Abstract
Abstract. The appearance of eruptive space plasma processes, e.g. in eruptive flares as observed in the solar atmosphere, is usually assumed to be caused by magnetic reconnection, often connected with singular points of the magnetic field. We are interested in the general relation between the eigenvalues of the Jacobians of the plasma velocity and the magnetic field and their relation to the shape of a spatially varying, localized non-idealness or resistivity, i.e. we are searching for the general solution. We perform a local analysis of almost all regular, generic, structurally stable non-ideal or resistive MHD solutions. Therefore we use Taylor expansions of the magnetic field, the velocity field and all other physical quantities, including the non-idealness, and with the method of comparison of coefficients, the non-linear resistive MHD system is solved analytically, locally in a close vicinity of the null point. We get a parameterised general solution that provides us with the topological and geometrical skeleton of the resistive MHD fields. These local solutions provide us with the "roots" of field and streamlines around the null points of basically all possible 2-D reconnection solutions. We prove mathematically that necessarily, the flow close to the magnetic X-point must also be of X-point type to guarantee positive dissipation of energy and annihilation of magnetic flux. We also prove that, if the non-idealness has only a one-dimensional, sheet-like structure, only one separatrix line can be crossed by the plasma flow, similar to known reconnective annihilation solutions.
Highlights
Magnetic reconnection is thought to be a process responsible for many eruptive plasma phenomena in space plasmas and astrophysical plasmas, like geomagnetical substorms or solar flares
The first reconnection scenarios by Petschek (1964) and Sweet-Parker proposed a magnetic null point and a stagnation point flow into the diffusion region, i.e. the stagnation point is inside this diffusion region
Priest and Cowley (1975) analysed the case of incompressible 2-D MHD with constant resistivity. They showed that either the magnetic field is of hyperbolic type (“X-type”) and the flow is a shear flow, or the magnetic field is of higher order and the flow has a typical shape of a stagnation point flow
Summary
Magnetic reconnection is thought to be a process responsible for many eruptive plasma phenomena in space plasmas and astrophysical plasmas, like geomagnetical substorms or solar flares. Priest and Cowley (1975) analysed the case of incompressible 2-D MHD with constant resistivity They showed that either the magnetic field is of hyperbolic type (“X-type”) and the flow is a shear flow, or the magnetic field is of higher order (and “sheared”) and the flow has a typical shape of a stagnation point flow (hyperbolic). The results found by Craig and Henton (1995) and Craig and Rickard (1994) confirm the results found earlier by Priest and Cowley (1975), who found more “shear-like” flows instead of typical stagnation point flows It was shown by Priest et al (1994) and later on in extended form by Watson and Craig (1998) that under certain circumstances, like constant resistivity or current depending/anomalous resistivity and sub-Alfvenic flow, etc., reconnection is impossible: the so-called anti-reconnection theorems. We prove in the following that “typical” stagnation point flows are possible (“Xtype”), and exclude here the “shear-like” flows
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