Theory of a thin one‐dimensional current sheet in collisionless space plasma

Abstract

It is widely believed that evolution of a current sheet in collisionless space plasma often results in fast magnetic field merging, for example, during substorm onsets. The current sheet structure on the merging sites should exhibit a considerable change, in order for the field energy transformation into the energy of particles to become possible. The specific current sheet structure is the quasi‐one‐dimensional kinetic forced current sheet. A full analytical theory of such a sheet has been constructed for the typical case when the plasma parameter in the background plasma is small, β ≪ 1, and bulk motions of the plasma are sub‐alfvenic, MA ≪ 1. Theoretical consideration of that equilibrium state is based on the existence of a specific adiabatic invariant, corresponding to ion oscillations about the sheet central plane in their “Speiser” orbits. The theory describes the sheet structure self‐consistently, identifying its dependence on the features of the ion distribution function. Detailed structure of the emerging equilibrium sheet has been numerically studied. For a certain current sheet profile, while outside the sheet the calculated ion distribution function is close to a pair of interpenetrating shifted Maxwellians, inside the sheet it is also highly anisotropic but quite different, involving all velocities from 0 up to 2vA. Dependence of the structure scale length on the parameters of the problem corresponds to estimates obtained earlier. This scale length also agrees with observational estimates of the current sheet thickness in the magnetotail during its extreme thinning near substorm onset.

Drift modes of a quasi-two-dimensional current sheet

“…Transient particles, along with the total energy, conserve the quasi adia batic integral of motion [27,28]. The first self consis tent analytical models of TCSs were proposed in [29,30] and were then developed in [31,32]. The results of these studies are consistent in many respects with numerical simulation results [33,34] and earlier esti mates [35].…”

“…Solving sequentially system (29) for various n, we reconstruct the time dependence of the vector poten tial.…”

A class of exact two‐dimensional kinetic current sheet equilibria

“…Beginning with the works by Eastwood [1972, 1974, 1975], the forced current sheets were discussed largely by means of numerical methods [ Burkhart et al , 1992; Pritchett and Coroniti , 1992b, 1993, 1994, 1995; Holland and Chen , 1993; Burkhart et al , 1993; Cargill et al , 1994; Harold and Chen , 1996; Hesse et al , 1996; Becker et al , 2001]. However, recently, semianalytical construction of the forced current sheet solutions have become available [ Kropotkin and Domrin , 1996; Kropotkin et al , 1997; Sitnov et al , 2000, 2003]. In these semianalytical works, particle distribution function is constructed with not only the total Hamiltonian and canonical momentum as in Harris‐type models but also with the so‐called quasi‐adiabatic sheet invariant.…”

Magnetic Reconnection

“…Schindler and Birn, 2002), different classes of kinetic equilibria can be found numerically. Another class of current sheet equilibria have been developed to take into account boundary conditions, the so-called forced current sheet (Kropotkin and Domrin, 1996;Sitnov et al, 2000). Semianalytic and numerical solutions have been found (Sitnov et al, 2003(Sitnov et al, , 2006 using anisotropic and nongyrotropic variations, for applications to the bifurcated current sheets observed in magnetospheric tails.…”