Kinetic description of intense nonneutral beam propagation through a periodic focusing field

Abstract

This article makes use of the nonlinear Vlasov–Poisson equations to investigate intense nonneutral beam propagation through a periodic solenoidal focusing field B sol ( x)=B z(s) e ̂ z−( 1 2 )B z′(s)(x e ̂ x+y e ̂ y) , where B z ( s+ S)= B z ( s), and S the axial length periodicity is a constant. The analysis is carried out for a thin beam with characteristic beam radius r b⪡ S, and the transverse momentum components and axial momentum spread of the beam particles are assumed to be small in comparison with the directed axial momentum γ b mβ b c. The general formalism is applied to a periodically focused Vlasov equilibrium with step-function radial density profile and average azimuthal motion of the beam corresponding to a rigid rotation (in the Larmor frame) about the axis of symmetry. A variety of beam equilibrium properties are presented, such as the average flow velocity, and the transverse temperature profile.