  Magnetic reconnection mediated by the hyper-resistive plasmoid instability is
studied with both linear analysis and nonlinear simulations. The linear growth
rate is found to scale as $S_{H}^{1/6}$ with respect to the hyper-resistive
Lundquist number $S_{H}\equiv L^{3}V_{A}/\eta_{H}$, where $L$ is the system
size, $V_{A}$ is the Alfv\'en velocity, and $\eta_{H}$ is the
hyper-resistivity. In the nonlinear regime, reconnection rate becomes nearly
independent of $S_{H}$, the number of plasmoids scales as $S_{H}^{1/2}$, and
the secondary current sheet length and width both scale as $S_{H}^{-1/2}$.
These scalings are consistent with a heuristic argument assuming secondary
current sheets are close to marginal stability. The distribution of plasmoids
as a function of the enclosed flux $\psi$ is found to obey a $\psi^{-1}$ power
law over an extended range, followed by a rapid fall off for large plasmoids.
These results are compared with those from resistive magnetohydrodynamic
studies.
