Halo Mitigation Using Nonlinear Lattices

This work shows that halos in beams with space charge effects can be controlled by combining nonlinear focusing and collimation. The study relies on Particle-in-Cell (PIC) simulations for a one dimensional, continuous focusing model. The PIC simulation results show that nonlinear focusing leads to damping of the beam oscillations thereby reducing the mismatch. It has been well established previously that reduced mismatch leads to reduced halo formation. However, the nonlinear damping is accompanied by emittance growth causing the beam to spread in phase space. As a result, inducing nonlinear damping alone cannot help mitigate the halo. To compensate for this expansion in phase space, the beam is collimated in the simulation and further evolution of the beam shows that the halo is not regenerated. The focusing model used in the PIC simulation will be briefly discussed based on a systematic analysis that has already been done through canonical averaging using Lie transform perturbation theory. This analysis shows that by averaging over a lattice period for a specific arrangement of linear and nonlinear elements, one can reduce the focusing force to a form that is identical to that used in the PIC simulation in an averaged sense, thus providing an equivalence between the model and a realistic system.