Equilibrium structure of equatorially mirroring radiation belt protons

Spjeldvik, W. N.

doi:10.1029/ja082i019p02801

Cited by 85 publications

(48 citation statements)

References 25 publications

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“…This work was done in the same way as for electrons (e.g., Newkirk and Walt, 1968;Lanzerotti et al, 1970;Tomassian et al, 1972;West et al, 1981;Chiu et al, 1990;Brautigam and Albert, 2000;Brautigam et al, 2005;Ma et al, 2016), protons and other ions/nuclei (e.g., Spjeldvik, 1977;Fritz and Spjeldvik, 1981;Jentsch, 1981;Westphalen and Spjeldvik, 1982;Panasyuk, 2004;Alinejad and Armstrong, 2006;Selesnick et al, 2016). The values of D LL obtained by this method differ from each other by 2 and more orders of magnitude.…”

Section: Introductionmentioning

confidence: 99%

Deduction of the rates of radial diffusion of protons from the structure of the Earth's radiation belts

Kovtyukh

2016

Ann. Geophys.

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Abstract. From the data on the fluxes and energy spectra of protons with an equatorial pitch angle of α 0 ≈ 90 • during quiet and slightly disturbed (Kp ≤ 2) periods, I directly calculated the value D LL , 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 SunEarth 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 D LL can be approximated by the following equivalent expressions:, where f d is the drift frequency of the protons (in mHz), D LL 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 D LL increases, and the expressions for D LL obtained here can change completely.

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Section: Introductionmentioning

confidence: 99%

Deduction of the rates of radial diffusion of protons from the structure of the Earth's radiation belts

Kovtyukh

2016

Ann. Geophys.

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“…[3] Diffusion of geomagnetically trapped particles has been studied by Nakada and Mead [1965], Falthammar [1966, Haerendel [1968Haerendel [ , 1970, Birmingham et al [1968], Roederer [1968aRoederer [ , 1968b, Walt [1970], Williams [1970], Cornwall [1972], Croley et al [1976], Spjeldvik [1977], Holzworth and Mozer [1979], Westphalen and Spjeldvik [1982], Jentsch [1984], Riley and Wolf [1992], Lui [1993], and Sheldon [1994]. Falthammar [1966] applied the one-dimensional Fokker-Planck equation to particles moving near the equatorial plane and found two different results for the diffusion coefficient depending on the assumed characteristics of the magnetic impulses compared to the azimuthal drift period.…”

Section: Introductionmentioning

confidence: 99%

“…For randomly repeated pulses with very short rise time and very long duration, the result was D / r 10 , and for pulses not much longer than the drift period the result was D / m 2 r 6 . Spjeldvik [1977] worked on a numerical solution of the Fokker-Planck equation by imposing boundary conditions to explain the equilibrium structure of equatorial radiation belt protons and compared the results with observations. The steady state transport equation at an arbitrary pitch angle has been used by Jentsch [1984] to study the radial distribution of radiation belt protons.…”

Section: Introductionmentioning

confidence: 99%

Radial diffusion of geomagnetically trapped protons observed by the Galileo Energetic Particle Detector

Alinejad

Armstrong²

2006

J. Geophys. Res.

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[1] The Galileo spacecraft encountered the Earth once on 8 December 1990 (Earth-I) and again on 8 December 1992 (Earth-II). These flybys provided excellent opportunities to evaluate the performance of the Energetic Particle Detector (EPD) and establish analysis procedures in a relatively well-known environment. Further, because Galileo's Earth flyby trajectories were very rapid and nearly radial, the radiation belt measurements provided an excellent ''snapshot'' of trapped radiation. Because of the rapid flyby and the 20-s spin period of Galileo, great care had to be taken to remove time aliasing from the pitch angle distributions. Large anisotropies were also present due to intrinsic density gradients. Spherical harmonics were fitted to the pitch and phase distributions in order to obtain fluxes from which phase space densities could be computed. The phase space density (PSD) was calculated from the fitted count rate for the particles (protons) that conserve the first and second adiabatic invariants 10, 0.15, 0.20, 0.25, 0.30, and 0.50 G 0.5 R E were used for the second adiabatic invariant to determine the PSD from Earth-I and Earth-II observations. The extracted PSDs were examined for radial diffusion. Results show there is no unique global dependency of the diffusion coefficient to L, except for a limited region of the first and second adiabatic invariants.

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“…The main contribution to the Coulomb losses of protons of the radiation belts make the cold plasma electrons (Tverskoy, 1964(Tverskoy, , 1965(Tverskoy, , 1968(Tverskoy, , 1969Nakada and Mead, 1965;Schulz and Lanzerotti, 1974;Spjeldvik, 1977, Jentsch, 1984, the density of which, N e , is strongly dependent on L (see Fig. 5).…”

Section: The Coulomb Losses Of Protonsmentioning

confidence: 99%

Radial dependence of ionization losses of protons of the Earth's radiation belts

Kovtyukh

2016

Ann. Geophys.

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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 ( L ∼ 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 L b = 4.71µ 0.32 , where, and at L > L b (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.

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Equilibrium structure of equatorially mirroring radiation belt protons

Cited by 85 publications

References 25 publications

Deduction of the rates of radial diffusion of protons from the structure of the Earth's radiation belts

Deduction of the rates of radial diffusion of protons from the structure of the Earth's radiation belts

Radial diffusion of geomagnetically trapped protons observed by the Galileo Energetic Particle Detector

Radial dependence of ionization losses of protons of the Earth's radiation belts

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