  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.
