Abstract
A rotating, relativistic electron beam is highly unstable if its net current is neutralized by a background plasma. The beam breaks up into a series of concentric doughnuts (ring tearing). The external magnetic field cannot inhibit this k=kz perturbation. Growth rates are calculated in the thin beam approximation. Numerical simulations bear out the linear growth times. Growth saturates when the relativistic electrons are sufficiently thermalized to satisfy a pinch equilibrium condition, and they oscillate in the magnetic wells formed by the field perturbations. An additional feature of the mode in this geometry is a radial electrostatic field which is necessary to drive the cross-field current.
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