Real Time Magnetic Field Line Tracing In The Magnetosphere Via Adaptive Error Bounded Integration
Taylan Demir
TL;DR
This work tackles the need for real-time, accurate magnetic field-line tracing in the Earth's magnetosphere by developing an adaptive error-bounded integration framework. It combines an embedded Runge–Kutta pair with robust event detection to solve the normalized field-line ODE and localize footprints on the Earth’s boundary, ensuring controllable geometric accuracy. The approach is validated on analytic dipole fields and demonstrated with IGRF-based internal-field configurations, showing that modest tolerance settings yield sub-millidegree footprint accuracy while maintaining reasonable computational cost. The methodology offers a practical, extensible pathway toward real-time footprint mapping and connectivity analyses, with planned extensions to include external-current coupling and batched/GPU-accelerated implementations for scalability.
Abstract
Field line tracing is one of the fundamental computational tools used in the study of the magnetosphere, which helps in many areas including footprint mapping, connectivity analysis and real-time visualisation. This note describes an implementation approach to error-bounded adaptive integration of the field line differential equation (ODE), where an embedded Runge-Kutta pair is used in conjunction with event detection, allowing robust localisation of footprint locations on spacecraft. The method is validated against an analytic dipole field model as well as an international geomagnetic reference field (IGRF)-based geomagnetic configuration.