Conditions of Loss Cone Filling by Scattering on the Curved Field Lines for 30 keV Protons During Geomagnetic Storm as Inferred From Numerical Trajectory Tracing

The rate of pitch angle scattering on the curved magnetic field lines is well parameterized by the ratio of the minimum field line curvature radius to the maximum effective particle gyroradius (K = RC/rg). The critical value of this ratio (Kcr) corresponding to the loss cone filling is of special interest since it corresponds to the low altitude isotropic boundaries (IBs). The early theoretical estimates gave Kcr = 8, whereas recent estimations of the K parameter on the field lines corresponding to the observed IBs during the geomagnetic storms revealed KIB values in the range of 3–30. We numerically trace the trajectories of the 30 keV protons in the magnetic field of the global magnetohydrodynamic simulation of the intense storm in order to infer statistical distribution of Kcr. The electric field and effects of nonstationarity are neglected in this study. It is found that although the Kcr values do show some variations during the course of the storm, its range is rather narrow 4 < Kcr < 8. The result suggests that higher KIB values found in the observational studies, if not caused by the magnetosphere-ionosphere mapping error, should be attributed to some other mechanism of pitch angle scattering. The Kcr values tend to be lower (4–6) during the main phase because the region of low K values approaches the Earth and the equatorial loss cone size becomes larger due to a larger equatorial magnetic field in the near earth
region. The remaining variation of Kcr is explained by the presence of the guide component of the magnetic field.