NSF Young Investigator:Spectral Methods in Plasma Kinetics

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9358344 Holloway The work carried out under this NYI research award is directed to improving our capabilities in modeling plasmas that are either collisionless or dominated by charged particle-neutral particle collisions, such as non-neutral plasmas in high power systems and in electrostatic traps, or processing plasmas. The algorithms being explored are based on the use of pseudospectral collocation for the spatial and velocity discretization of the kinetic equations and Maxwell's equations, with the discretization carried out so that much of the Hamiltonian structure of the exact system is preserved in the collisionless limit. The resulting semi-discrete systems can be made to exactly preserve the Hamiltonian of the original system, as well as some of its Casimirs, such as number of particles and square integral of the charged particle distribution function; methods tat exactly conserve momentum at finite grid size are also being sought. Time discretization methods that exactly preserve these important physical quantities at finite numerical grid size are used; these methods include explicit and nonlinearly implicit methods. The modeling of systems with phenomena occurring over very disparate time scales (such as in processing plasmas) is being studied by a combination of asymptotic methods (multiple time scale analysis) and spectral methods. ***