  We investigate the effect of non-ideal magnetohydrodynamics (MHD) on the
formation of binary stars using a suite of three-dimensional smoothed particle
magnetohydrodynamics simulations of the gravitational collapse of one solar
mass, rotating, perturbed molecular cloud cores. Alongside the role of Ohmic
resistivity, ambipolar diffusion and the Hall effect, we also examine the
effects of magnetic field strength, orientation and amplitude of the density
perturbation. When modelling sub-critical cores, ideal MHD models do not
collapse whereas non-ideal MHD models collapse to form single protostars. In
super-critical ideal MHD models, increasing the magnetic field strength or
decreasing the initial density perturbation amplitude decreases the initial
binary separation. Strong magnetic fields initially perpendicular to the
rotation axis suppress the formation of binaries and yield discs with magnetic
fields ~10 times stronger than if the magnetic field was initially aligned with
the rotation axis. When non-ideal MHD is included, the resulting discs are
larger and more massive, and the binary forms on a wider orbit. Small
differences in the super-critical cores caused by non-ideal MHD effects are
amplified by the binary interaction near periastron. Overall, the non-ideal
effects have only a small impact on binary formation and early evolution, with
the initial conditions playing the dominant role.
