THERMAL-EQUILIBRIUM PROPERTIES OF AN INTENSE RELATIVISTIC ELECTRON-BEAM

The thermal equilibrium properties of an intense relativistic electron beam with distribution function fb0 = Zb -1exp[ - (H - βbcPz - ω bPθ) /T] are investigated. This choice of f b0 allows for a mean azimuthal rotation of the beam electrons (when ωb≠0), and corresponds to an important generalization of the distribution function first analyzed by Bennett. Beam equilibrium properties, including axial velocity profile Vzb 0(r), azimuthal velocity profile Vθb0(r), beam temperature profile Tb0(r), beam density profile nb0(r), and equilibrium self-field profiles, are calculated for a broad range of system parameters. For appropriate choice of beam rotation velocity ωb, it is found that radially confined equilibrium solutions [with nb0(r→∞) = 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 ωb- < ωb < ωb+ for 0 ≤ (2ω̂pb2/ωcb2) (1 - f - βb2) ≤ 1, and 0 < ωb < ωcb for (2ω̂pb2/ ωcb2) (1 - f - βb2) < 0. Here, ωcb = eB0/γb mc is the relativistic cyclotron frequency, ωpb = (4πn̂ be2/γbm)1/2 is the on-axis (r = 0) plasma frequency, f = ni0(r)/nb 0(r) = const is the fractional charge neutralization, βbc = (1 - 1/γb2)1/2c is the mean axial velocity of the beam, and ωb± = (ωcb/2) {1±[1 - (2ω̂pb 2/ωcb2) (1 - f - βb 2)] 1/2} are the allowed equilibrium rotation frequencies in the limit of a cold electron beam(T→0) with uniform density n̂b. © 1979 American Institute of Physics.