Nonlinear δF simulation studies of intense non-neutral beam propagation in a solenoidal focusing field

This paper makes use of the nonlinear δF formalism and the Vlasov–Poisson equations to describe the propagation of an intense, nonneutral ion beam through a periodic solenoidal focusing field in the thin–beam approximation. The nonlinear δF-formalism is developed for numerical simulation applications by dividing the total distribution function Fb into a zero-order part (Fb0) plus a perturbation (δFb) which evolves nonlinearly in the zero-order and perturbed field configurations. To illustrate the application of the technique, nonlinear δF simulation results are presented for a thermal equilibrium background distribution Fb0(H⊥) for the case of beam propagation through a uniform focusing field.