One-dimensional Vlasov-Maxwell equilibrium for the force-free Harris sheet

Michael George Harrison, Thomas Neukirch

Research output: Contribution to journalArticlepeer-review

46 Citations (Scopus)


In this Letter, the first nonlinear force-free Vlasov-Maxwell equilibrium is presented. One component of the equilibrium magnetic field has the same spatial structure as the Harris sheet, but whereas the Harris sheet is kept in force balance by pressure gradients, in the force-free solution presented here force balance is maintained by magnetic shear. Magnetic pressure, plasma pressure and plasma density are constant. The method used to find the equilibrium is based on the analogy of the one-dimensional Vlasov-Maxwell equilibrium problem to the motion of a pseudoparticle in a two-dimensional conservative potential. The force-free solution can be generalized to a complete family of equilibria that describe the transition between the purely pressure-balanced Harris sheet to the force-free Harris sheet.

Original languageEnglish
Article number135003
Number of pages4
JournalPhysical Review Letters
Issue number13
Publication statusPublished - 3 Apr 2009


  • Hybrid drift instability
  • Sheared magnetic field
  • Plasma
  • Reconnection


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