Stability of inhomogeneous relativistic electron beams

The authors investigate the stability of a space-bounded relativistic beam of electrons accelerated by a nonuniform electric field under conditions where the transverse dimension of the beam is significantly greater than the Debye radius and a collective approach is necessary for describing small oscillations. For currents exceeding some critical value, there may develop in such a system an instability analogous to the ‘slipping’ instability of non-relativistic electron beams with a nonuniform velocity profile. The instability conditions are established and the instability growth rates calculated both in the absence and in the presence of a strong longitudinal magnetic field. The energy spread of the electrons has a stabilizing effect on the beam instability in question. In the Annex it is shown that the slipping instability is characteristic of any non-uniform plasma flow. In particular, it may develop in an isotropic plasma if the flow velocities exceed the thermal velocity of the ions.