Cosmic Ray Diffusion in Space: Insights from 2D Heat Equation Simulations

Abstract Galactic Cosmic Rays (GCRs) are high-energy particles originating from distant astrophysical sources, with significant implications for space environments and systems. Accurate modelling of GCR transport is essential for understanding their behaviour and mitigating their effects on space missions. This study presents a comparative analysis of two numerical methods, the Crank-Nicholson method and the Alternating Direction Implicit (ADI) method, for simulating GCR transport in a magnetized environment. The Crank-Nicholson method offers stability and accuracy, using an implicit approach to solve the advection-diffusion equation. We derive and implement the Crank-Nicholson method, demonstrating its ability to capture GCR distribution and interactions. On the other hand, the ADI method combines implicit and explicit schemes, allowing efficient simulations of separable PDEs. We provide a derivation and implementation of the ADI method for GCR transport, highlighting its computational advantages. Through numerical experiments, we compare the performance of both methods in capturing GCR propagation patterns and evaluate their efficiency. Results indicate that the Crank-Nicholson method excels in accuracy but demands higher computational resources. The ADI method offers computational efficiency while maintaining reasonable accuracy, making it a promising choice for scenarios with separable terms. This study contributes to the advancement of GCR modelling techniques, aiding in space mission planning, radiation protection, and space weather forecasting. The insights gained from this comparative analysis enhance our understanding of GCR behaviour and its implications for space systems, facilitating safer and more effective space exploration endeavours.