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The theory of non-linear diffusive shock acceleration (NLDSA) predicts the formation of a precursor upstream of the shock, where accelerated particles diffuse and induce magnetic field amplification (MFA) through streaming instability. The non-detection of this precursor in X-rays in Chandra observations of the north-eastern region of SN 1006 (G329.6+14.6) led the authors of some previous work to impose an upper limit to the X-ray emission generated by accelerated electrons diffusing in this precursor, at an emissivity level of <1.5 per cent of the emission from the downstream region. This has been used as an argument against Fermi acceleration at this shock. Here, we calculate the spectrum and spatial distribution of accelerated particles in SN 1006 and show that Chandra results (including more recent data) are in perfect agreement with the predictions of NLDSA suggesting efficient particle acceleration and MFA upstream of the shock by a factor of ∼10. [ABSTRACT FROM AUTHOR]