Nonlinear δf particle simulations of collective effects in high-intensity bunched beams

The collective effects in high-intensity bunched beams are described self-consistently by the nonlinear VlasovMaxwell equations. The nonlinear δf method, a particle simulation method for solving the nonlinear Vlasov-Maxwell equations, is being used to study the collective effects in high-intensity bunched beams. The δf method, as a nonlinear perturbative scheme, splits the distribution function into equilibrium and perturbed parts. The perturbed distribution function is represented as a weighted summation over discrete particles, where the particle orbits are advanced by equations of motion in the focusing field and self-generated fields, and the particle weights are advanced by the coupling between the perturbed fields and the zero-order distribution function. The nonlinear δf method exhibits minimal noise and accuracy problems in comparison with standard particle-in-cell simulations. A self-consistent kinetic equilibrium is first established for high intensity bunched beams. Then, the collective excitations of the equilibrium are systematically investigated using the δf method implemented in the Beam Equilibrium Stability and Transport (BEST) code.