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A diamond-like carbon circular target is proposed to improve the $\gamma$-ray emission and pair production with lasers intensity of $8\times 10^{22} ~\mathrm{W/cm^2}$ by using two-dimensional particle-in-cell simulations with quantum electrodynamics. It is found that the circular target can significantly enhance the density of $\gamma$-photons than plane target when two colliding circularly polarized lasers irradiate the target. By multi-lasers irradiate the circular target, the optical trap of lasers can prevent the high energy electrons accelerated by laser radiation pressure from escaping. Hence, high density as $5164 n_c$ $\gamma$-photons is obtained through nonlinear Compton back-scattering. Meanwhile, $2.7 \times 10^{11}$ positrons with average energy of $230 ~\mathrm{MeV}$ is achieved via multi-photon Breit-Wheeler process. Such ultrabright $\gamma$-ray source and dense positrons source can be useful to many applications. The optimal target radius and laser mismatching deviation parameters are also discussed in detail., Comment: 16 pages, 8 figures