Fine-structure investigation of turbulence-induced dissipation–diffusion in a nanoflare-loop with improved relativistic hybrid particle-in-cell and lattice Boltzmann method. II. Turbulence and instabilities

This evolution may comprise stages, such as arise, generate, develop, increase, and trigger, from initial linear to complex nonlinear chaos/turbulence. Based on the improved relativistic hybrid particle-in-cell and lattice Boltzmann method development in Paper I of this series of studies [Zhu et al., “Relativistic HPIC-LBM and its application in large temporal-spatial turbulent magnetic reconnection. Part I. Model development and validation,” Appl. Math. Modell. 78, 932–967 (2020); Zhu et al., “Electron acceleration in interaction of magnetic islands in large temporal-spatial turbulent magnetic reconnection,” Earth Planet. Phys. 3, 17–25 (2019); Zhu et al., “Relativistic HPIC-LBM and its application in large temporal-spatial turbulent magnetic reconnection. Part II. Role of turbulence in the flux rope interaction,” Appl. Math. Modell. 78, 968–988 (2020); Wang and Zhu, “HIP-based heterogeneous parallel 3D LBM fluid simulator (HIP-LBM3D) V1.0 [software],” Patent No. 2023SR0533996 (6 March 2023); Zhu et al., “Scalable simulations of 3D turbulence fine structure in nanoflare using a novel plasma statistical algorithm,” in Proceedings of the 5th International Conference on Statistics: Theory and Applications (ICSTA'23), 2023; Yan et al., “A new fluid numerical RHPIC-LBM algorithm from statistical physics,” China Patent No. 202311118994.2; Wang et al., “HIP-based heterogeneous parallel 3D LBM HD simulator (HIP-HDLBM) V1.0 [software],” Patent No. 2023SR0533996. (March 6, 2023); Zhu et al., “Software development of GeV-level-SEPs-induced extreme space weather disasters with plasma statistical physics theoretical model on domestic DCU accelerator heterogeneous supercomputer.” in Progress Report on China Nuclear Science &Technology: Computational Physics, 2024; Fu et al., “A new ARM-based CPU implementation of the RHPIC-LBM code,” in 32nd General Assembly International Union, 2024; Wang and Zhu, “HIP-based heterogeneous parallel 3D LBM MHD simulator (HIP-MHDLBM) V1.0 [software],” No. 2024SR2094116 (December 16, 2024); Zhu and Wang, “Dynamic-magnetohydrodynamic-kinetic coupled algorithm for RHPIC-LBM code,” China Patent No. 202511005823.8; Ma, “Fine-structure turbulence-induced dissipation–diffusion in the large temporal-spatial current sheet with mean field theory,” M.S. thesis (School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing, China, 2025); Ma et al., “Fine-structure investigation of the turbulence-induced dissipation-diffusion in Flare-CME current sheets,” Prog. Astron. 43(4), 1–26 (2025); Zhu et al., “Fine-structure investigation of turbulence-induced dissipation-diffusion in a nanoflare-loop with improved relativistic hybrid particle-in-cell and lattice Boltzmann method. I. Explicit expression and model,” Phys. Fluids ▪, ▪ (2025)], we validated, through simulations on a supercomputing platform, the basic features of turbulence and instabilities by considering anomalous viscosity and resistivity, and breaking of frozen-in condition. The simulation revealed that U-turbulence-induced viscosity dissipation-diffusion and B-turbulence-induced resistivity dissipation–diffusion interactions would lead to the following vortices/eddies—splitting and phase separating instabilities: (i) vortices/eddies-separation interface instabilities consisting of coupled B-Rayleigh–Taylor and U-Rayleigh–Taylor instabilities, and coupled B-Kelvin–Helmholtz and U-Kelvin–Helmholtz instabilities; (ii) twisted flux loop compression/expansion induced instabilities consisting of current/magnetic-driven multimode (m = 0, 1, 2, 3, 4……) Z- and {theta-pinch kink instabilities; and (iii) coupled B- and U-vortex shedding instabilities. This finding provides a comprehensive theoretical framework for elucidating the origins and sources of solar energetic particles (SEPs). It lays a pivotal foundation for clarifying the wave–particle interaction mechanisms responsible for extreme GeV-level SEP events, thereby facilitating the development of an early warning system for predicting SEP-induced space weather disasters.