A Nonlinear Dependence on the Geomagnetic Activity of the Ratio of the Maximum Stream Flux of Charged Particles in a Geostationary Orbit to the Minimum Stream Flux

Abstract

A new mathematical model was proposed using an ordinary differential equation that analytically(when the index of geomagnetic activity Kp = const or Kp ≈ const) or numerically (if Kp(t) ≠ const) describesperpendicular (for a pitch angle of 90°) differential or integral fluxes of relativistic electrons in a geostationary(geosynchronous) orbit, as well as in any circular orbit in the Earth’s magnetosphere. The model assumes thatthe fluxes depend on the local time LT in orbit, the Kp, MacIlvwaine parameter and L, and the perpendiculardifferential flux or integral flux of relativistic electrons taken at 0000:00 LT. We use observations of relativistic(2 MeV) electron fluxes averaged over the local time hour along the orbit of the GOES spacecraft from 1995to 2009. The model is compared with these data. Almost perfect agreement was obtained for observationswith the model, where the prediction efficiency of predicting the accuracy of the model at PE = 0.9989. Usingsimilar data from the GOES 10 allows one to obtain PE = 0.9924. The proposed formulas make it possible tofind, for example, the average value of the perpendicular integral flux of relativistic electrons per day and topredict the maximum perpendicular integral flux of relativistic electrons in the geostationary orbit approximately1 day ahead. The nonlinear effect is theoretically predicted in the form of a nonlinear dependence ofthe ratio of the maximum perpendicular integral flux to the minimum flux of charged particles in the geostationaryorbit from the Kp-index of geomagnetic activity. Thus far, comparison of the model has been madewith the averaged integral relativistic electron flows fluxes produced for the 0 ≤ Kp 6 range with a predictedmaximum flow flux ratio of 24.4139 times at Kp = 8 and with the prediction efficiency of predicting the accuracyof the nonlinear effect PE = 0.8678.