Generation of initial Vlasov distributions for simulation of charged particle beams with high space-charge intensity

Self-consistent Vlasov simulations of beams with high space-charge intensity often require specification of initial phase-space distributions that reflect properties of a beam that is well adapted to the transport channel, both in terms of low-order rms (envelope) properties as well as the higher-order phase-space structure. Here, we first review broad classes of distributions commonly in use as initial Vlasov distributions in simulations of beams with intense space-charge fields including: the Kapchinskij-Vladimirskij (KV) equilibrium, continuous-focusing equilibria with specific detailed examples, and various non-equilibrium distributions, such as the semi-Gaussian distribution and distributions formed from specified functions of linear-field Courant-Snyder invariants. Important practical details necessary to specify these distributions in terms of usual accelerator inputs are presented in a unified format. Building on this presentation, a new class of approximate initial distributions are constructed using transformations that preserve linear-focusing single-particle Courant-Snyder invariants to map initial continuous-focusing equilibrium distributions to a form more appropriate for non-continuous focusing channels. Self-consistent particle-in-cell simulations are employed to show that the approximate initial distributions generated in this manner are better adapted to the focusing channels for beams with high space-charge intensity. This improved capability enables simulation applications that more precisely probe intrinsic stability properties and machine performance.