Abstract
A study of the filamentation of a radially bounded relativistic electron beam propagating through a background plasma is presented. Through a careful consideration of all relevant boundary terms, both geometrically modified bulk as well as surface waves are exhibited. Approximate formulae for the growth rates of the two species of modes are derived. While no finite geometry effects arise to vitiate the stability criteria previously derived for the bulk modes in the homogeneous case, that found for the surface modes is slightly more stringent. Stability requires an external magnetic field twice as strong as that predicted by previous analyses. This added stringency is created by additional terms in the boundary conditions, which are displayed here for the first time. Selected numerical results demonstrate that the filamentation instability is unlikely to be the source of the strong beam disruption observed in recent experiments.
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