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Variational formulation of macro-particle algorithms for studying electromagnetic plasmas
The interaction of an intense laser pulse with a plasma can be well described by the Vlasov-Maxwell system of equations. However, due to the immense number of particles involved, only approximate solutions can be attained for problems of interest. Currently, the most common method for solving these equations is known as particle-in-cell (PIC). It is a macro-particle method, where an individual macro-particle represents a large quantity of electrons or ions characterized by a single momentum. While the traditional PIC code has been used successfully in many instances to model important physics, its inadequacies have long been understood. One example of this is the phenomenon known as grid-heating, which amounts to a failure of the code to conserve energy. Another important issue, identified more recently, is unphysical trapping that occurs due to inaccuracies in the representation of phase space. To address these issues, we have developed a rigorous variational formulation for deriving a set of discrete, self-consistent, macro-particle kinetic plasma equations from a discretized Lagrangian. The primary advantage of the variational technique is the well-known connection between the symmetries of a system and conservation laws. This inherent structure allows for the optimization of computational resources for a given physical problem. In my dissertation, I discuss the development of the variational approach, an illustration of how to utilize its flexibility with regard to coordinate transformations, the implementation of symplectic time integrators, and the application of this technique to examples drawn from important problems in laser-plasma interactions. I emphasize throughout the advantages over the traditional PIC method including proper energy conservation, improved smoothness of the density profile, and a more physical representation of the phase space for a similar, and often reduced, computational cost.
Stamm, Alexander B, "Variational formulation of macro-particle algorithms for studying electromagnetic plasmas" (2015). ETD collection for University of Nebraska - Lincoln. AAI3738970.