Vlasov Simulation with FARSIGHT and Unlimited Photon Acceleration

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 particle 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, (PAInf), a scheme for dephasingless photon acceleration in a particle-beam-driven wake. Photon acceleration and deceleration occurs when electromagnetic radiation experiences a time-varying plasma density; the time-varying density causes frequency changes in the laser pulse. In PAInf, a relativistic electron bunch propagates through a plasma and leaves density variations in its wake. A laser pulse propagates behind the electron beam so as to experience a region of frequency-upshifting density variation in the wake. Using a tapered density profile to keep the laser pulse at the phase in the wake where the frequency of the pulse is increasing, simulations suggest that the laser pulse can see sustained frequency shift, as well as energy gain, intensity enhancement, and pulse compression. 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. It is mathematically demonstrated that the frequency shift of the laser pulse is limited only by the ability to maintain the wake, that is, the photon acceleration is unlimited.PhDApplied and Interdisciplinary MathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/172624/1/ryansand_1.pd