[en] A relativistic electron beam magnetically self-focused in a plasma is subject to a transverse two stream or 'hose' instability. Linear evolution is described in terms of a tune distribution characterizing the beam, and an effective transverse impedance determined by the beam and the plasma profiles. This model is compared to cloud-in-cell simulations of three-dimensional transport of a beam with a Bennett profile, through a matched plasma channel. In the limit of large skin-depth this instability appears to be the primary limitation on stable beam transport. (author)