This dissertation presents two bodies of work on the theoretical and numerical study of plasma waves via kinetic models, resolving the fine-scale structures that arise in phase space, and the implications for plasma-based acceleration.

First, we present the plasma simulation method FARSIGHT, a first step toward solving problems in relativistic plasma physics such as photon acceleration. It is a forward semi-Lagrangian particle method for the Vlasov-Poisson system in which the particle number density is represented on adaptively refined and remeshed panels in phase space, and an integral form of the Poisson equation is solved using a regularized electric field kernel and a GPU-accelerated hierarchical treecode. We describe the method and implementation and present numerical results encompassing Landau damping, two-stream instability, and halo formation in a particle beam. These results show the method’s ability to resolve fine-scale features in phase space.

Second, we present unlimited photon acceleration, (PA1), a scheme for dephasingless photon acceleration in a particle-beam-driven wake. Electromagnetic radiation seeing a decreasing plasma gradient shifts up in frequency. In PA1, a laser pulse is situated in the wake behind a relativistic
electron bunch so that the laser pulse sees a decreasing density gradient. It is mathematically demonstrated that the frequency shift is limited only by the ability to maintain the wake, that is, the photon acceleration is unlimited. Using a tapered density profile to keep the laser pulse at the phase in the wake where the density is decreasing, simulations suggest that the laser pulse can be
significantly modified. In one dimension, the frequency increases 25X, energy 6X, intensity 25X, and compression 33X. In quasi-3d simulations, the frequency increases 10X, energy 5X, intensity 20X, and compression 3X.

Chairs: Alec Thomas and Robert Krasny Speaker(s): Ryan Sandberg (UM)