Exact Solutions for Spine Reconnective Magnetic Annihilation

Abstract

Solutions for spine reconnective annihilation are presented which satisfy exactly the three-dimensional equations of steady-state resistive incompressible magnetohydrodynamics (MHD). The magnetic flux function (A) and stream function ðÉÞ have the formin terms of cylindrical polar coordinates ðR, , zÞ. First of all, two non-linear fourth-order equations for A 1 and É 1 are solved by the method of matched asymptotic expansions when the magnetic Reynolds number is much larger than unity. The solution, for which a composite asymptotic expansion is given in closed form, possesses a weak boundary layer near the spine (R ¼ 0). These solutions are used to solve the remaining two equations for A 0 and É 0 . Physically, the magnetic field is advected across the fan separatrix surface and diffuses across the spine curve. Different members of a family of solutions are determined by values of a free parameter ðÞ and the components ðB Re , B ze Þ and ðv Re , v ze Þ of the magnetic field and plasma velocity at a fixed external point ðR, , zÞ ¼ ð1, =2, 0Þ, say.

Exact solutions for reconnective annihilation in magnetic configurations with three sources

“…Moreover, over the last few years there was a similar progress in the theory of threedimensional (3D) reconnection. In particular, some simplified forms of this process at null points of 3D magnetic fields have been found as well 9,10,11 .…”

“…In particular, some simplified forms of this process at null points of 3D magnetic fields have been found as well 9,10,11 .…”

Numerical experiments on wave propagation towards a 3D null point due to rotational motions

“…On the other hand, if the foot points move down on one side of the curved surface and up on the other, spine reconnection is driven with singular motions near the z axis. Exact solutions have been discovered for spine and fan reconnective annihilation [ Craig and Henton , 1995; Craig and Fabling , 1996; Mellor et al , 2002]. Furthermore, several numerical experiments on various aspects of 3D reconnection have been undertaken [e.g., Lau and Finn , 1996; Rickard and Titov , 1996; Galsgaard and Nordlund , 1996, 1997; Galsgaard et al , 1996, 1997; Dahlburg et al , 1997; Otto , 1995; Politano et al , 1995; Matthaeus et al , 1996].…”