Kinetic description of intense nonneutral beam propagation through a periodic solenoidal focusing field based on the nonlinear Vlasov-Maxwell equations

摘要

A kinetic description of intense nonneutral beam propagation through a periodic solenoidal focusing field B(sup sol)((rvec x)) is developed. The analysis is carried out for a thin beam with characteristic beam radius r(sub b) (much-lt) S, and directed axial momentum (gamma)(sub b)m(beta)(sub b)c (in the z-direction) large compared with the transverse momentum and axial momentum spread of the beam particles. Making use of the nonlinear Vlasov-Maxwell equations for general distribution function f(sub b)((rvec x),(rvec p),t) and self-consistent electrostatic field consistent with the thin-beam approximation, the kinetic model is used to investigate detailed beam equilibrium properties for a variety of distribution functions. Examples are presented both for the case of a uniform solenoidal focusing field B(sub z)(z) = B(sub 0) = const. and for the case of a periodic solenoidal focusing field B(sub z)(z + S) = B(sub z) (z). The nonlinear Vlasov-Maxwell equations are simplified in the thin-beam approximation, and an alternative Hamiltonian formulation is developed that is particularly well-suited to intense beam propagation in periodic focusing systems. Based on the present analysis, the Vlasov-Maxwell description of intense nonneutral beam propagation through a periodic solenoidal focusing field (rvec B)(sup sol)((rvec x)) is found to be remarkably tractable and rich in physics content. The Vlasov-Maxwell formalism developed here can be extended in a straightforward manner to investigate detailed stability behavior for perturbations about specific choices of beam equilibria.