Thin current sheet embedded within a thicker plasma sheet: Self‐consistent kinetic theory

A self‐consistent theory of thin current sheets, where the magnetic field line tension is balanced by the ion inertia rather than by the pressure gradient, is presented. Assuming that ions are the main current carriers and their dynamics is quasi‐adiabatic, the Maxwell‐Vlasov equations are reduced to the nonlocal analogue of the Grad‐Shafranov equation using a new set of integrals of motion, namely, the particle energy and the sheet invariant of the quasi‐adiabatic motion. It is shown that for a drifting Maxwellian distribution of ions outside the sheet the equilibrium equation can be reduced in the limits of strong and weak anisotropy to universal equations that determine families of equilibria with similar profiles of the magnetic field. In the region B n / B 0 < v T / v D ≪ 1 ( B 0 , B n , v D , and v T are the magnetic fields outside the sheet and close to its central plane, the ion drift velocity outside the sheet, and the ion thermal velocity, respectively) the thickness of such similar profiles is of the order of ( v T / v D ) 1/3 ρ 0 , where ρ 0 is the thermal ion gyroradius outside the sheet. In the limit of weak anisotropy ( v T / v D ≫ 1) the self‐consistent current sheet equilibrium may also exist with no indications of the catastrophe reported earlier by Burkhart et al. 1992a. On the contrary, it is found that in this limit the magnetic field profiles again become similar to each other with the characteristic thickness ∼ ρ 0 . The profiles of plasma and current densities as well as the components of the pressure tensor are calculated for arbitrary ion anisotropy outside the sheet. It is shown that the thin current sheet for the equilibrium considered here is usually embedded into a much thicker plasma sheet. Moreover, in the case of weak anisotropy the perturbation of the plasma density inside the sheet is shown to be proportional to the parameter v D / v T , and as a result the electrostatic effects should be small, consistent with observations. This model of the thin current sheet satisfies the basic force balance equations including the marginal fire‐hose condition and preserves the nonguiding center effects including the pressure nongyrotropy.