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

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