Fast Steady State Magnetic
F. Jamitzky and M. Scholer
We investigate the behaviour of a reconnecting current sheet by performing a
boundary layer analysis of the stationary incompressible MHD-equations with
spatially inhomogeneous resistivity. Steady state solutions for the
diffusion region are constructed and are matched to solutions of the ideal
MHD-equations in the outer region.
In the case of uniform resistivity it
found that the reconnection proceeds in a Sweet/Parker type behaviour which
leads to a very instationary and slow reconnection for large magnetic
The separatrices osculate and the characteristics,
which are the rays of the linear waves that emerge from the diffusion
region, are confined in the current sheet. They cannot escape into the
inflow region where they could steepen and become standing slow shocks.
For an elongated current sheet the waves
can escape at the ends of the sheet and produce here the observed standing
In the non-uniform resistivity case the picture changes
completely: the reconnection rate increases drastically and the diffusion
region stays small even for large magnetic Reynolds numbers. Petschek-type
magnetic reconnection is realized.
The separatrices cross under a finite
angle and, as a result, the slow waves also have a propagation direction in
the inflow region. The slow waves can immediately escape from the X-point,
be convected back and steepen to standing slow shocks. Slow shocks are much
more effective in converting magnetic energy into kinetic energy than an
elongated current sheet, which explains the strongly enhanced reconnection
rate. The effectiveness of the slow shocks manifests itself in the weak
dependence of the reconnection rate on
magnetic Reynolds numbers.
We thus have demonstrated that the important
difference between uniform and non-uniform resistivity magnetic reconnection
lies in the behaviour of the separatrices near the X-point.
Summarizing the occurrence of fast magnetic reconnection in resistive
astrophysical and space plasmas can be understood on the basis of Petschek
type reconnection if a gradient of the resistivity exists near the magnetic
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