  Accretion disks are ubiquitous in the universe and it is generally accepted
that magnetic fields play a pivotal role in accretion-disk physics. The spin
history of millisecond pulsars, which are usually classified as magnetized
neutron stars spun up by an accretion disk, depends sensitively on the magnetic
field structure, and yet highly idealized models from the 80s are still being
used for calculating the magnetic field components. We present a possible way
of improving the currently used models with a semi-analytic approach. The
resulting magnetic field profile of both the poloidal and the toroidal
component can be very different from the one suggested previously. This might
dramatically change our picture of which parts of the disk tend to spin the
star up or down.
