse dynamics of a relativistic electron beam in a plasma less dense than the beam is analyzed, with particular attention to the electron-hose instability as it appears in a plasma channel of finite radius. A comparison is made between analytic asymptotic forms, linearized "beam break-up" simulations, and particle-in-cell simulations. The analysis provides a framework for the interpretation of projected and time-resolved diagnostics in such a system. Examples used for illustration correspond to parameters of an experiment in progress, employing a 30 GeV electron beam in a 1.5 m plasma cell, with the amplification of beam-centroid offsets on the order of 10⁰-10²×, depending on experimental settings.