Radial diffusion coefficient for electrons at 1.76 <L< 5

Abstract

Radial diffusion by nonconservation of the third adiabatic invariant of particle motion is assumed in analyzing experiments in which electrons appeared to move across field lines. Time‐dependent solutions of the Fokker‐Planck diffusion equation are obtained numerically and fitted to the experimental results by adjusting the diffusion coefficient. Values deduced for the diffusion coefficient vary from 1.3 × 10−5 RE²/day at L = 1.76 to 0.10 RE²/day at L = 5. In the interval 2.6 < L < 5, the coefficient varies as L10±1. Assuming a constant electron source of arbitrary magnitude at L = 6 and the above diffusion coefficients, the equatorial equilibrium distribution is calculated for electrons with energies above 1.6 Mev. The calculation yields an outer belt of electrons whose radial distribution is in good agreement with the observed belt. The calculated distribution also exhibits an inner belt at L ≈ 1.5. However, the calculated intensity of the inner belt relative to the outer belt is several orders of magnitude smaller than the experimental ratio.

The Magnetosphere

“…Fig. Newkirk and Walt (1968) appear to have accounted quite well for the evolution of the > 1.6 MeV electron-flux profile during late December 1962 by postulating a reasonable post-storm radial-diffusion coefficient {DLL = 5 X 10"^ L^^ day"^) and a fairly reasonable (cf. Indeed, purely collisional scattering seems (cf.…”

Source of High-Energy Protons in the Van Allen Radiation Belt

“…7 We have assumed that D is of the form 5X10"* 9 XL 10 (earth radii) 2 d"* 1 from theoretical considerations, 17 ' 18 and because of its apparent suitability as determined by studies of other radiation belt particle populations. 19 ' 20 We have obtained equilibrium solutions of the diffusion equation for n in the two-dimensional domain 200 < p,<4000 MeV G^and 1.15<L<1.7. We have used the experimental values for n at L = 1.7 as a boundary condition, and have set n equal to 0 at L = 1.15 for all M, and 0 at M = 4000 MeV G"" 1 for all L. The solution for L 3 j ± is compared with experimental data in Fig.…”

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

“…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.…”