Streamlined Darwin methods for particle beam injectors

Physics issues that involve inductive effects, such as beam fluctuations, electromagnetic (EM) instability, or interactions with a cavity require a time-dependent simulation. The most elaborate time-dependent codes self-consistently solve Maxwell's equations and the force equation for a large number of macroparticles. Although these full EM particle-in-cell (PIC) codes have been used to study a broad range of phenomena, including beam injectors, they have several drawbacks. In an explicit solution of Maxwell's equations, the time step is restricted by a Courant condition. A second disadvantage is the production of anomalously large numerical fluctuations, caused by representing many real particles by a single computational macroparticle. Last, approximate models of internal boundaries can create nonphysical radiation in a full EM simulation. In this work, many of the problems of a fully electromagnetic simulation are avoided by using the Darwin field model. The Darwin field model is the magnetoinductive limit of Maxwell's equations, and it retains the first-order relativistic correction to the particle Lagrangian. It includes the part of the displacement current necessary to satisfy the charge-continuity equation. This feature is important for simulation of nonneutral beams. Because the Darwin model does not include the solenoidal vector component of the displacement current, it cannotmore » be used to study high-frequency phenomena or effects caused by rapid current changes. However, because wave motion is not followed, the Courant condition of a fully electromagnetic code can be exceeded. In addition, inductive effects are modeled without creating nonphysical radiation.« less