Variational formulation of macro-particle plasma simulation algorithms

Abstract

A variation formulation of macro-particle kinetic plasma models is discussed. In the electrostatic case, the use of symplectic integrators is investigated and found to offer advantages over typical generic methods. For the electromagnetic case, 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. V C 2014 AIP Publishing LLC.

Variational formulation of E & M particle simulation algorithms in cylindrical geometry using an angular modal decomposition

“…Building on previous work [6][7][8], we have derived a macro-particle model that exploits the near cylindrical symmetry of the laser-plasma interaction by introducing a poloidal mode expansion of the potentials. We have obtained a set of continuous-time equations of motion for the macro-particles and potentials that exactly conserves energy.…”

“…Here we apply this technique to a incorporate a modal decomposition of the electromagnetic fields into a macro-particle model. As in previous work [6][7][8], we begin with the relativistic Low Lagrangian [9] and introduce a distribution function consisting of a collection of fixed-size macro-particles of the form…”

“…Recently a variation formulation of macro-particle model has been developed [6][7][8] that inherits all the benefits of a Lagrangian approach, specifically the connection between symmetries and conservation laws and the flexibility in choosing coordinates. Here we apply this technique to a incorporate a modal decomposition of the electromagnetic fields into a macro-particle model.…”

Summary report of working group 2: Computations for accelerator physics

“…A novel variational formulation was presented by B. Shadwick, A. Stamm, and J. Reyes [19,20,21]. The formulation is a superset of the variational formulation that was proposed by Lewis in the 1970s.…”

Explicit high-order noncanonical symplectic algorithms for ideal two-fluid systems

“…The development of geometric algorithms for these systems can be challenging. However, recently significant advances have been achieved in the development of structure preserving geometric algorithms for charged particle dynamics [37][38][39][40][41][42][43][44][45][46][47][48][49][50], the Vlasov-Maxwell systems [3,4,[51][52][53][54][55][56][57][58][59][60][61], compressible ideal MHD [62,63], and incompressible fluids [64,65]. All of these methods have demonstrated unparalleled long-term numerical accuracy and fidelity compared with conventional methods.…”