Synchronous post-acceleration of laser-driven protons in helical coil targets by controlling the current dispersion

Post-acceleration of protons in helical coil targets driven by intense, ultrashort laser pulses can enhance ion energy by utilizing the transient current from the targets’ self-discharge. The acceleration length of protons can exceed a few millimeters, and the acceleration gradient is of the order of GeV/m. How to ensure the synchronization between the accelerating electric field and the protons is a crucial problem for efficient post-acceleration. In this paper, we study how the electric field mismatch induced by current dispersion affects the synchronous acceleration of protons. We propose a scheme using a two-stage helical coil to control the current dispersion. With optimized parameters, the energy gain of protons is increased by four times. Proton energy is expected to reach 45 MeV using a hundreds-of-terawatts laser, or more than 100 MeV using a petawatt laser, by controlling the current dispersion.