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The original motivation behind the Regionally-Implicit DG method was to develop an efficient solver for the relativistic Vlasov-Maxwell (RVM) system in order to model laser-plasma interactions. The unique difficulty inherent to the relativistic regime of plasmas is that operator splitting of the relativistic Lorentz Force term leads to unphysical instabilities [Huot et. al 2003]. Our approach implements Cheng-Knorr splitting, using a Semi-Lagrangian DG method for the advection term and the electromagnetic field update, and RIDG for the Lorentz force term.
Our current work centers around two popular relativistic phenomena:
- Weibel instability, where momentum anisotropies cause electromagnetic wave growth [Weibel 1959]
- Wakefield acceleration, where a laser causes plasma waves to accelerate to nearly the speed of light.
Particle-in-cell (PIC) simulations are commonly used to generate models of such plasma applications, as seen in this video:
<iframe width="560" height="315" src="https://www.youtube.com/embed/lgxVYl_pslI" frameborder="0" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>More details can be found in this paper: