  We present a radio polarization study of SN 1006, based on combined VLA and
ATCA observations at 20 cm that resulted in sensitive images with an angular
resolution of 10 arcsec. The fractional polarization in the two bright radio
and X-ray lobes of the SNR is measured to be 0.17, while in the southeastern
sector, where the radio and non-thermal X-ray emission are much weaker, the
polarization fraction reaches a value of 0.6 +- 0.2, close to the theoretical
limit of 0.7. We interpret this result as evidence of a disordered, turbulent
magnetic field in the lobes, where particle acceleration is believed to be
efficient, and a highly ordered field in the southeast, where the acceleration
efficiency has been shown to be very low. Utilizing the frequency coverage of
our observations, an average rotation measure of ~12 rad/m2 is determined from
the combined data set, which is then used to obtain the intrinsic direction of
the magnetic field vectors. While the orientation of magnetic field vectors
across the SNR shell appear radial, a large fraction of the magnetic vectors
lie parallel to the Galactic Plane. Along the highly polarized southeastern
rim, the field is aligned tangent to the shock, and therefore also nearly
parallel to the Galactic Plane. These results strongly suggest that the ambient
field surrounding SN 1006 is aligned with this direction (i.e., from northeast
to southwest) and that the bright lobes are due to a polar cap geometry. Our
study establishes that the most efficient particle acceleration and generation
of magnetic turbulence in SN 1006 is attained for shocks in which the magnetic
field direction and shock normal are quasi-parallel, while inefficient
acceleration and little to no generation of magnetic turbulence obtains for the
quasi-perpendicular case.
