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.

Carbon nanotube foams (CNFs) have been successfully used as near-critical-density targets in the laser-driven acceleration of high-energy ions and electrons. Here we report the recent advances in the fabrication technique of such targets. With the further developed floating catalyst chemical vapor deposition (FCCVD) method, large-area ($>25\kern0.5em {\mathrm{cm}}^2$) and highly uniform CNFs are successfully deposited on nanometer-thin metal or plastic foils as double-layer targets. The density and thickness of the CNF can be controlled in the range of $1{-}13\kern0.5em \mathrm{mg}/{\mathrm{cm}}^3$ and $10{-}200\kern0.5em \mu \mathrm{m}$, respectively, by varying the synthesis parameters. The dependence of the target properties on the synthesis parameters and the details of the target characterization methods are presented for the first time.