Relativistic beam loading, recoil-reduction, and residual-wake acceleration with a covariant retarded-potential integrator

An algorithm is demonstrated that performs first-principles tracking of relativistic charged-particles. A covariant approach is used which relies on retarded vector potentials for trajectory integration instead of performing electromagnetic field calculations. When accounting for retardation effects, the peak vector potential and corresponding Lorentz force in the direction of travel increase asymptotically for high-$β$ particles. This produces a very strong field distribution at small angles from the particle's direction of travel, which can result in considerable change in momentum when approaching a conducting surface or another charged particle. We quantify the former effect for protons and electrons at various energies and aperture sizes, where substantial power deposition can be avoided by ensuring that particles do not pass within roughly 10 microns of the aperture surface. We also simulate breaking a test particle's line of sight with a conductor or other charged body. After this instant, the test particle continues to accelerate due to residual fields, but no longer produces an opposing force on any charged or conducting object; thus any recoil on the enclosing structure is effectively reduced. Resulting acceleration dynamics are characterized using protons and electrons at various energies; with, for example, a 1% energy gain for an 85 MeV electron traversing its reflected wake while approaching a pinhole aperture. We then integrate a micro-scale dielectric laser acceleration (DLA) device into our simulations: compared with a solitary 2 mm DLA, we find a factor of two increase in energy gain when combining the DLA with a series of conducting-surface choppers.