Abstract
Abstract. Coulomb losses and charge exchange of protons are considered in detail. On the basis of modern models of the plasmasphere and the exosphere, the radial dependences of the rates of ionization losses of protons, with μ from 0.3 to 10 keV nT−1, of the Earth's radiation belts near the equatorial plane are calculated for quiet periods. For calculation of Coulomb losses of protons we used data of ISEE-1 satellite (protons with energy from 24 to 2081 keV) on L from 3 to 9, data of Explorer-45 satellite (protons with energy from 78.6 to 872 keV) on L from 3 to 5 and data of CRRES satellite (protons with energy from 1 to 100 MeV) on L ≤ 3 (L is the McIlwain parameter). It is shown that with decreasing L the rate of ionization losses of protons of the radiation belts is reduced; for protons with μ > 1.2 keV nT−1 in a narrow region (ΔL ∼ 0.5) in the district of plasmapause in this dependence may form a local minimum of the rate. We found that the dependence from μ of the boundary on L between Coulomb losses and charge exchange of the trapped protons with hydrogen atoms is well approximated by the function Lb = 4.71μ0.32, where [μ] = keV nT−1. Coulomb losses dominate at L < Lb(μ), and at L > Lb(μ) dominates charge exchange of protons. We found the effect of subtracting the Coulomb losses from the charge exchange of protons of the radiation belts at low μ and L, which can simulate a local source of particles.
Highlights
The Earth’s radiation belt of protons is stationary in quiet time
Under certain conditions, which performed for protons of the radiation belts, the equation is reduced to the ordinary diffusion equation (e.g., Tverskoy, 1968; Roederer, 1970; Schulz and Lanzerotti, 1974)
Note that we do not have enough experimental data on the cross section of charge exchange of protons with E > 100 keV and enough experimental data necessary to carry out the extrapolation, which can lead to errors much more than 30 %
Summary
The Earth’s radiation belt of protons is stationary in quiet time. Only the 11-year solar cycle variations and the small seasonal variations are observed. The first invariant is associated with the giration of charged particles in a magnetic field, the second invariant is associated with the oscillations of the particles in the magnetic tube between the mirror points and the third invariant is associated with drift of the particles around the Earth in a magnetic trap Radial diffusion of these protons is described by the Fokker–Planck differential equation. To extract DLL from the data on radiation belts, using the diffusion equation (the inverse problem), it is necessary to have the complete and reliable values of the loss rates of trapped particles. The most fully loss mechanisms are studied for protons They depend on the distribution of cold plasma and atoms in the geomagnetic trap. Near the equatorial plane the most reliable model of the plasmasphere are derived from the data obtained near the equatorial plane
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