Introduction to Magnetic Reconnection
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abstract

We review the basic concepts of magnetic reconnection and propose a general
framework for the astrophysical reconnection at large scales. Magnetic
reconnection is the rearrangement of magnetic field topology. The conventional
Sweet-Parker scheme and some of its extensions presume a non-turbulent medium
and generally produce very slow reconnection or an unstable configuration.
However, the assumption of laminar flow is unrealistic in astrophysics since,
even in an initially quiet environment, magnetic reconnection by itself can
drive turbulence. The resulting turbulence has the potential to enhance the
reconnection rate. This can lead to an unstable feedback loop as reconnection
drives turbulence and turbulence drives reconnection. Stochastic reconnection
was proposed, and subsequently tested by numerical simulations, for high
$\beta$ plasmas with a magnetic Prandtl number of order unity, $Pr_m\sim 1$.
This model predicts reconnection speeds comparable to the large scale turbulent
eddy velocity. A recent study of stochastic reconnection for $Pr_m>1$ has shown
that the width of the outflow layer and the ejection velocity of matter from
the reconnection region seem to be unaffected by viscosity in typical
astrophysical systems. However if $Pr_m>1$ viscosity can suppress small scale
reconnection events near and below the Kolmogorov or viscous damping scale.
This will produce a threshold for the suppression of large scale reconnection
by viscosity when $Pr_m$ is larger than the root of the Reynolds number,
$Pr_m>\sqrt{Re}$. For $Pr_m>1$ this leads to the spectral index $\sim-4/3$ for
length scales between the viscous dissipation scale and eddies larger by
roughly $Pr_m^{3/2}$.