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Title: On the time needed to reach an equilibrium structure of the radiation belts

In this paper, we complement the notion of equilibrium states of the radiation belts with a discussion on the dynamics and time needed to reach equilibrium. We solve for the equilibrium states obtained using 1D radial diffusion with recently developed hiss and chorus lifetimes at constant values of Kp = 1, 3 and 6. We find that the equilibrium states at moderately low Kp, when plotted vs L-shell (L) and energy (E), display the same interesting S-shape for the inner edge of the outer belt as recently observed by the Van Allen Probes. The S-shape is also produced as the radiation belts dynamically evolve toward the equilibrium state when initialized to simulate the buildup after a massive dropout or to simulate loss due to outward diffusion from a saturated state. Physically, this shape, intimately linked with the slot structure, is due to the dependence of electron loss rate (originating from wave-particle interactions) on both energy and L-shell. Equilibrium electron flux profiles are governed by the Biot number (τ Diffusionloss), with large Biot number corresponding to low fluxes and low Biot number to large fluxes. The time it takes for the flux at a specific (L, E) to reach themore » value associated with the equilibrium state, starting from these different initial states, is governed by the initial state of the belts, the property of the dynamics (diffusion coefficients), and the size of the domain of computation. Its structure shows a rather complex scissor form in the (L, E) plane. The equilibrium value (phase space density or flux) is practically reachable only for selected regions in (L, E) and geomagnetic activity. Convergence to equilibrium requires hundreds of days in the inner belt for E > 300 keV and moderate Kp (≤3). It takes less time to reach equilibrium during disturbed geomagnetic conditions (Kp ≥ 3), when the system evolves faster. Restricting our interest to the slot region, below L = 4, we find that only small regions in (L, E) space can reach the equilibrium value: E ~ [200, 300] keV for L = [3.7, 4] at Kp = 1, E ~ [0.6, 1] MeV for L = [3, 4] at Kp = 3, and E ~ 300 keV for L = [3.5, 4] at Kp = 6 assuming no new incoming electrons.« less
 [1] ;  [1] ;  [2] ;  [2] ;  [3]
  1. CEA, DAM, DIF, Arpajon (France)
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  3. Germany and Univ. of Potsdam, Potsdam (Germany); Univ. of California, Los Angeles, CA (United States)
Publication Date:
Report Number(s):
Journal ID: ISSN 2169-9380
Grant/Contract Number:
Accepted Manuscript
Journal Name:
Journal of Geophysical Research. Space Physics
Additional Journal Information:
Journal Name: Journal of Geophysical Research. Space Physics; Journal ID: ISSN 2169-9380
American Geophysical Union
Research Org:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org:
National Aeronautic and Space Administration (NASA); USDOE
Country of Publication:
United States
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Heliospheric and Magnetospheric Physics
OSTI Identifier: