Ripoll J. -., V. Loridan, G. S. Cunningham, G. D. Reeves, Y. Y. Shprits, (2016), On the time needed to reach an equilibrium structure of the radiation belts, J. Geophys. Res. [Space Physics], 121, 7684-7698, doi:10.1002/2015JA022207
Abstract
Abstract In this study, 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 1-D 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 versus 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 (τDiffusion/τloss), 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 the 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.Authors (sorted by name)
Cunningham Loridan Reeves Ripoll ShpritsJournal / Conference
Journal Of Geophysical Research (Space Physics)Acknowledgments
This work was performed under the auspices of an agreement between CEA/DAM and NNSA/DP on cooperation on fundamental science. G.S.C. would like to acknowledge the Los Alamos National Laboratory LDRD program. Y.Y.S. would like to acknowledge support by the NASA grants NNX10AK99G and NNX13AE34G, NSF grant 443869‐YS‐21686, UC Lab Fee grant 116720, and Horizon 2020 637302. For further information or right to access to the material used in this paper, readers can contact the authors.
Grants
116720 443869-YS-21686 637302 NNX10AK99G NNX13AE34GBibtex
@article{doi:10.1002/2015JA022207,
author = {Ripoll, J.-F. and Loridan, V. and Cunningham, G. S. and Reeves, G. D. and Shprits, Y. Y.},
title = {On the time needed to reach an equilibrium structure of the radiation belts},
year={2016},
journal = {Journal of Geophysical Research: Space Physics},
volume = {121},
number = {8},
pages = {7684-7698},
keywords = {equilibrium structure, radiation belts, radial diffusion, wave particle interactions, electron lifetimes, hiss waves},
doi = {10.1002/2015JA022207},
url = {https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1002/2015JA022207},
eprint = {https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/2015JA022207},
abstract = {Abstract In this study, 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 1-D 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 versus 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 (τDiffusion/τloss), 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 the 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.}
}