  Theoretical studies of the plasmoid instability generally assume that the
reconnecting magnetic fields are symmetric. We relax this assumption by
performing two-dimensional resistive magnetohydrodynamic simulations of the
plasmoid instability during asymmetric inflow magnetic reconnection. Magnetic
asymmetry modifies the onset, scaling, and dynamics of this instability.
Magnetic islands develop preferentially into the weak magnetic field upstream
region. Outflow jets from individual X-points impact plasmoids obliquely rather
than directly as in the symmetric case. Consequently, deposition of momentum by
the outflow jets into the plasmoids is less efficient, the plasmoids develop
net vorticity, and shear flow slows down secondary merging between islands.
Secondary merging events have asymmetry along both the inflow and outflow
directions. Downstream plasma is more turbulent in cases with magnetic
asymmetry because islands are able to roll around each other after exiting the
current sheet. As in the symmetric case, plasmoid formation facilitates faster
reconnection for at least small and moderate magnetic asymmetries. However,
when the upstream magnetic field strengths differ by a factor of four, the
reconnection rate plateaus at a lower value than expected from scaling the
symmetric results. We perform a parameter study to investigate the onset of the
plasmoid instability as a function of magnetic asymmetry and domain size. There
exist domain sizes for which symmetric simulations are stable but asymmetric
simulations are unstable, suggesting that moderate magnetic asymmetry is
somewhat destabilizing. We discuss the implications for plasmoid and flux rope
formation in solar eruptions, laboratory reconnection experiments, and space
plasmas. The differences between symmetric and asymmetric simulations provide
some hints regarding the nature of the three-dimensional plasmoid instability.
