Intensity-Dependent Dimensionality Effects on Laser-Accelerated Protons in 1D, 2D, and 3D Particle-in-Cell Simulations

Lower-dimensional 1D/2D Particle-In-Cell (PIC) simulations are often used in place of more realistic 3D simulations for modeling laser-ion acceleration, but the consequences are not fully understood. We build upon previous work by exploring a large parameter space consisting of nineteen fully 3D PIC simulations with laser intensities ranging from 10¹⁷ W/cm² to 10²¹ W/cm² and spot sizes from 1 μm to 8 μm. The 3D calculations for maximum proton energy, conversion efficiency, and target transparency are compared to corresponding 1D/ 2D simulations and the effects of laser polarization in 2D are explored. Many of the quantitative trends of 1D/2D simulations agree with 3D, but inconsistently. For example, the maximum proton energy increases with laser intensity for all simulations, but 1D and 2D simulations overpredict 3D results and the degree of this overprediction shows pronounced differences for higher intensities and smaller spot sizes. These results highlight the complexity of comparing 1D, 2D, and 3D simulations quantitatively and caution the use of a constant scale factor to compare lower dimensional simulation results with 3D simulations or experiments that span different regimes of ion acceleration. We also fit the time-dependent growth of maximum proton energy with existing analytic models, which elucidates the effects simulation dimensionality on ion acceleration and allows the extrapolation of final ion energy in 3D simulations from the initial behavior.