The evolution of the magnetic field of an accreting magnetic white dwarf with an initially dipolar field at the surface has been studied for non-spherical accretion under simplifying assumptions .
Accretion on to the polar regions tends to advect the field toward the stellar equator which is then buried .
This tendency is countered by Ohmic diffusion and magneto-hydrodynamic instabilities .
It is argued that if matter is accreted at a rate of \dot { M } _ { crit } \sim 10 ^ { 16 } g s ^ { -1 } and the total mass accreted exceeds a critical value \Delta M _ { crit } \sim 0.1 - 0.2 M _ { \odot } , the field may be expected to be restructured , and the polar field to be reduced reaching a minimum value of \sim 10 ^ { 3 } G ( the “ bottom field ” ) independently of the initial field strength .
Below this critical accretion rate , the field diffuses faster than it can be advected , and accretion has little effect on field strength and structure .

In polars , where the magnetic field strength ( \sim 10 ^ { 7 } -10 ^ { 8 } G ) is strong enough to lock the magnetic white dwarf into synchronous rotation with the orbit and a disc does not form , magnetic braking is severely curtailed as the stellar wind from the secondary becomes trapped in the combined magnetosphere of the two stars .
The mass transfer rate in such systems is typically \mbox { $ \stackrel { \scriptstyle < } { \scriptstyle \sim } $ } 10 ^ { 16 } g s ^ { -1 } , and field restructuring is not expected .
In systems with fields not strong enough to achieve synchronism and where accretion occurs via a truncated disc ( the intermediate polars ) , normal magnetic braking may be expected .
The mass transfer rates are then typically \mbox { $ \stackrel { \scriptstyle > } { \scriptstyle \sim } $ } 10 ^ { 16 } g s ^ { -1 } above the 2 - 3 hour Cataclysmic Variable period gap , and thus a significant reduction of the polar field strength could occur if such a system accumulates the required critical mass M _ { crit } .
However , due to mass loss during nova eruptions , only a small fraction of such systems ( those that first come into contact at long orbital periods ) may accumulate sufficient mass to reach the bottom field configuration .
We argue that the observed properties of the Magnetic Cataclysmic Variables ( MCVs ) can generally be explained by a model where the field is at most only partially restructured due to accretion .
If there are systems that have reached the bottom field , they may be found among the dwarf novae , and be expected to exhibit quasi periodic oscillations .