Space-charge limiting currents for magnetically focused intense relativistic electron beams

The self-consistent differential equations, which describe a laminar-flow equilibrium state in a magnetically focused intense relativistic electron beam propagating inside a conducting waveguide, are presented. The canonical angular momentum, p(theta), defined under the conditions at the source, uniquely determines the possible solutions of these equations. By numerically solving these equations, the space-charge limited current and the externally applied magnetic field are obtained in a solid beam and a hollow beam in two cases of p(theta) = o (magnetically shielded source) and p(theta) = const. (immersed source) separately. It is shown that the hollow beam is more beneficial to the propagation of the intense relativistic beam through a drift tube than the solid beam.