Cone-guided phase-space control of laser-driven proton beams

Laser-driven ion acceleration offers a promising route toward compact high-energy particle sources, yet achieving control of beam collimation, spectral width, and laser-to-ion energy conversion remains a central challenge for most applications. Using two- and three-dimensional particle-in-cell simulations, we investigate proton acceleration from a solid target consisting of a thin foil followed by a converging hollow plasma cone and irradiated by a relativistic laser pulse. The cone length critically controls the proton beam collimation and spectral width by regulating the lifetime and spatial structure of electron-driven sheath fields sustained along the cone walls. Specifically, the cone walls collapse throughout the irradiation process, and these sheath fields-enhanced by strong azimuthal magnetic fields that improve electron trapping-provide a tunable tradeoff. Matching the proton transit time to the cone collapse time reduces beam divergence, while an earlier cone collapse reduces the spectral width. Using a linearly polarized pulse in the radiation pressure acceleration plus target normal sheath acceleration regime exploits target heating to create these sheath field and magnetic field structures. These results identify cone-length-controlled sheath-field dynamics as a robust mechanism for proton beam control. Relative to the planar foil case, optimized cone lengths reduce the relative proton energy spread by approximately 63% in two-dimensional simulations and reduce the 25%-energy containment radius by approximately 46% in three-dimensional simulations after 200 µm of ballistic propagation.