Kinetic Equations

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:

More details can be found in this paper:

(coming soon) P.T. Guthrey and J.A. Rossmanith. The regionally-implicit discontinuous Galerkin method: Application to the Relativistic Vlasov-Maxwell System.

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