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Center for Nonlinear Studies |
The Vlasov-Landau-Maxwell (VLM) equation is often regarded as the first-principle physics model for plasmas, which collectively accounts for particle transport, electromagnetic field effects, and particle collisions. Building on our previous work on the spatially homogeneous Landau equation [1], we introduce a novel particle method for the VLM equation [2]. The method is based on a proper regularization of the Landau collision operator in both physical space and velocity space so that it can be naturally coupled with the classical particle-in-cell (PIC) method to preserve the essential physical properties including conservation of mass, momentum, and energy, and the decay of entropy (from the collision part). To showcase its effectiveness, we present several plasma benchmark tests such as the collisional Landau damping and two-stream instability.
[1] J. Carrillo, J. Hu, L. Wang, and J. Wu. A particle method for the homogeneous Landau equation. J. Comput. Phys. X, 7:100066, 2020.
[2] R. Bailo, J. Carrillo, and J. Hu. The collisional particle-in-cell method for the Vlasov-Landau-Maxwell System. Preprint, 2023.
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