Exact Solutions for Reconnective Magnetic Annihilation
Annihilation 

Eric R Priest Submitted: 20000111 11:04
A family of exact solutions of the steady, resistive nonlinear magnetohydrodyna magnetohydrodynamic equations in two dimensions (x, y) is presented for reconnective annihilation, in which the magnetic field is advected across one pair of separatrices and diffuses across the other pair. They represent a twofold generalization of the previous CraigHenton solution, since a dimensio dimensionless free parameter (gamma) in the new solutions equals unity in the previous solutions and the components (v_{xe}, v_{ye}) and (B_{xe}, B_{ye}) of plasma velocity and magnetic field at a fixed external point (x, y) = (1, 0), say, may all be imposed, whereas only three of these four components are free in the previous solutions. The solutions have the exact forms eq A=A_{0} (x) + A_{1} (x), y , quad psi = psi_{0} (x) + psi_{1} (x) , y onumber eeq for the magnetic flux function (A) and stream function (psi), so that the electric current is no longer purely a function of x as it was previously. The origin (0, 0) represents both a stagnation point and a magnetic null point, where the plasma velocity ({f v = abla imes psi hat{f z}}) and magnetic field ({f B = abla} imes A hat{f z}) both vanish. A current sheet extends along the yaxis. The nonlinear fourthorder equations for A_{1} and psi_{1} are solved in the limit of small dimensionless resistivity (large magnetic Reynolds number) using the method of matched asymptotic expansions. Although the solution has a weak boundary layer near x=0, we show that a composite asymptotic representation on 0 leq x leq 1 is given by the leading order outer solution, which has a simple closedform structure. This enables the equations for A_{0} and psi_{0} to be solved explicitly from which their representation for small resistivity is obtained. The effect of the five parameters (v_{xe}, v_{ye}, B_{xe}, B_{ye}, gamma) on the solutions is determined, including their influence on the width of the diffusion region and the inclinations of the streamlines and magnetic field lines at the origin. Several possibilities for generalizing these solutions for asymmetric reconnective annihilation in two and three dimensions are also presented.
Authors: E.R. Priest, V.S. Titov, R.E. Grundy and A.W.
Hood
Projects:

Publication Status: Proc. Roy. Soc (in press)
Last Modified: 20000111 11:04



The Heating of the Solar Corona 

Eric R Priest Submitted: 20000111 11:03
One of the paradigms about coronal heating has been the belief that the mean or summit temperature of a coronal loop is completely insensitive to the nature of the heating mechanisms. However, we point out that the temperature profile along a coronal loop is highly sensitive to the form of the heating. For example, when a steadystate heating is balanced by thermal conduction, a uniform heating function makes the heat flux a linear function of distance along the loop, while T^{7/2} increases quadratically from the coronal footpoints; when the heating is concentrated near the coronal base, the heat flux is small and the T^{7/2} profile is flat above the base; when the heat is focussed near the summit of a loop, the heat flux is constant and T^{7/2} is a linear function of distance below the summit. This realisation may act as an incentive to proponents of particular heating mechanisms to determine how the heat deposition varies spatially within coronal structures such as loops or arcades and to observers to deduce the temperature profiles with as low an error as possible. We therefore propose a new twopart approach to try and solve the coronal heating problem, namely first of all to use observed temperature profiles to deduce the form of the heating, and secondly to use that heating form to deduce the likely heating mechanism. In particular, we apply this philosophy to a preliminary analysis of Yohkoh observations of the largescale solar corona. This gives strong evidence against heating concentrated near the loop base for such loops and suggests that heating uniformly distributed along the loop is slightly more likely than heating concentrated at the summit. The implication is that largescale loops are heated in situ throughout their length, rather than being a steady response to lowlying heating near their feet or at their summits. Unless waves can be shown to produce a heating close enough to uniform, the evidence is therefore at present for these large loops more in favour of turbulent reconnection at many small randomlydistributed current sheets, which is likely to be able to do so. In addition, we address briefly the questions: why does the coronal intensity reduce by a factor of 100 from solar maximum to solar minimum; why is the temperature maximum in largescale closed regions about 2.3 MK at an altitude 1.5 R_{odot}; and why are the corresponding values in coronal holes about 1.5 MK and 1.5 R_{odot}?
Authors: E. R. Priest, C. R. Foley, J. Heyvaerts, T.D. Arber$^{*}$, D. Mackay$^{*}$,
J. L. Culhane$^{+}$ and L.W. Acton
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Publication Status: Ap J (submitted)
Last Modified: 20000111 11:03



Aspects of 3D Magnetic Reconnection 

Eric R Priest Submitted: 20000111 11:02
In this review paper we discuss several aspects of magnetic reconnection theory, focussing on the fieldline motions that are associated with reconnection. A new exact solution of the nonlinear MHD equations for {it reconnective annihilation annihilation} is presented which represents a twofold generalisation of the previous solutions. Magnetic reconnection at null points by several mechanisms is summarised, including {it spine reconnection, fan reconnection} and {it separator reconnection}, where it is pointed out that two common features of separator reconnection are the rapid flipping of magnetic field lines and the collapse of the separator to a current sheet. In addition, a formula for the rate of reconnection between two flux tubes is derived. The magnetic field of the corona is highly complex, since the magnetic carpet consists of a multitude of sources in the photosphere. Progress in understanding this compexity may, however, be made by constructing the {it skeleton} of the field and developing a theory for the local and global bifurcations between the different topologies. The eruption of flux from the Sun may even sometimes be due to a change of topology caused by {it emerging flux breakout}. A CD Rom attached to this paper presents the results of a toy model of vacuum reconnection, which suggests that rapid flipping of field lines in fan and separator reconnection is an essential ingredient also in real nonvacuum conditions. In addition, it gives an example of {it binary reconnection} between a pair of unbalanced sources as they move around, which may contribute significantly to coronal heating. Finally, we present examples in TRACE movies of geometrical changes of the coronal magnetic field that are a likely result of largescale magnetic reconnection.
Authors: Priest, ER and Schrijver, CJ
Projects:

Publication Status: Solar Phys. (in press)
Last Modified: 20000111 11:02




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