The north east shell of SN 1006 is the most probable acceleration site of high energy electrons ( up to \sim 100 TeV ) with the Fermi acceleration mechanism at the shock front .
We resolved non-thermal filaments from thermal emission in the shell with the excellent spatial resolution of Chandra .
The thermal component is extended widely over about \sim 100 arcsec ( about 1 pc at 1.8 kpc distance ) in width , consistent with the shock width derived from the Sedov solution .
The spectrum is fitted with a thin thermal plasma of kT = 0.24 keV in non-equilibrium ionization ( NEI ) , typical for a young SNR .
The non-thermal filaments are likely thin sheets with the scale widths of \sim 4 arcsec ( 0.04 pc ) and \sim 20 arcsec ( 0.2 pc ) at upstream and downstream , respectively .
The spectra of the filaments are fitted with a power-law function of index 2.1–2.3 , with no significant variation from position to position .
In a standard diffusive shock acceleration ( DSA ) model , the extremely small scale length in upstream requires the magnetic field nearly perpendicular to the shock normal .
The injection efficiency ( \eta ) from thermal to non-thermal electrons around the shock front is estimated to be \sim 1 \times 10 ^ { -3 } under the assumption that the magnetic field in upstream is 10 \mu G. In the filaments , the energy densities of the magnetic field and non-thermal electrons are similar to each other , and both are slightly smaller than that of thermal electrons .
in the same order for each other .
These results suggest that the acceleration occur in more compact region with larger efficiency than previous studies .