Dual-pulse micronozzle acceleration of sub-GeV-class protons

We propose a dual-pulse micronozzle acceleration scheme that enables phase-locked acceleration of laser-driven protons, mitigating the trade-off between maximum proton energy and laser-to-proton conversion efficiency. A delay-tuned synchronization window injects a compact proton front generated by a shaping prepulse into a quasistatic axial electric field driven by a delayed main pulse in a micronozzle cavity. Phase locking preserves the relative phase between the proton bunch and the accelerating field, suppresses thermal debunching, and prolongs the acceleration stage. At main-pulse intensities of order 10^21 W/cm^2, sub-GeV proton cutoff energies are obtained with a total laser-to-proton conversion efficiency of about 20%. The efficiency for protons above 100 MeV exceeds about 13%, indicating preferential energy loading into a compact proton population. Simulations with an unconfined dual-pulse hydrogen rod show that the improvement results from temporal synchronization and geometric confinement, which sustain a long-lived axial accelerating channel. An analytical synchronization model agrees with the simulations. Three-dimensional particle-in-cell simulations confirm that phase locking and spectral hardening are preserved in slit-nozzle geometries, with cutoff energies about 60% higher than those of an unconfined hydrogen rod. These results establish phase-locked acceleration as a practical design principle for compact, high-yield sub-GeV proton drivers for secondary-particle applications.