Efficient muon acceleration in laser wakefields driven by single or combined laser pulses

Laser plasma wakefields can provide extremely high fields both in transverse and longitudinal directions, which are very suitable for short-lived charged particle acceleration, such as muons. To get efficient capture and acceleration, we have numerically investigated the acceleration of externally injected muons in laser wakefields driven by usual Gaussian or flying focus lasers. The muons are produced from high-energy electrons interacting with high-Z solid targets, which typically have a broad energy spectrum ranging from hundreds of MeV to several GeV. We classify these muons into three categories according to their initial energies and suggest different drivers for the wakefield acceleration. For low-energy muons (such as E 0 similar to 600 MeV), as their velocity is much smaller than the phase velocity of a typical wakefield, the optimal driver laser is the combination of a Gaussian laser with a flying focus laser. For moderate-energy muons (such as E 0 similar to 1.5 GeV), using a Gaussian laser as the driver is the best choice due to its ability to achieve phase-locked acceleration. For high-energy muons (such as E 0 similar to 5 GeV), in order to avoid dephasing, which usually happens in LWFA, the flying focus laser is suggested to realize phase-locked acceleration. The final muon energies obtained in three cases are 1.2, 2.6, and 6.0 GeV, respectively, with trapping efficiencies of 88%, 92%, and 86%, and the relative energy spread of 2%, 13%, and 10%. Our study demonstrates the possibility for efficient muon acceleration by all optical acceleration with hundred terawatt-class lasers.