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 the ion energy by utilizing the transient current originating from the self-discharging of the targets. The acceleration length of the protons can exceed a few millimeters, and the accelerating gradient is in the order of GeV/m. How to ensure the synchronization of the accelerating electric field with the protons is a crucial problem for an efficient post-acceleration. In this paper, we study how the electric field mismatch induced by the current dispersion affects the synchronous acceleration of the 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 enhanced by 4 times. And it is expected that the proton energy would reach 45 MeV using a hundreds-terawatt laser, or over 100 MeV using a petawatt laser, by controlling the current dispersion.