Progress in Simulations of Solar Energetic Particles Propagation in Large-scale Structures of Interplanetary Background Solar Wind

This comprehensive review synthesizes pivotal advances in simulating Solar Energetic Particle (SEP) propagation through large-scale solar wind structures, integrating three complementary methodologies: analytical Parker-like magnetic fields for steady-state backgrounds, data-driven frameworks assimilating multi-satellite observations (STEREO, WIND) to reconstruct 2D Stream Interaction Regions (SIRs), and 3D Magnetohydrodynamic (MHD) simulations resolving tilted-dipole Corotating Interaction Regions (CIRs) with about 35° inclinations. The work quantifies how solar wind topology governs SEP dynamics, revealing that magnetic focusing dominates flux enhancements in compression zones by trapping particles in mirror-like structures, enabling multi-reflection acceleration without shocks and amplifying peak fluxes by up to 200% in simulated CIRs, while adiabatic cooling primarily drives flux decay in fast solar wind streams, with pitch-angle diffusion modulating intensity levels without altering temporal profiles. Critically, vertical diffusion reconciles multi-satellite discrepancies through cross-field transport, smoothing flux evolution as validated in the 2016 STA event (simulations matched observations within 10% error when α = 0.018～0.025), and CIR geometry—controlled by solar wind speed contrasts (ΔV > 500ΔV > 500 km·s^–1 widening compression regions), dipole tilt angles optimizing latitudinal spread, and fast-stream widths modulating longitudinal confinement—dictates acceleration efficiency, where reverse compressions accelerate 0.5～5 MeV protons twice as effectively as forward zones due to steeper magnetic gradients. Event validations confirm these mechanisms: STEREO-A’s August 2016 CIR showed magnetic trapping explained 95% of flux rise, and STEREO-B’s September 2007 anomalous proton enhancement arose from shorter magnetic pathlengths to compression sources. Computationally, the framework synergizes focused transport equations with Stochastic Differential Equations (SDEs), where backward SDEs efficiently map observational points to source distributions and forward SDEs visualize system-wide transport, achieving 100× acceleration over finite-difference methods. Future work targets transient structures (e.g., embedding CME-driven shocks via EUHFORIA/iPATH coupling) and kinetic-scale turbulence, with next-phase efforts developing unified acceleration-transport models incorporating stochastic re-acceleration, leveraging Parker Solar Probe and Solar Orbiter data to resolve magnetic islands/current sheets, and deploying machine learning to optimize background parameterization for real-time space weather forecasting.