# Asymmetric kinetic equilibria: Generalization of the BAS model for rotating magnetic profile and non-zero electric field

Published in Physics of Plasmas DOI : http://dx.doi.org/10.1063/1.4930210

Nicolas Dorville, Gérard Belmont, Nicolas Aunai, Jérémy Dargent and Laurence Rezeau

Finding kinetic equilibria for non-collisional/collisionless tangential current layers is a key issue as well for their theoretical modeling as for our understanding of the processes that disturb them, such as tearing or Kelvin Helmholtz instabilities. The famous Harris equilibrium [E. Harris, Il Nuovo Cimento Ser. 10 23, 115–121 (1962)] assumes drifting Maxwellian distributions for ions and electrons, with constant temperatures and flow velocities; these assumptions lead to symmetric layers surrounded by vacuum. This strongly particular kind of layer is not suited for the general case: asymmetric boundaries between two media with different plasmas and different magnetic fields. The standard method for constructing more general kinetic equilibria consists in using Jeans theorem, which says that any function depending only on the Hamiltonian constants of motion is a solution to the steady Vlasov equation [P. J. Channell, Phys. Fluids (1958–1988) 19, 1541 (1976); M. Roth et al., Space Sci. Rev. 76, 251–317 (1996); and F. Mottez, Phys. Plasmas 10, 1541–1545 (2003)]. The inverse implication is however not true: when using the motion invariants as variables instead of the velocity components, the general stationary particle distributions keep on depending explicitly of the position, in addition to the implicit dependence introduced by these invariants. The standard approach therefore strongly restricts the class of solutions to the problem and probably does not select the most physically reasonable. The BAS (Belmont-Aunai-Smets) model [G. Belmont et al., Phys. Plasmas 19, 022108 (2012)] used for the first time the concept of particle accessibility to find new solutions: considering the case of a coplanar-antiparallel magnetic field configuration without electric field, asymmetric solutions could be found while the standard method can only lead to symmetric ones. These solutions were validated in a hybrid simulation [N. Aunai et al., Phys. Plasmas (1994-present) 20, 110702 (2013)], and more recently in a fully kinetic simulation as well [J. Dargent and N. Aunai, Phys. Plasmas (submitted)]. Nevertheless, in most asymmetric layers like the terrestrial magnetopause, one would indeed expect a magnetic field rotation from one direction to another without going through zero [J. Berchem and C. T. Russell, J. Geophys. Res. 87, 8139–8148 (1982)], and a non-zero normal electric field. In this paper, we propose the corresponding generalization: in the model presented, the profiles can be freely imposed for the magnetic field rotation (although restricted to a 180 rotation hitherto) and for the normal electric field. As it was done previously, the equilibrium is tested with a hybrid simulation.