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### THE ANALYTICAL DESCRIPTION OF THE EARTH’S RING CURRENT PROTON FLUX FOR THE PITCH ANGLE OF 90 DEGREES

#### Smolin S.V.

As mathematical model is offered the ordinary differential equation for the analytical description of a perpendicular differential flux of the charged particles in the Earth’s magnetosphere which depends on time \(t\) and several parameters (the McIlwain parameter, the magnetic local time or geomagnetic eastern longitude, the geomagnetic activity index, parameter of the charged particle pitch angle distribution or the pitch angle distribution anisotropy index but is taken for the pitch angle of 90 degrees at \(t = 0\), the average parameter of the charged particle pitch angle distribution on an interval of time of calculation, the lifetime due to wave-particle interactions). Under the certain geophysical conditions and on a time interval approximately no more than three hours (when a geomagnetic activity index \( Kp = const\)) or on a greater time interval, when \( Kp \approx const\), the equation is solved analytically. The simple analytical solution is received which depends on time and several parameters. Comparison of results on the offered model and on full model for the pitch angle range from 0 up to 180 degrees is lead. For a perpendicular differential flux of the Earth’s ring current protons very good consent with the maximal relative error approximately some percent (for the considered example 3.23 percent) is received. Experimental data have been collected by the Cluster satellite. The model allows to estimate also for different geophysical conditions a lifetime due to wave-particle interactions. A conclusion of the equations is presented in an appendix.

** Keywords:** magnetosphere, pitch angle diffusion equation, perpendicular differential flux, wave-particle interactions, new model.

** UDC:** 533.951, 550.385

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

** DOI:** 10.17238/issn2226-8812.2019.2.64-69

*Please cite this article in English as:*

Smolin S.V. The analytical description of the Earth’s ring current proton flux for the pitch angle of 90 degrees. Space, Time and Fundamental Interactions, 2019, no. 2, pp. 64-69.