Dynamic modeling of the Earth’s trapped proton environment

Context: Reliable prediction of space radiation exposure is critical for safeguarding spacecraft systems and ensuring astronaut health during missions. Accurate radiation risk assessment for space mission requires advanced models of the Earth’s trapped proton environment. These models must reflect temporal variations driven by geomagnetic field evolution and solar cycle modulation. Existing static models, such as AP8 and IRENE-AP9, are not designed to fully capture these evolving conditions. Aims: This paper presents a dynamic modeling method for the prediction of trapped proton fluxes, which incorporate time-dependent variations due to geomagnetic field evolution and solar cycle fluctuations. Methods: The new model consists of two primary components. The first model component calculates flux within a strictly adiabatic geomagnetic system. The second model component quantifies atmospheric collisional losses with solar cycle modulation embedded. The final flux is obtained by applying the collisional loss function to the output of the adiabatic system. Model development is based on cleaned and cross-calibrated satellite observations from the Relativistic Proton Spectrometer (RPS-b) onboard the Van Allen Probes (2013) and the Space Environment Monitor (SEM2) onboard POES satellites (1998–2013). This study utilizes satellite observations of protons with energies greater than 70 MeV. Although the current implementation addresses only this integral energy bin, the methodology is designed to be extensible to a broader energy range. Results: The model reproduces the observations with high accuracy. It captures the northwestward drift of the South Atlantic Anomaly (SAA), solar cycle variations, and hysteresis effects. It also successfully reconstructs the SAA’s 1965 location. Conclusion: The present work demonstrates a model of the integral proton flux above 70 MeV. This model’s physics-based structure effectively represents trapped proton dynamics and provides a foundation for future expansion to full energy spectrum and angular-dependent flux configurations.