Thermal equilibrium properties of an intense ion beam with rotational and axial motion

Abstract

The Vlasov equilibrium properties of a rotating, nonrelativistic, cylindrically symmetric ion beam propagating parallel to a uniform applied magnetic field B₀ê_z are investigated. Equilibrium properties are calculated for the choice of ion beam distribution function corresponding to thermal equilibrium, i.e., f_b⁰(H,P_ϑ, P_z) = (const)exp[−(H+ω_bP_ϑ−V_z P_z)/T], where H is the energy, P_ϑ is the canonical angular momentum, P_z is the axial canonical momentum, V_z= const is the mean axial velocity, and −ω_b=const is the angular velocity of mean rotation. The investigations include: (a) exact analytical solutions in special limiting cases, (b) properties of the general solutions, (c) necessary and sufficient conditions for radially confined equilibria, and (d) numerical solutions in regimes where solutions are not accessible analytically.