Predicting proton pressure in the outer part of the inner magnetosphere using machine learning

Information on plasma pressure in the outer part of the inner magnetosphere is important for simulating the ring current and improving our understanding of its dynamics. Using 17 years of Cluster mission observations, we developed machine learning models to predict proton plasma pressure at energies ranging from ~40 eV to 4 MeV for stably trapped particles at L* = 5–9. The L*, location in the magnetosphere, as well as parameters of solar and geomagnetic activity, were used as predictors. The results demonstrate that the Extra-Trees Regressor model performs best. The Spearman correlation between the observations and the model's predictions is ~70%. The most important parameter for predicting proton pressure is the L* value. The most important predictor related to solar and geomagnetic activity is the F10.7 index. We demonstrate how the model performs during geomagnetically quiet periods and during moderate magnetic storms. Our results have practical applications, such as providing inputs for ring current simulations or reconstructing the three-dimensional inner magnetospheric electric current system based on magnetostatic equilibrium.