Figure 5: Scaling to higher laser intensity and multistage acceleration.

(a) Total charge carried by the pulse moving along the wire connected to the laser-irradiated target, plotted against incident laser intensity on target (black solid line). The blue solid line shows the accelerating gradient inside a helical coil of same diameter and pitch as the one used in our experiment. (b) Schematic representation of a double-stage acceleration setup using two helical coils driven by two laser pulses. (c) Comparison between the simulated proton spectra, taken at 50 mm from the proton source over a 2 mm × 2 mm area, obtained for: flat-foil proton source (black-input spectrum in the simulation), single-stage (blue) and double-stage (red) coil re-acceleration. Both coils were of 0.5 mm internal diameter and 10 mm long, with variable pitch suited to their input proton energies (∼40 and ∼70 MeV, respectively, for the first and second stages). The parameters for the charge pulse in both coils were taken as those expected from the interaction of a PW, 30 fs laser (e.g. as available at GIST, Korea³³) with a thin target, leading to an acceleration gradient of ∼3 GeV m⁻¹ (discussed in the text). The shaded areas A, B1 and B2 represent, respectively, the proton bunch accelerated from the first coil and the proton bunches accelerated and decelerated by the second coil. The total number of particles in the bunches B1 and B2 is approximately equal to the number of particles in the bunch A. The time of arrival of the charge pulse at the entrance of the second coil was synchronized with the arrival of the ∼70 MeV proton bunch produced by the first coil.