Some remarks on one-dimensional force-free Vlasov-Maxwell equilibria

Michael George Harrison, Thomas Neukirch

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)


The conditions for the existence of force-free nonrelativistic translationally invariant one-dimensional (1D) Vlasov-Maxwell (VM) equilibria are investigated using general properties of the 1D VM equilibrium problem. As has been shown before, the 1D VM equilibrium equations are equivalent to the motion of a pseudoparticle in a conservative pseudopotential, with the pseudopotential being proportional to one of the diagonal components of the plasma pressure tensor. The basic equations are here derived in a way different from previous work. Based on this theoretical framework, a necessary condition on the pseudopotential (plasma pressure) to allow for force-free 1D VM equilibria is formulated. It is shown that linear force-free 1D VM solutions, which so far are the only force-free 1D VM solutions known, correspond to the case where the pseudopotential is an attractive central potential. A general class of distribution functions leading to central pseudopotentials is discussed.

Original languageEnglish
Article number022106
Number of pages9
JournalPhysics of Plasmas
Issue number2
Publication statusPublished - Feb 2009


  • Maxwell equations
  • Plasma kinetic theory
  • Plasma pressure
  • Vlasov equation


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