Why are there two electron radiation belts
rather than just one?
Notes from a discussion held 17 Feb 2012 at APL
and led by:
Michael Schulz
Aerospace Corporation Retiree
Lockheed Martin Retiree
1037 Twin Oaks Court
Redwood City, CA 94061 (U.S.A.)
Radiation
Belts
Fig. 21
Why are there two radiation belts with a gap
(slot region) between them?
• Essentially because MeV-electron lifetimes against
scattering by whistler-mode waves (plasmaspheric hiss)
are especially long (~ years) at L ~ 1.5 (heart of inner
belt), to which radial transport typically requires a long
time, whereas electron transport from external source to
L ~ 5 (heart of outer belt) is quite rapid (requiring only
1−2 days).
• Electron lifetimes are a week to a month (depending on
energy) at L > 3, and inward transport can easily
maintain the outer belt against such losses.
Gap between inner and outer electron
radiation belts is not permanent
• Vampola [1971, 1972] has noted that the “slot region”
becomes re-filled during large geomagnetic storms and
then empties out again between storms. The re-filling is
a consequence of enhanced diffusive radial transport.
• The inner belt persists between storms because electron
lifetimes are so long there. The outer belt persists
because even ordinary (quiet-time) radial diffusion is
strong enough to maintain it.
• Thus, the gap remains a feature of the time-averaged
electron radiation environment.
Why are electron lifetimes so long in the
inner belt but so short in the slot region and
outer belt?
• Larry Lyons explained this with a quantitative model calculation in his 1972 PhD thesis [Lyons et al., JGR, 77,
3455−3474, 1972].
• The reduced scattering rates (i.e., greater life-times) at
low L values seem to result from wave-particle resonance conditions that require wave frequencies above
the heart of the plasmaspheric hiss band in regions of so
much stronger equatorial B.
What were the ingredients of Larry Lyons’
calculation?
• He assumed a spatially uniform distribution of hiss
(whistler-mode waves with a certain smooth frequency
spectrum and specific distribution of wave-normal angles
relative to B) throughout the plasmasphere.
• He calculated the resulting bounce-averaged
momentum-space diffusion tensor for a very large
sample of test particles with various energies and
equatorial pitch angles at various L values.
• From this he obtained the pitch-angle distributions
corresponding to the lowest eigenmode of the pitchangle diffusion operator.
• He plotted the reciprocals of corresponding eigenvalues (decay rates) and identified these correctly
(see Slide #9) as electron lifetimes against (weak)
pitch-angle diffusion.
Steady-State Solutions of Radial-Diffusion
Equation
• Lyons and Thorne [JGR, 78, 2142−2149, 1973] showed
that a realistic two-zone pattern of electron radiation
intensity results even from a steady-state model of
diffusive particle transport.
• For this study they needed to take account of collisional
(atmospheric) scattering at the lower L values.
• The quantity held constant in the following plots is the
first adiabatic invariant for equatorially mirroring
electrons (energy varies as L−3).
Lyons and Thorne [JGR, 78, 2142−2149, 1973]
Fig. 22
Interpretation
• The left panel in Slide #17 above (Fig 22 from Schulz,
2007) shows profiles of phase-space density f
corresponding to specified values of M (first adiabatic
invariant) for equatorially mirroring electrons (normalized
to their respective values of f at L = 5.5).
• The right panel in Slide #17 shows resulting profiles of
particle flux (f /p 2) at selected kinetic energies (with
normalization of f provided by the measured electron
spectrum at L = 5.5).
Radiation
Belts
Fig. 21
Further References
• Schulz, M., Space Sci Rev, 17, 481−536, 1975.
• Schulz, M., in Geomagnetism, v. 4, J. A. Jacobs (ed.),
pp. 87−293, Academic Press, London, 1991.
• Schulz, M., in Handbook of the Solar-Terrestrial
Environment, Y. Kamide and A. C.-L. Chian (eds.), pp.
155 −188, Springer, Heidelberg, 2007.
• Vampola, A. L., JGR, 76, 4685−4688, 1971.
• Vampola, A. L., in Proceedings of the National Symposium on Natural and Manmade Radiation in Space,
E. A. Waxman (ed.), pp. 539 −547, NASA TM X-2440,
Washington, DC, 1972.