Laser-driven high-energy proton beams from cascaded acceleration regimes

High-intensity laser-driven particle accelerators have garnered growing interest because they can produce pulsed, high-intensity multi-MeV ion beams suitable for applications in science, medicine and industry. A key research objective is to increase the maximum attainable proton energies, particularly beyond 100 MeV. Historically, record energies were achieved with large, low-repetition (>100 J) lasers driving target normal sheath acceleration (TNSA) from micrometre-thick foils, where the maximum proton energy scales as the square root of laser energy. Alternative, more coherent acceleration mechanisms have been explored to improve scaling and reduce laser energy requirements, enabling compact ultrashort-pulse lasers to reach similar performance with higher repetition rates. Under realistic experimental conditions, multiple mechanisms often coexist or occur sequentially, complicating their isolation and optimization. This work investigates and demonstrates a route to high-energy proton beams using ultrashort petawatt laser pulses incident on nanometre-scale plastic foils, where preheating by preceding light leads to a near-critical density profile and the onset of relativistically induced transparency (RIT) at the arrival of the main pulse. The study aims to identify optimal interaction conditions at the onset of RIT, elucidate the cascade of contributing acceleration mechanisms, and establish an experimentally accessible control parameter (target transparency) to reliably reach a high-performance domain for proton acceleration.

Prior studies established TNSA from micrometre-thick foils as a robust ion acceleration mechanism, with proton energies scaling approximately with the square root of laser energy (for example, Snavely et al., Fuchs et al.). To surpass 100 MeV using more compact systems, alternative mechanisms driven by radiation pressure and transparency have been explored: radiation pressure acceleration (RPA) including hole-boring and relativistic transparency-front RPA, collisionless shock acceleration, and hybrid schemes near the transition from opaque to transparent plasmas. Numerical and experimental works have shown enhanced acceleration when the main pulse arrives at the onset of RIT, leading to improved energy, directionality and, under idealized conditions, narrow energy spreads. Previous demonstrations approached near-100 MeV using transparency-enhanced hybrid schemes and highlighted the roles of prompt j×B-driven electrons, thermal/recirculating electrons establishing rear-side sheaths, and multi-species effects. Nevertheless, under realistic shot-to-shot variations, the superposition or cascade of mechanisms can yield ambiguous spectral signatures, motivating combined experimental-simulation approaches to identify and optimize the coupling of mechanisms in the RIT regime.

Experimental: Experiments were performed at the DRACO-PW Ti:sapphire laser (810 nm) delivering 30 fs FWHM pulses with up to 22.4 J on target at ≥1 Hz repetition. The temporal contrast was <10^-12 at 100 ps and <10^-6 at 10 ps before the peak. Pulses (p-polarized) were focused by an f/2.3 off-axis parabola to a 2.5 µm FWHM spot containing 32% of the total energy, corresponding to an estimated peak intensity of 6.5 × 10^20 W cm^-2 (a0 ≈ 55). The laser was incident at 50° on 210–270 nm Formvar (C5H8O2, ρ = 1.2 g cm^-3) foils; nominal targets were 250 ± 25 nm thick. Fundamental laser light transmitted through the target was recorded on a calibrated ceramic screen (16 cm × 16 cm) placed ~33 cm downstream and imaged with an 800 ± 25 nm bandpass for shot-resolved transparency quantification. Particle diagnostics: Two Thomson parabola spectrometers (TPS) at 15° (TPS15, pinhole 1 mm) and 45° (TPS45, pinhole 0.3 mm) relative to the laser axis measured proton and ion spectra with minimal detectable proton energy of 7 MeV. Energy uncertainty was better than ±10% at 150 MeV (TPS15) and ±4% at 60 MeV (TPS45), dominated by pinhole size; MCP detectors were cross-calibrated to a scintillator up to 60 MeV, and a 3 mm Al filter in front of the MCP suppressed heavier ions for unambiguous proton identification. Time-of-flight (TOF) detection at 31° used a Menlo APD210 placed ~4 m from the target, with a 2 mm Cu filter (threshold 34 MeV for protons) and fast oscilloscope readout; TOF confirmed maximum energies but did not yield reliable particle numbers for the highest energies. A scintillator-based proton beam profiler (DRZ High, 100 × 100 mm) at 87 mm distance provided angular profiles with energy thresholds set by Al absorbers (8, 25, 38 mm Al corresponding to proton thresholds of 42, 80, 102 MeV). A central horizontal slit enabled simultaneous TPS/TOF operation. For selected shots, a radiochromic film (RCF) stack (Gafchromic EBT3, 100 × 50 mm, 0.1–20 Gy) interleaved with Cu absorbers at 55 mm provided energy-resolved angular dose maps. Simulations: The interaction was modeled in two stages. (1) A 2D, radially symmetric hydrodynamic simulation (FLASH v4.6.2) of a 270 nm Formvar foil captured target pre-expansion from ~100 ps before the main pulse (onset of dielectric breakdown determined from measured contrast and optical probing) to 1 ps before peak. The model used tabulated EOS (FEOS), Lee–More conductivity and heat exchange; the resultant electron density profile was rotated around the symmetry axis for use in PIC. (2) A fully relativistic 3D particle-in-cell simulation (PIConGPU; 900 A100 GPUs, ~35,000 steps) used the hydrodynamic profile (densities below 0.04 ne discarded), p-polarized Gaussian laser focused to w0 = 2.14 µm at 45° oblique incidence, temporal profile matched to measurements with two exponential pedestals and a 30 fs Gaussian main pulse (peak a0 ≈ 50). The cell size was 20 nm with one carbon and eight hydrogen macroparticles per cell (13 electrons). The simulation reproduced ~4% forward transmission at the onset of RIT and generated angularly resolved proton spectra for comparison with measurements.

- Proton beams with a spectrally separated high-energy component up to 150 MeV were produced from 250 ± 25 nm plastic foils using ultrashort petawatt pulses without plasma mirrors or specialized target conditioning. - Optimal performance correlated with 0.5–3% transmitted fundamental light, identifying the onset of relativistically induced transparency (RIT) as the high-performance domain. Shots with >5% transmission exhibited strongly reduced acceleration (<25 MeV maximum protons) in both TPS axes. - Directional energy and scaling: TPS15 (15° from laser axis) recorded up to 150 MeV; TPS45 (45°) recorded up to 63 ± 3 MeV. With varied laser pulse energy El, maximum proton energy scaled ∝ El^1/2 at 45° (sheath-dominated) but increased linearly at 15° (prompt-driven), indicating distinct dominant mechanisms by angle. - Angular-spectral structure: Diagnostics consistently showed two components: (i) a medium-energy (<70 MeV) broadband component centered near target-normal with large divergence (≈±15°), and (ii) a spectrally and angularly separated high-energy (>100 MeV) component directed closer to the laser axis with reduced divergence (≈±3°), persisting to at least 104 MeV in RCF data. - Simulations revealed a cascade of mechanisms: front surface acceleration (FSA: hole-boring RPA, relativistic transparency-front RPA, collisionless shock) injects protons with ~20 MeV; subsequent acceleration occurs in fields driven by prompt j×B electron bunches and by a diffuse thermal/recirculating-electron sheath at the rear surface. Additional Coulomb repulsion (CR) arising from charge separation within the rear sheath contributes substantially in the laser-forward direction. - Energy partition from PIC tracer analysis: Fastest protons gain >50% of their energy during the prompt or thermal phases after an initial ~20 MeV from FSA. In the laser direction, CR adds >25% of the total energy, whereas at 45° CR contributes ~13%, consistent with the observed angular dependence and spectral modulations. The simulation reproduced the measured angular emission distribution, spectral modulation near the laser direction, and ~4% transmission.

The study demonstrates that operating at the onset of relativistically induced transparency with ultrashort petawatt pulses enables efficient coupling of a cascade of acceleration mechanisms, producing high-energy, directionally confined proton beams in a compact system. The experimental correlation between transmitted light and maximum energy provides a practical, shot-resolved proxy for identifying optimal interaction conditions despite inherent shot-to-shot fluctuations. The distinct angular scaling—linear with laser energy near the laser axis versus square-root scaling near target normal—supports the interpretation that prompt j×B-driven electron dynamics dominate the highest-energy proton acceleration toward the laser direction, while a thermal sheath governs target-normal emission. Three-dimensional PIC simulations, seeded by hydrodynamic pre-expansion, elucidate the sequential roles of FSA, prompt electron fields, thermal sheath acceleration, and additional Coulomb repulsion in shaping the spectra and angular distributions. Compared with earlier work in the RIT regime, the present results highlight the enhanced role of prompt electrons for ultrashort pulses and appropriate pre-expansion, facilitating efficient energy transfer both during and shortly after the main pulse. These findings address the challenge of reaching application-relevant energies with high-repetition compact lasers and provide a framework and control metric (transparency) for stabilization and optimization.

This work provides a proof-of-principle generation of spectrally modulated proton beams exceeding 100 MeV, reaching up to 150 MeV, by exploiting cascaded acceleration regimes initiated at the onset of relativistically induced transparency in ultrathin foils with ultrashort petawatt pulses. The identification of transmitted fundamental light as a robust feedback metric enables the selection of a high-performance regime and paves the way for automated optimization of laser and target parameters at high repetition rates. Based on the observed linear scaling near the laser axis, maximum proton energies beyond 250 MeV are projected at twice the laser pulse energy, contingent on maintaining suitable interaction conditions. Future work should integrate advanced diagnostics of transmitted and self-generated light with data-driven and Bayesian optimization frameworks in simulations and experiments to enhance stability, reproducibility and scalability toward application-ready laser-driven ion sources.

Shot-to-shot fluctuations in the focused intensity and target pre-expansion lead to variability in transmitted light and maximum energy. Performance deteriorates outside the narrow transparency window (>~5% transmission or too little transmission). The TOF detector has reduced sensitivity for quantifying particle numbers at the highest energies. While the simulations qualitatively reproduce average good-shot behavior, assigning a specific simulated case to an individual experimental shot is limited by uncertainties in exact interaction parameters, diagnostic metrology, and numerical simplifications; improved in-situ measurements and greater computational resources are needed for one-to-one comparisons.