Thermal equilibrium properties of an intense relativistic electron beam
Abstract
The thermal equilibrium properties of an intense relativistic electron beam with distribution function f^{0}_{b}=Z^{1}_{b}exp[(Hβ_{b}cP_{z}ω_{b}P_{ϑ}) /T] are investigated. This choice of f^{0}_{b} allows for a mean azimuthal rotation of the beam electrons (when ω_{b}≠0), and corresponds to an important generalization of the distribution function first analyzed by Bennett. Beam equilibrium properties, including axial velocity profile V^{0}_{zb}(r), azimuthal velocity profile V^{0}_{ϑb}(r), beam temperature profile T^{0}_{b}(r), beam density profile n^{0}_{b}(r), and equilibrium selffield profiles, are calculated for a broad range of system parameters. For appropriate choice of beam rotation velocity ω_{b}, it is found that radially confined equilibrium solutions [with n^{0}_{b}(r→∞) =0] exist even in the absence of a partially neutralizing ion background that weakens the repulsive spacecharge force. The necessary and sufficient conditions for radially confined equilibria are ω^{}_{b}<ω_{b}<ω^{+}_{b} for 0⩽ (2ω̂^{2}_{pb} /ω^{2}_{cb}) (1fβ^{2}_{b}) ⩽1, and 0<ω_{b}<ω_{cb} for (2ω̂^{2}_{pb}/ω^{2}_{cb}) (1fβ^{2}_{b}) <0. Here, ω_{cb}=eB_{0}/γ_{b} mc is the relativistic cyclotron frequency, ω_{pb}= (4πn̂_{b}e^{2}/γ_{b}m)^{1/2} is the onaxis (r=0) plasma frequency, f=n^{0}_{i}(r)/n^{0}_{b}(r) = const is the fractional charge neutralization, β_{b}c= (11/γ^{2}_{b})^{1/2}c is the mean axial velocity of the beam, and ω^{±}_{b}= (ω_{cb}/2) {1±[1(2ω̂^{2}_{pb}/ω^{2}_{cb}) (1fβ^{2}_{b})] ^{1/2}} are the allowed equilibrium rotation frequencies in the limit of a cold electron beam(T→0) with uniform density n̂_{b}.
 Publication:

Physics of Fluids
 Pub Date:
 July 1979
 DOI:
 10.1063/1.862750
 Bibcode:
 1979PhFl...22.1375D
 Keywords:

 Relativistic Electron Beams;
 Thermodynamic Equilibrium;
 Distribution Functions;
 Graphs (Charts);
 Numerical Analysis;
 Temperature Profiles;
 Velocity Distribution;
 Nuclear and HighEnergy Physics