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In low ionization gas, a magnetic field tied only to the ions can slip past the neutral gas, because of the weak collisional coupling between the low density ions and the neutral gas. This process is known as ambipolar diffusion. It acts in protostellar accretion disks, as well as in molecular clouds and star-forming cores.
We have added ambipolar diffusion to ZEUS-3D, an Eulerian, second-order astrophysical MHD code. We used an explicit method which we describe. We have found two test problems to compare against our code. The first is 1D collapse of a magnetized slab under self-gravity. This test is unsatisfactory as there are no analytic solutions for the dynamics of the collapse, only for the final state, which does not directly depend on the diffusion. The second test is an oblique C-shock in 1.5D. We have found a semi-analytic solution for its structure, and compare this to our numerical solution, with good results.
Finally, we describe our first application of this code, to modeling Balbus-Hawley instabilities in the presence of ambipolar diffusion. The Balbus-Hawley instability occurs when a weak magnetic field threads a Keplerian accretion disk. The field can act like a viscous couple to transport angular momentum through the disk. Ambipolar diffusion can reduce the effectiveness of this process or prevent it entirely. We present preliminary computations in agreement with a recent linear analysis that found the criterion for ambipolar diffusion to prevent the instability. Our ultimate goal is to include disk stratification in order to model magnetocentrifugal winds.
