Action principle for Coulomb collisions in plasmas

Authors:  E. Hirvijok

Abstract: In this letter we derive an action principle  for Coulomb  collisions in plasmas. 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 potentials.  Exact  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.  Being  suitable  for discretization, the presented action allows construction of variational integrators. Numerical implementation is left for a future study.
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