Nonlinear perturbative electromagnetic (Darwin) particle simulation of high intensity beams

A multi-species perturbative nonlinear (deltaf) electromagnetic particle si mulation scheme has been developed for studying the propagation of intense charged particle beams in high-intensity accelerators and transport systems . The scheme is based on the Darwin approximation of Ampere's law, in which the transverse inductive electric field is neglected, resulting in the eli mination of high-frequency transverse electromagnetic effects and, conseque ntly, the associated numerical restrictions from the simulation. However, a s noted previously, the presence of the time derivative of the vector poten tial in the equations of motion for the Darwin model can cause numerical in stability. To circumvent this difficulty, we have adopted an approach by re placing the mechanical momentum, p(z) in the direction of beam propagation, by the canonical momentum, P-z = p(z) + qA(z)/c, as the phase-space variab le. The resulting Ampere's law is then modified by the presence of an addit ional shielding term associated with the skin depth of the species. In orde r to minimize the numerical noise and to easily access both linear and nonl inear regimes for the physics of interest, we have also adopted the deltaf formalism for the Darwin model. The absence of unwanted high-frequency wave s also enables us to use the adiabatic particle pushing scheme to compensat e for the mass-ratio disparities for the various species of charge. The sch eme is ideal for studying two-stream and filamentation instabilities, which may cause deterioration of the beam quality in the heavy ion fusion driver and fusion chamber. (C) 2001 Elsevier Science B.V. All rights reserved.