This paper reports the first discovery of TeV gamma-ray emission from a supernova remnant made with the CANGAROO 3.8 m Telescope. TeV gamma rays were detected at the sky position and extension coincident with the north-east (NE) rim of shell-type Supernova remnant (SNR) SN1006 (Type Ia). SN1006 has been a most likely candidate for an extended TeV Gamma-ray source, since the clear synchrotron X-ray emission from the rims was recently observed by ASCA (Koyama et al. 1995), which is a strong evidence of the existence of very high energy electrons up to hundreds of TeV in the SNR. The observed TeV gamma-ray flux was $(2.4pm 0.5(statistical) pm 0.7(systematic)) times 10^{-12}$ cm$^{-2}$ s$^{-1}$ ($ge 3.0pm 0.9$ TeV) and $ (4.6pm 0.6 pm 1.4) times 10^{-12}$ cm$^{-2}$ s$^{-1}$ ($ge 1.7pm 0.5$ TeV) from the 1996 and 1997 observations, respectively. Also we set an upper limit on the TeV gamma-ray emission from the SW rim, estimated to be $ 1.1 times 10^{-12}$ cm$^{-2}$ s$^{-1}$ ($ge 1.7pm 0.5$ TeV, 95% CL) in the 1997 data. The TeV gamma rays can be attributed to the 2.7 K cosmic background photons up-scattered by electrons of energies up to about 10$^{14}$ eV by the inverse Compton (IC) process. The observed flux of the TeV gamma rays, together with that of the non-thermal X-rays, gives firm constraints on the acceleration process in the SNR shell; a magnetic field of $6.5pm2$ $mu$G is inferred from both the synchrotron X-rays and inverse Compton TeV gamma-rays, which gives entirely consistent mechanisms that electrons of energies up to 10$^{14}$ eV are produced via the shock acceleration in SN1006.
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