Enhanced Laser-Driven Ion Acceleration in the Relativistic Transparency Regime

We report on the acceleration of ion beams from ultrathin diamondlike carbon foils of thickness 50, 30, and 10 nm irradiated by ultrahigh contrast laser pulses at intensities of $\sim 7\times {10}^{19}\mathrm{W}/{\mathrm{cm}}^2$. An unprecedented maximum energy of 185 MeV ($15\mathrm{MeV}/\mathrm{u}$) for fully ionized carbon atoms is observed at the optimum thickness of 30 nm. The enhanced acceleration is attributed to self-induced transparency, leading to strong volumetric heating of the classically overdense electron population in the bulk of the target. Our experimental results are supported by both particle-in-cell (PIC) simulations and an analytical model.

Figure 1

Experimental setup at TRIDENT (a) and a characteristic image of the proton beam profile at 20 MeV energy as obtained from a 50 nm DLC target (b).

Figure 2

Observed spectra of fully ionized carbon ions (a) for foil thicknesses of 50, 30, and 10 nm. An optimum in acceleration is seen for the 30 nm target, in excellent agreement with maximum energies of ${\mathrm{C}}^{6+}$ and protons deduced from 1D PIC simulations (b). The normalized instantaneous laser intensity at burnthrough time as derived from the presented analytical model (green diamonds) closely follows the cutoff energy curve.

Figure 3

Electric field in $y$ direction as deduced from a 2D PIC simulation at times $t_1=-355\mathrm{fs}$ (a) and $t_2=-211\mathrm{fs}$ (b) before the peak of the laser pulse reaches the 10 nm target initially located at $x=5\mu \mathrm{m}$ (color scale given in units of ${10}^{13}\mathrm{V}/\mathrm{m}$). The black curve shows the normalized electron density $n_e/n_{\mathrm{cr}}$, while the longitudinal electric field $E_x$ is marked in red. Each quantity represents an average over $2\mu \mathrm{m}$ in transverse ($z$) direction around the focal spot center.

Figure 4

Two-dimensional spatial distribution of proton energies as seen in a 2D PIC simulation of a 10 nm foil at times $t_1=-355\mathrm{fs}$ (a) and $t_2=-211\mathrm{fs}$ (b) before the arrival of the main pulse at the target (color scale given in units of MeV). Overlaid are the proton energies (blue curve) and the ${\mathrm{C}}^{6+}$ energies (red curve) at $z=0$.