INCORPORATION OF AMBIPOLAR DIFFUSION INTO THE ZEUS MAGNETOHYDRODYNAMICS CODE

Magnetic fields tied to ions can diffuse through mostly neutral gas: t his occurs in protostellar disks and in the cores of molecular clouds. We describe an algorithm that includes ambipolar diffusion in the ast rophysical magnetohydrodynamics code ZEUS. We use the approximations t hat both electrons and ions have equal and constant temperature, that the ion inertia is negligible, and that the ion density is proportiona l to a power of the neutral density. Our algorithm is fully explicit, and treats the magnetic field using constrained transport and the meth od of characteristics. We test the algorithm by computing the gravitat ional collapse of a magnetically supported slab, and by comparing the computed solution for an oblique C-shock to a semi-analytic solution t hat we have derived. We then compute the development of the magnetorot ational instability described by Balbus and Hawley in a magnetized acc retion disk, including the effects of ambipolar diffusion. Our computa tion agrees with the published linear analysis of how diffusion preven ts instability, and it allows us to describe the nonlinear development of the instability when diffusion is important but not dominant. We f ind that ambipolar diffusion indeed creates the sharp structures predi cted by Brandenburg and Zweibel.