Action principle for Coulomb collisions in plasmas

Hirvijoki, Eero

doi:10.1063/1.4962506

Title: Action principle for Coulomb collisions in plasmas

Journal Article · Wed Sep 14 00:00:00 EDT 2016 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.4962506· OSTI ID:1328855

Hirvijoki, Eero ^[1]

Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)

In this study, an action principle for Coulomb collisions in plasmas is proposed. Although no natural Lagrangian exists for the Landau-Fokker-Planck equation, an Eulerian variational formulation is found considering the system of partial differential equations that couple the distribution function and the Rosenbluth-MacDonald-Judd potentials. Conservation laws are derived after generalizing the energy-momentum stress tensor for second order Lagrangians and, in the case of a test-particle population in a given plasma background, the action principle is shown to correspond to the Langevin equation for individual particles.

View Accepted Manuscript (DOE)

View Accepted Manuscript (Publisher)

Cite

Export

Save

Research Organization:: Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC02-09CH11466

OSTI ID:: 1328855

Alternate ID(s):: OSTI ID: 1324488

Report Number(s):: 5259; PHPAEN

Journal Information:: Physics of Plasmas, Vol. 23, Issue 9; ISSN 1070-664X

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

References (12)

Discrete mechanics and variational integrators Marsden, J. E.; West, M. Acta Numerica, Vol. 10 https://doi.org/10.1017/S096249290100006X	journal	May 2001
Volume-preserving algorithm for secular relativistic dynamics of charged particles Zhang, Ruili; Liu, Jian; Qin, Hong Physics of Plasmas, Vol. 22, Issue 4 https://doi.org/10.1063/1.4916570	journal	April 2015
Action principles for the Vlasov equation Ye, Huanchun; Morrison, P. J. Physics of Fluids B: Plasma Physics, Vol. 4, Issue 4 https://doi.org/10.1063/1.860231	journal	April 1992
Development of variational guiding center algorithms for parallel calculations in experimental magnetic equilibria Ellison, C. Leland; Finn, J. M.; Qin, H. Plasma Physics and Controlled Fusion, Vol. 57, Issue 5 https://doi.org/10.1088/0741-3335/57/5/054007	journal	April 2015
Action principle and the Hamiltonian formulation for the Maxwell–Vlasov equations on a symplectic leaf Flå, Tor Physics of Plasmas, Vol. 1, Issue 8 https://doi.org/10.1063/1.870569	journal	August 1994
Integrating factors, adjoint equations and Lagrangians Ibragimov, Nail H. Journal of Mathematical Analysis and Applications, Vol. 318, Issue 2 https://doi.org/10.1016/j.jmaa.2005.11.012	journal	June 2006
A new conservation theorem Ibragimov, Nail H. Journal of Mathematical Analysis and Applications, Vol. 333, Issue 1 https://doi.org/10.1016/j.jmaa.2006.10.078	journal	September 2007
Variational integrators for nonvariational partial differential equations Kraus, Michael; Maj, Omar Physica D: Nonlinear Phenomena, Vol. 310 https://doi.org/10.1016/j.physd.2015.08.002	journal	August 2015
Variational Symplectic Integrator for Long-Time Simulations of the Guiding-Center Motion of Charged Particles in General Magnetic Fields Qin, Hong; Guan, Xiaoyin Physical Review Letters, Vol. 100, Issue 3 https://doi.org/10.1103/PhysRevLett.100.035006	journal	January 2008
Geometric integration of the Vlasov-Maxwell system with a variational particle-in-cell scheme Squire, J.; Qin, H.; Tang, W. M. Physics of Plasmas, Vol. 19, Issue 8 https://doi.org/10.1063/1.4742985	journal	August 2012
Fokker-Planck Equation for an Inverse-Square Force Rosenbluth, Marshall N.; MacDonald, William M.; Judd, David L. Physical Review, Vol. 107, Issue 1 https://doi.org/10.1103/PhysRev.107.1	journal	July 1957
The Langevin Equation: With Applications to Stochastic Problems in Physics, Chemistry and Electrical Engineering Coffey, W. T.; Kalmykov, Yu P.; Waldron, J. T. World Scientific Series in Contemporary Chemical Physics https://doi.org/10.1142/9789812795090	book	March 2004

Similar Records

Study of the Interaction Operator Between Two Groups of Particles in a Completely Ionized Plasma. Development of the Distribution Functions in a Series of Orthogonal Polynomials (thesis); ETUDE DE L'OPERATEUR D'INTERACTION ENTRE DEUX GROUPES DE PARTICULES DANS UN PLASMA COMPLETEMENT IONISE. DEVELOPPMENT DES FONCTIONS DE DISTRIBUTION EN SERIES DE POLYNOMES ORTHOGONAUX (theses)

Technical Report · Tue Jan 01 00:00:00 EST 1963 · OSTI ID:1328855

Fain, A

Exact collisional moments for plasma fluid theories

Journal Article · Sat Apr 01 00:00:00 EDT 2017 · Physics of Plasmas · OSTI ID:1328855

Pfefferlé, D.; Hirvijoki, E.; Lingam, M.

A particle-in-cell method for modeling small angle Coulomb collisions in plasmas

Conference · Sun Jan 01 00:00:00 EST 1989 · OSTI ID:1328855

Parker, S E

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
Langrangian mechanics
conservation laws
partial differential equations
Langevin equation
plasma collisions

Title: Action principle for Coulomb collisions in plasmas

Citation Formats

References (12)

Similar Records

Related Subjects