Self‐consistent gyroviscous fluid model of rotational discontinuities

Abstract

One‐dimensional steady state equilibrium structures of rotational discontinuities (RDs) have been constructed by use of a nondissipative gyroviscous two‐fluid model in which electron inertia is neglected. The gyroviscous terms in the pressure tensor, due to first‐order finite ion Larmor radius effects, are included, but the plasma pressure is assumed to be isotropic. The gyroviscous two‐fluid RDs presented in this paper satisfy the MHD jump conditions for RDs exactly, i.e., all plasma properties as well as the magnetic field magnitude are identical and uniform on both sides of the layer, and νx, the normal flow speed there, is equal to the Alfvén speed based on the normal magnetic field component Bx. A necessary condition for the existence of RD solutions is derived by performing fixed‐point analysis at the possible upstream and downstream states of RDs. This analysis shows that in the ByBz plane the magnetic structure near the fixed point is either a center or a saddle point. For those upstream conditions that give rise to a center point, no RD structure exists; when the fixed point examined is a saddle point, numerical integration of the one‐dimensional, steady state, nonlinear gyroviscous two‐fluid equations indicates that self‐consistent complete RD structures may sometimes (but not always) exist. These structures involve a rotation of the tangential magnetic field by an angle ϕ that is determined by the angle θ between the upstream (or downstream) magnetic field and the vector normal to the discontinuity, by the plasma beta value, β = 2μop/B², and by the electron to ion temperature ratio Te/Ti. Only electron‐polarized structures have been found to date: within these discontinuities the field magnitude |B| always displays a maximum. If ion‐polarized RDs exist, they would contain a minimum in |B|. However, no such structures have been found. Instead, ion polarization leads to what appears to be chaotic behavior in which a solution “trajectory” emerging from one fixed point (the upstream state, say) is extremely sensitive to initial conditions and integration step length. It does not connect to a second fixed point (the downstream state) but rather winds around indefinitely in solution space. RD structures in the limit of the ordinary two‐fluid model, i.e., including the electron inertia terms as well as the Hall term but excluding gyroviscous stresses, are examined in an appendix. Under certain, rather special conditions, a pulselike two‐fluid RD structure can be found, in which the tangential field rotates in the ion sense by a fixed but now very small angle ϕ. These solutions owe their existence to the electron inertia terms in the generalized Ohm's law; the ion inertia (Hall current) term alone leads to an RD of infinite thickness.