Hamiltonian and action principle (HAP) formulations of plasma physics are reviewed for the purpose of explaining structure preserving numerical algorithms. Geometric structures associated with and emergent from HAP formulations are discussed. These include conservative integration, which exactly conserves invariants, symplectic integration, which exactly preserves the Hamiltonian geometric structure, and other Hamiltonian integration techniques. Basic ideas of variational integration and Poisson integration, which can preserve the noncanonical Hamiltonian structure, are discussed. Metriplectic integration, which preserves the structure of conservative systems with both Hamiltonian and dissipative parts, is proposed. Two kinds of simulated annealing, a relaxation technique for obtaining equilibrium states, are reviewed: one that uses metriplectic dynamics, which maximizes an entropy at fixed energy, and the other that uses double bracket dynamics, which preserves Casimir invariants. Throughout, applications to plasma systems are emphasized. The paper concludes with a discussion of geometric electromagnetic particle-in-cell [Kraus et al., J. Plasma Phys. (to be published); e-print arXiv:1609.03053v1 [math.NA]], a particle in cell code that incorporates Hamiltonian and geometrical structure preserving properties.
Morrison, P. J.. "Structure and structure-preserving algorithms for plasma physics." Physics of Plasmas, vol. 24, no. 5, Apr. 2017. https://doi.org/10.1063/1.4982054
Morrison, P. J., "Structure and structure-preserving algorithms for plasma physics," Physics of Plasmas 24, no. 5 (2017), https://doi.org/10.1063/1.4982054
@article{osti_1535308,
author = {Morrison, P. J.},
title = {Structure and structure-preserving algorithms for plasma physics},
annote = {Hamiltonian and action principle (HAP) formulations of plasma physics are reviewed for the purpose of explaining structure preserving numerical algorithms. Geometric structures associated with and emergent from HAP formulations are discussed. These include conservative integration, which exactly conserves invariants, symplectic integration, which exactly preserves the Hamiltonian geometric structure, and other Hamiltonian integration techniques. Basic ideas of variational integration and Poisson integration, which can preserve the noncanonical Hamiltonian structure, are discussed. Metriplectic integration, which preserves the structure of conservative systems with both Hamiltonian and dissipative parts, is proposed. Two kinds of simulated annealing, a relaxation technique for obtaining equilibrium states, are reviewed: one that uses metriplectic dynamics, which maximizes an entropy at fixed energy, and the other that uses double bracket dynamics, which preserves Casimir invariants. Throughout, applications to plasma systems are emphasized. The paper concludes with a discussion of geometric electromagnetic particle-in-cell [Kraus et al., J. Plasma Phys. (to be published); e-print arXiv:1609.03053v1 [math.NA]], a particle in cell code that incorporates Hamiltonian and geometrical structure preserving properties.},
doi = {10.1063/1.4982054},
url = {https://www.osti.gov/biblio/1535308},
journal = {Physics of Plasmas},
issn = {ISSN 1070-664X},
number = {5},
volume = {24},
place = {United States},
publisher = {American Institute of Physics (AIP)},
year = {2017},
month = {04}}
Morrison, P. J.; Eliasson, Bengt; Shukla, Padma K.
NEW DEVELOPMENTS IN NONLINEAR PLASMA PHYSICS: Proceedings of the 2009 ICTP Summer College on Plasma Physics and International Symposium on Cutting Edge Plasma Physics, AIP Conference Proceedingshttps://doi.org/10.1063/1.3266810