Effect of the Number of Cylindrical Azimuthal Modes on Electron Energy and Angular Spectra in Simulations of Laser-Plasma Acceleration in Subcritical Plasma

Particle-in-cell (PIC) simulations of laser-plasma interaction using cylindrical geometry with azimuthal mode decomposition (AMD) significantly reduce computational costs compared with 3D simulations; however, for regimes in which axial symmetry is broken, the simulation accuracy depends on the number of modes (m) taken into account. This paper presents a systematic analysis of the AMD approach for two laser-plasma acceleration regimes: conventional laser wakefield acceleration (LWFA) in underdense plasma (ne = 0.005ncr) and self-modulated laser wakefield acceleration (SM-LWFA) in higher-density plasma (ne = 0.03ncr). It is shown that for axially symmetric LWFA, two modes (m = 2) are sufficient. For SM-LWFA, which is characterized by the development of symmetry-breaking instabilities, the requirements for the number of modes are more stringent: accurately reproducing the energy spectrum of accelerated electrons requires four modes (m = 4), while reproducing the angular spectrum requires twelve modes (m = 12). Even with twelve modes retained, the computational cost of the AMD simulation is approximately eight times lower than that of a full 3D simulation. These results are of particular importance for high-repetition-rate terawatt laser systems, in which SM-LWFA is the dominant acceleration mechanism, enabling higher acceleration gradients and larger beam charge.