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


