Modelling the particle dynamics in turbulent plasmas using the innovative multi-scale Box-In-Box (BIB) approach

The solar wind is an accessible natural laboratory for investigating thermal and energetic particles in space plasmas. The particle dynamics in the solar wind has a highly multi-scale nature, covering 8 orders of magnitude of spatial scales, from the lengths characteristic of the electron gyromotion around magnetic field lines ( ~1 km) to those characteristic of particle transport from the Sun to the Earth ( ~ 1 au). Studying such dynamics is a difficult endeavour, especially due to the solar wind’s strongly turbulent nature. Current models of particle dynamics in turbulent plasmas suffer from one or more limitations, such as unrealistic plasma background (e.g., 2D modelling, lack of the correct statistical turbulent properties such as anisotropy and intermittency of structures) or limited accuracy (e.g., small computational grids, low resolution in phase space). Most importantly, they only employ one simulation at a time and thus they only model the turbulent energy cascade over three decades of scales at best. 
We present our innovative solution to overcome all those limitations: the multi-scale Box-in-Box (BIB) approach.  The first step is to model the turbulent energy cascade from very large to very small scales, using a portion of a large simulation as initial condition for another one with higher resolution and repeating this process multiple times in sequence while coupling different physical models, e.g., MHD at the largest scales, hybrid across the ion scales, and fully kinetic at electron ones. The second step is advancing test-particles trajectories using the turbulence simulations as an evolving background from small to large scales, starting from the fully kinetic simulation and then switching to the hybrid and finally to the MHD one as the energy (and thus the gyroradius) of the test particles increases. We will show and discuss the main technical challenges of this kind of approach, the required operations in the different steps of the procedure, and some successful results. Our innovative BIB approach makes it possible to model the large-scale propagation of energetic particles in the turbulent solar wind while retaining a realistic and self-consistent description of the microphysics responsible for particle energization. Our BIB simulations will be particularly useful for developing and testing new visualisation and analysis techniques for future multi-scale space missions such as HelioSwarm and Plasma Observatory.