Prompt acceleration of a μ⁺ beam in a toroidal wakefield driven by a shaped steep-rising-front Laguerre–Gaussian laser pulse

Recent experimental data for anomalous magnetic moments strongly indicates the existence of new physics beyond the Standard Model. Energetic μ⁺ bunches are relevant to μ⁺ rare decay, spin rotation, resonance and relaxation (μSR) technology, future muon colliders, and neutrino factories. In this paper, we propose prompt μ⁺ acceleration in a nonlinear toroidal wakefield driven by a shaped steep-rising-front Laguerre–Gaussian (LG) laser pulse. An analytical model is described, which shows that a μ⁺ beam can be focused by an electron cylinder at the centerline of a toroidal bubble and accelerated by the front part of the longitudinal wakefield. A shaped LG laser with a short rise time can push plasma electrons, generating a higher-density electron sheath at the front of the bubble, which can enhance the acceleration field. The acceleration field driven by the shaped steep-rising-front LG laser pulse is about four times greater than that driven by a normal LG laser pulse. Our simulation results show that a 300 MeV μ⁺ bunch can be accelerated to 2 GeV and its transverse size is focused from an initial value of w₀ = 5 μm to w = 2 μm in the toroidal bubble driven by the shaped steep-rising-front LG laser pulse with a normalized amplitude of a = 22.