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### Modeling of relativistic electron flux at geostationary orbit in the Earth’s magnitosphere

#### Smolin S.V.

The new mathematical model describing analytically (when \(K_p = const \) or \(K_p \approx const \)) and numerically (if \(K_p \neq const \)) perpendicular differential and integrated fluxes of relativistic electrons with energy more 2 MeV in a geostationary (geosynchronous) orbit in the Earth’s magnetosphere, and also in any circular orbit depending on local time LT in an orbit and the geomagnetic activity index \(K_p\) is offered. It are used the observations of relativistic (>2 MeV) electron fluxes averaged by local hour LT around geosynchronous orbit from 1995 to 2009 collected by GOES satellite. Comparison of a modeling perpendicular (for a pitch angle of 90 degrees) integrated flux of relativistic electrons with energy more 2 MeV at geosynchronous orbit when \(K_p \approx const \) const, for example, within one day with averaged experimental data of satellite GOES in a geosynchronous orbit is made. The good consent is received, especially with 0000 LT up to 1100 LT and with 1800 LT up to 2400 LT. The analytical formula for definition of the modeling (predicted) ratio of the maximal integrated flux (at noon) to the minimal integrated flux (at midnight) in nonlinear dependence on an index of geomagnetic activity \(K_p\) (\( 0 \leq K_p \leq 10 \)) with a maximum of the ratio of fluxes in 20.37 times at \(K_p = 8 \) is received. The same formula allows to predict forward for day in the next noon of the maximal (integrated or differential) flux of relativistic electrons in a geostationary (geosynchronous) orbit if the flux at midnight is known and approximately within one day \(K_p = const \) or \(K_p \approx const \).

** Keywords:** the Earth’s magnetosphere, geostationary orbit, modeling of relativistic electron flux, new model.

** UDC:** 533.951; 550.385

** PACS:** 52.65.-y; 94.30.-d

** DOI:** 10.17238/issn2226-8812.2018.2.75-85

*Please cite this article in English as:*

Smolin S.V. Modeling of relativistic electron flux at geostationary orbit in the Earth’s magnitosphere. Space, Time and Fundamental Interactions, 2018, no. 2, pp. 75–85.