Thermal equilibrium properties of an intense relativistic electron beam

The thermal equilibrium properties of an intense relativistic electron beam with distribution function f0/sub b/=Z-1/sub b/exp[-(H-β/sub b/cP/sub z/-ω/sub b/P/sub theta/) /T] are investigated. This choice of f0/sub b/ allows for a mean azimuthal rotation of the beam electrons (when ω/sub b/not =0), and corresponds to an important generalization of the distribution function first analyzed by Bennett. Beam equilibrium properties, including axial velocity profile V0/sub z/b(r), azimuthal velocity profile V0/sub thetab/(r), beam temperature profile T0/sub b/(r), beam density profile n0/sub b/(r), and equilibrium self-field profiles, are calculated for a broad range of system parameters. For appropriate choice of beam rotation velocity ω/sub b/, it is found that radially confined equilibrium solutions [with n0/sub b/(r→infinity) =0] exist even in the absence of a partially neutralizing ion background that weakens the repulsive space-charge force. The necessary and sufficient conditions for radially confined equilibria are ω-/sub b/<ω/sub b/<ω+/sub b/ for 0< or = (2omega-circumflex2/sub b/p /ω2/sub b/c) (1-f-β2/sub b/) < or =1, and 0<ω/sub b/<ω/sub b/c for (2omega-circumflex2/sub b/p/ω2/sub b/c) (1-f-β2/sub b/) <0