Novel Collisional Particle-In-Cell (CPIC) Methods for Kinetic Equations in Plasma Physics
Abstract
Plasmas are the most common form of matter, comprising more than 99 percent of the visible universe. Understanding the complex behaviors of plasmas has led to many important scientific and engineering advances. Dynamics of plasmas is well described by the kinetic Vlasov-Landau equation coupled with Maxwell’s equations, in which particles undergo free streaming until they collide with another particle; meanwhile, they are subject to magnetic-electric forces generated by themselves or external fields. Albeit being an integral part of any accurate plasma description, collisions are often lacking in current plasma simulations, for example, in the popular particle-in-cell (PIC) methods, largely due to that the Landau collision operator is extremely difficult and expensive to approximate. Even though one can add collisions using some Monte Carlo algorithms, many nice physical properties preserved in the original (collisionless) PIC method such as momentum or energy conservation are not guaranteed in the whole algorithm. This loss of physical structure may generate unphysical solutions which severely decrease the fidelity in numerical simulations. Therefore, there is a critical need to appropriately incorporate collisions in current plasma simulations. By viewing the Landau equation as a transport equation with a properly regularized velocity field, we are able to define a particle solution. Furthermore, the method can preserve all the important physical properties including conservation of charge, momentum and energy, and even the decay of entropy. This new characteristic viewpoint of the Landau equation offers a natural particle framework to handle collisions and field effects in a unified way and opens door to many exciting research directions.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Mar 07, 2023
- Source ID
- FA95502110358
Entities
People
- Jingwei Hu
Organizations
- Air Force Office of Scientific Research
- United States Air Force
- University of Washington