1：Experimental Design and Method Selection:

The study employs a fully relativistic particle-in-cell (PIC) simulation to investigate the ion acceleration dynamics of the LS-RPA and the HB-RPA. The transition and competition between LS- and HB-RPA modes are explored with a one-dimensional (1D) theoretical model, and two-dimensional simulations are conducted to validate the 1D results and examine multi-dimensional effects.

2：Sample Selection and Data Sources:

The simulations use a low-density planar target consisting of fully ionized carbon (C6+) with an initial ion density of ni0 ≈ 60 to 300 nc. The laser intensity is maintained in the range of 1020 ? 1021 W/cm2, corresponding to the normalized vector potential a0 of ～10 to

3：List of Experimental Equipment and Materials:

The simulations are performed using the fully relativistic 2D PIC code EPOCH. A circularly polarized laser pulse with a wavelength of λL = 1.0μm is used, with a Gaussian spatial profile and a flat-top temporal profile.

4：0μm is used, with a Gaussian spatial profile and a flat-top temporal profile. Experimental Procedures and Operational Workflow:

4. Experimental Procedures and Operational Workflow: The laser pulse is irradiated onto the left boundary of the simulation box and propagates to the right. The target is located in region 100λL ≤ x ≤ d, where d is the target’s thickness. The temporal step size is auto-applied under the Courant-Friedrichs-Lewy (CFL) condition.

5：Data Analysis Methods:

The ion velocity spectra and maximum ion velocity are analyzed as functions of the target’s thickness to classify the dynamics in each RPA mode.