Geomagnetic shielding in the spectra of high-energy particles

The Earth’s magnetosphere acts as an energy- and direction-selective filter for high-energy charged particles and, thus, modifies the nonthermal radiation spectrum observed at the ground. The authors developed a physically motivated description of geomagnetic shielding in terms of an effective phase-space potential barrier, introduced the magnetospheric transmission function T(R, t), and formulated a criterion for the transition to the spectral-modulation regime by the magnetic field. To quantify T(R, t) and the temporal evolution of the cutoff rigidity Rc(t), Monte Carlo trajectory tracing in realistic magnetic-field configurations (IGRF internal field plus external current systems) is employed. Using the June 7–8, 2024, event, we compared the model with neutron monitor data (Apatity, Oulu, South Pole) and calibrated the linear parameterization Rc(t) = Rc,0 + αDst(t). It was found that α = (4 ± 0.6) × 10−5 GV/nT within the event window, implying very small cutoff variations (≲1.5 × 10−3 GV) under modest Dst changes (tens of nT). This separation of magnetospheric filtering from source-driven processes (acceleration/transport) suggests that the observed spectral evolution in this event is predominantly of solar/heliospheric origin.