It is established that the formation of rotationally supported disks duringthe main accretion phase of star formation is suppressed by a moderately strongmagnetic field in the ideal MHD limit. Non-ideal MHD effects are expected toweaken the magnetic braking, perhaps allowing the disk to reappear. Weconcentrate on one such effect, ambipolar diffusion, which enables the fieldlines to slip relative to the bulk neutral matter. We find that the slippagedoes not sufficiently weaken the braking to allow rotationally supported disksto form for realistic levels of cloud magnetization and cosmic ray ionizationrate; in some cases, the magnetic braking is even enhanced. Only in dense coreswith both exceptionally weak fields and unreasonably low ionization rate dosuch disks start to form in our simulations. We conclude that additionalprocesses, such as Ohmic dissipation or Hall effect, are needed to enable diskformation. Alternatively, the disk may form at late times when the massiveenvelope that anchors the magnetic brake is dissipated, perhaps by aprotostellar wind.
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