Design and simulation of a radius-varying active plasma lens for focusing laser-accelerated protons

With plasma as the medium, laser driven accelerator can generate high energy pulsed particles with initially micron scale source size and broad energy spread. Efficient transport of the beam with above characteristics is a challenging task. Active plasma lenses (APLs) provide strong, tunable, axisymmetric focusing with weak chromatic dependencies, making them highly beneficial for compact laser accelerators. However, due to the large divergence angle of the laser-accelerated proton beams, a majority of the protons cannot be transmitted through the APLs, resulting in losses. In this study, we propose a radius-variable APL (RV-APL) that optimizes the capillary's geometry based on the beam envelope. The collection angle of RV-APL under the design parameters in the article can be increased by about 80% compared to a cylindrical APL (C-APL) with a constant radius, achieving the transmission capacity of traditional magnets. The magnetic field distribution of the RV-APL was predicted using a two-dimensional axisymmetric plasma discharge model, and the focused beam's chromaticity and emittance properties were theoretically analyzed through particle tracking simulation.