Full 3-D MHD calculations of accretion flow Structure in magnetic   cataclysmic variable stars with strong and complex magnetic fields
  We performed 3D MHD calculations of stream accretion in cataclysmic variable stars for which the white dwarf primary star possesses a strong and complex magnetic field. These calculations are motivated by observations of polars; cataclysmic variables containing white dwarfs with magnetic fields sufficiently strong to prevent the formation of an accretion disk. So an accretion stream flows from the L1 point and impacts directly onto one or more spots on the surface of the white dwarf. Observations indicate that the white dwarf, in some binaries, possesses a complex (non-dipolar) magnetic field. We perform simulations of 10 polars or equivalently one asynchronous polar at 10 different beat phases. Our models have an aligned dipole plus quadrupole magnetic field centered on the white dwarf primary. We find that for a sufficiently strong quadrupole component an accretion spot occurs near the magnetic equator for slightly less than half of our simulations while a polar accretion zone is active for most of the rest of the simulations. For one or two configurations; accretion at the dominant polar region and at an equatorial zone occurs simultaneously. These are the first 3D MHD calculations to confirm the existence of complex magnetic fields in magnetic CVs. We conclude, that it might be difficult observationally determine if the field is a pure dipole or if it is complex for polars, but there will be indications for some systems. Specifically, a complex magnetic field should be considered if the there is an accretion zone near the white dwarf's spin equator (orbital plane) or if there are two or more accretion regions that cannot be fit by a dipole magnetic field. For asynchronous polars, magnetic field constraints are expected to be substantially stronger, with clearer indicators of complex field geometry due to changes in accretion flow structure as a function of spin-orbit beat phase. 
A. G. Zhilkin, D. V. Bisikalo, P. A. Mason
astro-ph.HE