  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.
