@article{RipollLoridanCunninghametal.2016,
  author    = {Ripoll, Jean-Fran{\c{c}}ois and Loridan, Vivien and Cunningham, G. S. and Reeves, Geoffrey D. and Shprits, Yuri Y.},
  title     = {On the time needed to reach an equilibrium structure of the radiation belts},
  series = {Journal of geophysical research : Space physics},
  volume    = {121},
  journal   = {Journal of geophysical research : Space physics},
  publisher = {American Geophysical Union},
  address   = {Washington},
  issn      = {2169-9380},
  doi       = {10.1002/2015JA022207},
  pages     = {7684 -- 7698},
  year      = {2016},
  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 (tau(Diffusion)/tau(loss)), 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 similar to [200, 300] keV for L= [3.7, 4] at Kp= 1, E similar to[0.6, 1] MeV for L = [3, 4] at Kp = 3, and E similar to 300 keV for L = [3.5, 4] at Kp = 6 assuming no new incoming electrons.},
  language  = {en}
}
@article{BoydSpenceHuangetal.2016,
  author    = {Boyd, A. J. and Spence, Harlan E. and Huang, Chia-Lin and Reeves, Geoffrey D. and Baker, Daniel N. and Turner, D. L. and Claudepierre, Seth G. and Fennell, Joseph F. and Blake, J. Bernard and Shprits, Yuri Y.},
  title     = {Statistical properties of the radiation belt seed population},
  series = {Journal of geophysical research : Space physics},
  volume    = {121},
  journal   = {Journal of geophysical research : Space physics},
  publisher = {American Geophysical Union},
  address   = {Washington},
  issn      = {2169-9380},
  doi       = {10.1002/2016JA022652},
  pages     = {7636 -- 7646},
  year      = {2016},
  abstract  = {We present a statistical analysis of phase space density data from the first 26 months of the Van Allen Probes mission. In particular, we investigate the relationship between the tens and hundreds of keV seed electrons and >1 MeV core radiation belt electron population. Using a cross-correlation analysis, we find that the seed and core populations are well correlated with a coefficient of approximate to 0.73 with a time lag of 10-15 h. We present evidence of a seed population threshold that is necessary for subsequent acceleration. The depth of penetration of the seed population determines the inner boundary of the acceleration process. However, we show that an enhanced seed population alone is not enough to produce acceleration in the higher energies, implying that the seed population of hundreds of keV electrons is only one of several conditions required for MeV electron radiation belt acceleration.},
  language  = {en}
}