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Annales Geophysicae An open-access journal of the European Geosciences Union
Ann. Geophys., 34, 1085-1098, 2016
http://www.ann-geophys.net/34/1085/2016/
doi:10.5194/angeo-34-1085-2016
© Author(s) 2016. This work is distributed
under the Creative Commons Attribution 3.0 License.
Regular paper
23 Nov 2016
Deduction of the rates of radial diffusion of protons from the structure of the Earth's radiation belts
Alexander S. Kovtyukh Skobeltsyn Institute of Nuclear Physics, Moscow State University, 119899, Moscow, Russia
Abstract. From the data on the fluxes and energy spectra of protons with an equatorial pitch angle of α0 ≈ 90° during quiet and slightly disturbed (Kp ≤ 2) periods, I directly calculated the value DLL, which is a measure of the rate of radial transport (diffusion) of trapped particles. This is done by successively solving the systems (chains) of integrodifferential equations which describe the balance of radial transport/acceleration and ionization losses of low-energy protons of the stationary belt. This was done for the first time. For these calculations, I used data of International Sun–Earth Explorer 1 (ISEE-1) for protons with an energy of 24 to 2081 keV at L = 2–10 and data of Explorer-45 for protons with an energy of 78.6 to 872 keV at L = 2–5. Ionization losses of protons (Coulomb losses and charge exchange) were calculated on the basis of modern models of the plasmasphere and the exosphere. It is shown that for protons with μ from  ∼ 0.7 to ∼ 7 keV nT−1 at L ≈ 4.5–10, the functions of DLL can be approximated by the following equivalent expressions: DLL ≈ 4.9 × 10−14μ−4.1L8.2 or DLL ≈ 1.3 × 105(EL)−4.1 or DLL ≈ 1.2 × 10−9fd−4.1, where fd is the drift frequency of the protons (in mHz), DLL is measured in s−1, E is measured in kiloelectronvolt and μ is measured in kiloelectronvolt per nanotesla. These results are consistent with the radial diffusion of particles under the action of the electric field fluctuations (pulsations) in the range of Pc6 and contradict the mechanism of the radial diffusion of particles under the action of sudden impulses (SIs) of the magnetic field and also under the action of substorm impulses of the electric field. During magnetic storms DLL increases, and the expressions for DLL obtained here can change completely.

Citation: Kovtyukh, A. S.: Deduction of the rates of radial diffusion of protons from the structure of the Earth's radiation belts, Ann. Geophys., 34, 1085-1098, doi:10.5194/angeo-34-1085-2016, 2016.
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Short summary
From the data on the protons of the Earth’s radiation belts, the rate of radial diffusion of these particles is directly calculated. This is done by solving the systems of equations which describe the balance of radial transport/acceleration and ionization losses of protons. These results are very consistent with the radial diffusion of particles under the influence of the electric field pulsations in the range of the drift frequencies of the protons around Earth.
From the data on the protons of the Earth’s radiation belts, the rate of radial diffusion of...
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