Sayram: A Positivity-Preserving Open Source 3D Radiation Belt Modeling Code

Abstract

Radiation belt dynamics is typically modeled using a quasilinear diffusion equation. However, standard numerical methods often produce non-physical negative or oscillatory solutions due to cross-diffusion terms. Here, we present Sayram, an open-source 3D radiation belt modeling code that employs a positivity-preserving finite volume method to address this decades-old numerical challenge. Sayram incorporates key physical processes of the radiation belts, including local wave–particle interactions, radial diffusion, and losses due to precipitation and magnetopause shadowing. We validate Sayram using 1D radial diffusion, 2D pitch-angle and momentum diffusion, and a 3D model diffusion problem. Additionally, we apply it to a GEM challenge storm-time radiation belt event, demonstrating consistency with previous results. Compared to other 3D radiation belt codes, Sayram employs an implicit time integration scheme, preserves positivity, and ensures conservation properties. The code is developed in C++ with a highly modular design, allowing for easy adaptation to similar tasks. By making Sayram open source, we aim to provide the radiation belt community with a robust tool to improve radiation belt modeling and forecasting.