Laser Driving Highly Collimated $\gamma$-ray Pulses for the Generation of $\mu^-\mu^+$ and $e^-e^+$ Pairs in $\gamma-\gamma$ Collider

A scheme to generate highly collimated $\gamma$-ray pulse is proposed for the production of muon and electron pairs in $\gamma-\gamma$ collider. The $\gamma$-ray pulse, with high conversion efficiency, can be produced as the result of electron phase-locked acceleration in longitudinal electric field through the interaction between an ultra-intense laser pulse and a narrow tube target. Numerical simulation shows that 18\% energy of a 10-PW laser pulse is transferred into the forward $\gamma$-rays in a divergence angle less than $ 3^\circ$. The $\gamma$-ray pulse is applied in $\gamma-\gamma$ collider, in which muon pairs can be produced and electron pairs can be enhanced by more than 3 orders of magnitude. This scheme, which could be realized with the coming 10PW class laser pulses, would allow the observation of a $\gamma-\gamma$ collider for electron and muon pairs in laboratory.