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A Nonlinear Dependence on the Geomagnetic Activity of the Ratio of the Maximum Flux of Charged Particles in a Geostationary Orbit to the Minimum 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, McIlwain parameter L and the perpendicular differential flux or integral flux of relativistic electrons taken at 00 LT. We use observations of relativistic (>2 MeV) electron fluxes averaged over the local 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 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 fluxes produced for the 0 ≤ Kp < 6 range with a predicted maximum flux ratio of 24.4139 times at Kp = 8 and with the prediction efficiency of accuracy of the nonlinear effect \(PE\) = 0.8678.

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This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.

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  1. Siberian Federal University, Krasnoyarsk, Russia

    S. V. Smolin

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Smolin, S.V. A Nonlinear Dependence on the Geomagnetic Activity of the Ratio of the Maximum Flux of Charged Particles in a Geostationary Orbit to the Minimum Flux. Geomagn. Aeron. 63, 574–583 (2023). https://doi.org/10.1134/S0016793223600534

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