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

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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) describes
perpendicular (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 that
the fluxes depend on the local time LT in orbit, the Kp, MacIlvwaine parameter and L, and the perpendicular
differential 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 1995
to 2009. The model is compared with these data. Almost perfect agreement was obtained for observations
with the model, where the prediction efficiency of predicting the accuracy of the model at PE = 0.9989. Using
similar data from the GOES 10 allows one to obtain PE = 0.9924. The proposed formulas make it possible to
find, for example, the average value of the perpendicular integral flux of relativistic electrons per day and to
predict the maximum perpendicular integral flux of relativistic electrons in the geostationary orbit approximately
1 day ahead. The nonlinear effect is theoretically predicted in the form of a nonlinear dependence of
the ratio of the maximum perpendicular integral flux to the minimum flux of charged particles in the geostationary
orbit from the Kp-index of geomagnetic activity. Thus far, comparison of the model has been made
with the averaged integral relativistic electron flows fluxes produced for the 0 ≤ Kp < 6 range with a predicted
maximum flow flux ratio of 24.4139 times at Kp = 8 and with the prediction efficiency of predicting the accuracy
of the nonlinear effect PE = 0.8678.

About the authors

S. V. Smolin

Siberian Federal University

Author for correspondence.
Email: smolinsv@inbox.ru
Krasnoyarsk, Russia

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