Abstract
We calculate exact one-dimensional collisionless plasma equilibria for a continuum of flux tube models, for which the total magnetic field is made up of the “force-free” Gold-Hoyle magnetic flux tube embedded in a uniform and anti-parallel background magnetic field. For a sufficiently weak background magnetic field, the axial component of the total magnetic field reverses at some finite radius. The presence of the background magnetic field means that the total system is not exactly force-free, but by reducing its magnitude, the departure from force-free can be made as small as desired. The distribution function for each species is a function of the three constants of motion; namely, the Hamiltonian and the canonical momenta in the axial and azimuthal directions. Poisson's equation and Ampère's law are solved exactly, and the solution allows either electrically neutral or non-neutral configurations, depending on the values of the bulk ion and electron flows. These equilibria have possible applications in various solar, space, and astrophysical contexts, as well as in the laboratory.
Highlights
There has been significant recent work on VlasovMaxwell (VM) equilibria that are consistent with nonlinear force-free1–8 and “nearly force-free”9 magnetic fields in Cartesian geometry
We calculate exact one-dimensional collisionless plasma equilibria for a continuum of flux tube models, for which the total magnetic field is made up of the “force-free” Gold-Hoyle magnetic flux tube embedded in a uniform and anti-parallel background magnetic field
This study was motivated by a desire to extend the existing methods for solutions of the “inverse problem in Vlasov equilibria” in Cartesian geometry, to cylindrical geometry
Summary
There has been significant recent work on VlasovMaxwell (VM) equilibria that are consistent with nonlinear force-free and “nearly force-free” magnetic fields in Cartesian geometry. We shall present particular VM equilibria for 1D magnetic fields which are nearly force-free in cylindrical geometry, i.e., flux tubes/ropes. It is typical to consider solar, space, and astrophysical flux tubes within the framework of MHD, e.g., see Ref. 48 Many of these plasmas can be weakly collisional or collisionless, with values of the collisional free path large against any fluid scale, making a description using collisionless kinetic theory necessary. It is the intention of this paper to study the GH flux tube model beyond the MHD description, since - apart from the very recent work in Ref. 62, we see no other attempts in the literature of a microscopic description of the GH field. Appendix B contains the mathematical details of the existence and location of multiple maxima of the DF in velocity-space
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