Development of a Renormalization Group Approach to Multi-Scale Plasma Physics Computation

NumerEx/UCLA propose advanced theoretical and computational research in the application of the renormalization group (RG) to speed the development of advanced methods to simulate dense plasmas exhibiting critical kinetic phenomena.  These dense plasmas combine a wealth of length and time scales by virtue of their high plasma frequencies and short Debye lengths, while still requiring long length/time scale simulation due to the large size of plasma, and the evolution of the critical system physics.  Starting with an analytic approach to a fundamental plasma process, namely that of electrostatic shielding, we will demonstrate how short length scale behavior can be incorporated in coarse representations.  This naturally leads to a numerical weighting approach that can be used in conjunction with kinetic methods to systematically handle dense plasmas in a kinetic framework.  Additionally, we propose extending temporal renormalization group methods to investigate the role of the collision operator in dense plasma situations.  This complements our spatial RG approach by suggesting the means to ensure the fidelity of multi-scale numerical methods dynamically.  These two approaches will be combined to provide for a multi-dimensional plasma physics tool based on RG methods. BENEFIT: Renormalization Group (RG) methods will dramatically increase the capability to accurately and efficiently model multi-scale phenomena in plasma physics.  A wide range of devices from directed energy sources of electromagnetic energy, spacecraft thrusters, plasma processing devices, to fusion reactors all exhibit behavior where short length/time scale events influence the system-level performance of the device.  RG-based modeling tools naturally capture multi-scale physics, leading to both improved modeling codes and novel high technology devices.  Potential applications include first-principles modeling software based on RG methods for fundamental research, parametric tools with well-characterized domains of application to aid the development of plasma-based technology, and engineering services leading to improved experimental hardware in the fusion science, directed energy, and thruster arenas.