We present ~400ks NuSTAR observations of the northeast (NE) and southwest (SW) non-thermal limbs of the Galactic SNR SN1006. We discovered three sources with X-ray emission detected at >50keV. Two of them are identified as background AGN. We extract the NuSTAR spectra from a few regions along the non-thermal limbs and jointly analyze them with the XMM-Newton spectra and the radio data. The broad-band radio/X-ray spectra can be well described with a synchrotron emission model from a single population of CR electrons with a power law energy distribution and an exponential cutoff. The power law index of the electron particle distribution function (PDF) is ~1.88-1.95 for both the NE and SW limbs, and we do not find significant evidence for a variation of this index at different energy (curvature). There are significant spatial variations of the synchrotron emission parameters. The highest energy electrons are accelerated in regions with the lowest expansion velocity, which is opposite to what has been found in the Tychos SNR. In addition to a gradual steepening of synchrotron emission from the center of the non-thermal limbs to larger azimuthal angles, we also find that both the emission spectrum and the PDF are significantly flatter in three regions in the SW limb where the shock encounters higher density ambient medium. The NE limb also shows significantly higher cutoff energy in the PDF than the SW limb. By comparing with the roughly symmetric TeV emission and largely asymmetric GeV emission from the two non-thermal limbs, we conclude that the asymmetry in the ambient medium and magnetic fields may have largely modified the acceleration and emission of CR leptons.
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