Jan S. Hesthaven
Division of Applied Mathematics
Brown University
"A first few steps toward a new generation of particle-in-cell (PIC) modeling tools for kinetic plasma physics"
Since the 1960's, the classic particle-in-cell (PIC) methods has become a standard computational tool for the modeling of kinetic plasma phenomena. However, as successful as these finite difference technique based methods have been, their limitations are quickly becoming a bottleneck in the attempt to model many problems of contemporary interest such as next generation particle accelerators, high-power microwave generation, and fusion devises.
To set the stage for this talk, we shall begin by discussing some of these inherent limitations and use this to motivate the ongoing development of a high-order accurate PIC method on unstructured grids. The field solver is based on a Discontinuous Galerkin (DG) scheme for the time-domain Maxwell equations. This approach ensures geometric flexibility through a fully unstructured grid at arbitrary order of accuracy and enables the efficient and accurate modeling of multiscale phenomena, possibly in a hybrid formulation. The particle mover is flexible in terms of particle shapes and a level set approach is employed to implement elastic/inelastic interactions with boundaries. Divergence control is done either through a fully hyperbolic Lagrange multiplier technique or using a classical Boris projection scheme.
We shall illustrate the performance of the two-dimensional and three-dimensional algorithm through a few examples, e.g., plasmawaves, Landau damping, magnetrons etc. Both non-relativistic and fully relativistic cases shall be considered as well as some simple magnetron cases and wave-field computations with more complex geometries. We conclude the talk with a brief discussion of some of the many open challenges and questions in need of answers to make this a mature computational tool.
This work has been done in collaboration with Prof G. Jacobs (SDSU), A Kloeckner (Brown), A Narayan (Brown) and has been funded by AFOSR and NSF.
Hosted by Prof. Thomas Pedersen
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