A Reduction of the Vlasov--Maxwell System Using Phase-Space Blobs

We develop a new computational approach to solving the Vlasov-Maxwell equation by representing the distribution function by a supper-position of finite-extent phase- space ``blobs.'' Each blob evolves as a warm beamlet\footnote{B.~A. Shadwick, \textit{et al.}, ``Hamiltonian Reductions for Modeling Relativistic Laser-Plasma Interactions,'' \textbf{Commun.\ Nonlinear Sci.\ Numer.\ Sim.} in press (2011).} driven by the collective plasma fields. The underlying approximation treats each blob as a different plasma species and, as such, makes a counting error which we expect to be reflected in the system entropy. This approach results in a non-canonical Hamiltonian model, inheriting various properties of the original system. The primary advance of this technique over traditional Lagrangian particle methods is the near elimination of macro-particle ``noise.'' Since we are evolving elements of phase-space, the distribution function can be readily reconstructed at any instant. We discuss the performance and convergence of this model using a variety of standard examples.