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Space satellite observations show that current sheets in the space plasma environment are often characterized by bifurcated structures. In a recent paper a two-fluid model of the bifurcated current sheet was constructed on the basis of the pseudo potential method. A straightforward generalization of Janaki et al.'s two-fluid model to kinetic formalism, however, leads to an unphysical situation of negative particle velocity distribution function occurring over a certain range of velocity space. If one assumes an isotropic background plasma population, however, one can show that a rigorous, physically valid kinetic solution of the bifurcated current sheet can be obtained.

[1] Recent satellite observations show that current sheets in the space plasma environment are often characterized by bifurcated structures. The majority of the available models of the bifurcated current sheet in the literature are based upon equilibrium Vlasov-Maxwell kinetic theory. While in principle, kinetic models are more fundamental, investigations based on fluid theory can sometimes be advantageous. For instance, because of its inherent simplicity, fluid models of the current sheet can be used in the detailed nonlocal or global analysis of fluid stability. The present paper puts forth a two-fluid model of the bifurcated current sheet on the basis of the pseudo-potential method. According to the present model, double peaked current sheet is characterized by a transverse non-uniform flow and a profile of plasma density that has a plateau in the region between the current peaks. Further, the plasma pressure tensor associated with such a bifurcated current sheet is shown to be anisotropic and non-gyrotropic.

[1] Homotopy formulas are obtained for the magnetic vector potential A, where B = ∇ × A is the magnetic induction, which gives alternative methods for calculating A for a given B, different from the Biot-Savart formulas. The homotopy formulas are used to obtain A for multipole potential fields and other potential fields, which are useful in relative helicity calculations. However, the formulas do not work for monopole and split monopole magnetic fields. In the latter case, there is no global continuous solution for A, but a global discontinuous A can be constructed, which is continuous on two open sets that cover the sphere. The differential and integral forms of the helicity and relative helicity transport equations using both Eulerian and Lagrangian perspectives are discussed. The approach to magnetic helicity and magnetic helicity injection, based on a toroidal-poloidal decomposition of the field, in which the field is represented by Euler potentials is also used in the analysis. The relative magnetic helicity and helicity injection rate for the Parker spiral interplanetary magnetic field, in which there is either a flat current sheet or a warped current sheet in the helioequatorial plane, are discussed. One of the homotopy formulas is used to provide an efficient way to calculate the relative helicity of interplanetary magnetic flux rope configurations observed by the WIND spacecraft.