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Arts & Sciences
[PAST EVENT] Physics Seminar
March 2, 2015
4pm - 5pm
Abstract:
Macro-Particle based simulations methods are in widespread use in plasma physics; their computational efficiency and intuitive nature are largely responsible for their longevity. In the main, these algorithms are formulated by approximating the continuous equations of motion. For systems governed by a variational principle (such as collisionless plasmas), approximations of the equations of motion is known to introduce anomalous behavior especially in system invariants. I will present a variational formulation of particle algorithms for plasma simulation based on a reduction of the distribution function onto a finite collection of macro-particles. As in the usual Particle-In-Cell (PIC) formulation, these macro-particles have a definite momentum and are spatially extended. The primary advantage of this approach is the preservation of the link between symmetries and conservation laws. For example, nothing in the reduction introduces explicit time dependence to the system and thus the continuous-time equations of motion exactly conserve energy; thus, these models are free of grid-heating. The variational formulation allows for constructing models of arbitrary spatial and temporal order. In this approach the macro-particle shape is arbitrary; the spatial extent is completely decoupled from both the grid-size and the "smoothness" of the shape; smoother particle shapes are not necessarily larger. Gauge invariance and momentum conservation are considered in detail. It is shown that, while the symmetries responsible for these conservation laws are broken in the presence of a spatial grid, the conservation laws hold in an average sense. The requirements for exact invariance are explored and it is shown that one viable option is to represent the potentials with a truncated Fourier basis.
Macro-Particle based simulations methods are in widespread use in plasma physics; their computational efficiency and intuitive nature are largely responsible for their longevity. In the main, these algorithms are formulated by approximating the continuous equations of motion. For systems governed by a variational principle (such as collisionless plasmas), approximations of the equations of motion is known to introduce anomalous behavior especially in system invariants. I will present a variational formulation of particle algorithms for plasma simulation based on a reduction of the distribution function onto a finite collection of macro-particles. As in the usual Particle-In-Cell (PIC) formulation, these macro-particles have a definite momentum and are spatially extended. The primary advantage of this approach is the preservation of the link between symmetries and conservation laws. For example, nothing in the reduction introduces explicit time dependence to the system and thus the continuous-time equations of motion exactly conserve energy; thus, these models are free of grid-heating. The variational formulation allows for constructing models of arbitrary spatial and temporal order. In this approach the macro-particle shape is arbitrary; the spatial extent is completely decoupled from both the grid-size and the "smoothness" of the shape; smoother particle shapes are not necessarily larger. Gauge invariance and momentum conservation are considered in detail. It is shown that, while the symmetries responsible for these conservation laws are broken in the presence of a spatial grid, the conservation laws hold in an average sense. The requirements for exact invariance are explored and it is shown that one viable option is to represent the potentials with a truncated Fourier basis.
Contact
Host: Gene Tracy