We propose to use a 10 petawatt (PW) laser irradiating onto a target with a concave surface, which can focus the laser beam and attain a more intense laser field, so as to increase both the yield and mean energy of emitted γ-rays. 2D particle-in-cell simulation results show that the peak electric field after the reflection of the laser from the target in this new scheme can reach 1.8 times as high as that in the plane target case. Such an enhanced laser field enables an increase in the number of hot electrons in front of the incident plane and raises the probability rate of generating high-energy γ-rays significantly by non-linear Compton scattering. As a result, 1.5×1013γ photons with a mean energy of 9.2MeV are obtained. These photons mainly point toward two directions and distribute in pulses with the duration of each pulse of 400as. A brightness as high as 3.6×1025photons/(mm2mrad2s0.1%BW) is obtained in one pulse. Compared to no positron observed for a plane target, a positron yield of 3.0×108 can be achieved in this new scheme.

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