  Magnetic flux redistribution lies at the heart of the problem of star
formation in dense cores of molecular clouds that are magnetized to a realistic
level. If all of the magnetic flux of a typical core were to be dragged into
the central star, the stellar field strength would be orders of magnitude
higher than the observed values. This well-known "magnetic flux problem" can in
principle be resolved through non-ideal MHD effects. Two dimensional
(axisymmetric) calculations have shown that ambipolar diffusion, in particular,
can transport magnetic flux outward relative to matter, allowing material to
enter the central object without dragging the field lines along. We show
through simulations that such axisymmetric protostellar accretion flows are
unstable in three dimensions to magnetic interchange instability in the
azimuthal direction. The instability is driven by the magnetic flux
redistributed from the matter that enters the central object. It typically
starts to develop during the transition from the prestellar phase of star
formation to the protostellar mass accretion phase. In the latter phase, the
magnetic flux is transported outward mainly through advection, by strongly
magnetized low-density regions that expand against the collapsing inflow. The
tussle between the gravity-driven infall and magnetically driven expansion
leads to a filamentary inner accretion flow, more disordered than previously
pictured. The efficient outward transport of magnetic flux by advection lowers
the field strength at small radii, making the magnetic braking less efficient
and the formation of rotationally supported disks easier in principle. However,
we find no evidence for such disks in any of our rotating collapse simulations.
We conclude that the inner protostellar accretion flow is shaped to a large
extent by this magnetic interchange instability. How disks form in such an
environment is unclear.
