Plasma physics is the study of the dynamics of ionized gases. Because plasma, often referred to as the fourth state of matter, is the most abundant form of ordinary matter in the universe, there exist many important application problems for which an understanding would be advantageous. The motivating application for this research is high-energy particle acceleration using laser-plasma interactions. The production of high-energy particle beams is important in the process of creating synchrotron radiation, which is used for small scale imaging in many application areas including materials science, biology, and medicine. Laser-plasma acceleration is a mechanism for generating high-energy electrons by hitting a plasma with a specifically-tuned ultra-short laser beam. This approach provides the possibility to create high-energy particles with a device much smaller than standard particle accelerators. The big challenge with this approach is to be able to generate a relativistic electron beam with a small energy spread. The objective of this research is to develop highly accurate and efficient computational methods for simulating the acceleration of high-energy electrons. This research aims to develop novel computational techniques for so-called 'kinetic models' of plasma that achieve accuracy and robustness by exactly conserving certain important properties (e.g., mass and energy conservation and positivity of the solution). These methods will be implemented in computer code that will take advantage of modern computer architectures. The resulting methods will be used to simulate various scenarios of laser-plasma interactions with the aim to elucidate the mechanisms of electron acceleration and the features of the produced electron bream.
The primary objective of this research is to develop accurate and efficient computational methods for solving nonlinear partial differential equations used to model plasma dynamics. The mathematical models considered in this work arise from an important application problem: laser plasma accelerators, which provide a promising mechanism for generating high-energy electrons by hitting a plasma with a specifically-tuned ultra-short laser beam. The research will focus on developing efficient high-order discontinuous Galerkin schemes for kinetic Vlasov systems. The two main challenges that will be addressed are the development of (1) efficient time-stepping procedures that allow for time-steps that are dictated by physically important time scales and (2) high-order discretizations that numerically conserve important physical properties such as mass, momentum, and energy, as well as properties such as the positivity of the solution. One approach that will be explored in this research in order to improve the efficiency of the kinetic Vlasov numerical methods is the coupling of kinetic Vlasov solvers to fluid solvers to obtain a multiscale fluid/kinetic method. Part of the work will be done in collaboration with an experimental physicists, Prof. Dr. Malte Kaluza (Jena), who will help guide the mathematical modeling in order to keep the models relevant to the important physics of laser-plasma accelerators. Correspondingly, the resulting computational results will be used to influence laser-plasma experiments. The software that will result from this research project, along with proper documentation, will be made freely available on the web as part of the open-source package DoGPack.
