Nonlinear delta F simulation studies of high-intensity ion beam propagation in a periodic focusing field

This paper makes use of the nonlinear Vlasov-Poisson equations to describe the propagation of an intense, non-neutral ion beam through a periodic focu sing solenoidal field with coupling coefficient kappa(z) (s + S) = kappa(z) (s) in the thin-beam approximation (r(b) much less than S). The nonlinear delta F formalism is developed for numerical simulation applications by div iding the total distribution function F-b into a zero-order part (F-b(0)) t hat propagates through the average focusing field <(kappa)over bar>(z) = co nst, plus a perturbation (delta F-b) which evolves nonlinearly in the zero- order and perturbed field configurations. To illustrate the application of the technique to axisymmetric, matched-beam propagation, nonlinear delta F- simulation results are presented for the case where F-b(0) corresponds to a thermal equilibrium distribution, and the oscillatory component of the cou pling coefficient, delta kappa(z)(s) = kappa(z)(s) - <(kappa)over bar>(z), turns on adiabatically over many periods S of the focusing lattice. For adi abatic turn-on of delta kappa(z)(s) over 20-100 lattice periods, the amplit ude of the mismatch oscillation is reduced by more than one order of magnit ude compared to the case where the field oscillation is turned on suddenly. Quiescent, matched-beam propagation at high beam intensities is demonstrat ed over several hundred lattice periods. (C) 1999 American Institute of Phy sics. [S1070-664(99)02401-5].