Brillouin Flow in Relativistic Beams†

Abstract

ABSTRACT A solution in closed form for Brillouin flow under relativistic conditions in a cylindrical geometry is derived in the limit of low beam temperature. Curves and formulae are given relating density, magnetic field, energy and tangential velocity throughout the beam. In particular it is found that the forward velocity is constant to all orders in the radial coordinate, that under ultra-relativistic conditions the beam of maximum perveance has a forward velocity approaching c/√2, and that the maximum current is proportional in the ultra-relativistic limit to the square of the energy of the outermost particles.