@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{RipollLoridanDentonetal.2019,
  author    = {Ripoll, Jean-Francois and Loridan, Vivien and Denton, Michael H. and Cunningham, Gregory and Reeves, G. and Santolik, O. and Fennell, Joseph and Turner, Drew L. and Drozdov, Alexander and Villa, Juan Sebastian Cervantes and Shprits, Yuri Y. and Thaller, Scott A. and Kurth, William S. and Kletzing, Craig A. and Henderson, Michael G. and Ukhorskiy, Aleksandr Y.},
  title     = {Observations and Fokker-Planck Simulations of the L-Shell, Energy, and Times},
  series = {Journal of geophysical research : Space physics},
  volume    = {124},
  journal   = {Journal of geophysical research : Space physics},
  number    = {2},
  publisher = {American Geophysical Union},
  address   = {Washington},
  issn      = {2169-9380},
  doi       = {10.1029/2018JA026111},
  pages     = {1125 -- 1142},
  year      = {2019},
  abstract  = {The evolution of the radiation belts in L-shell (L), energy (E), and equatorial pitch angle (alpha(0)) is analyzed during the calm 11-day interval (4-15 March) following the 1 March 2013 storm. Magnetic Electron and Ion Spectrometer (MagEIS) observations from Van Allen Probes are interpreted alongside 1D and 3D Fokker-Planck simulations combined with consistent event-driven scattering modeling from whistler mode hiss waves. Three (L, E, alpha(0)) regions persist through 11 days of hiss wave scattering; the pitch angle-dependent inner belt core (L similar to <2.2 and E < 700 keV), pitch angle homogeneous outer belt low-energy core (L > similar to 5 and E similar to < 100 keV), and a distinct pocket of electrons (L similar to [4.5, 5.5] and E similar to [0.7, 2] MeV). The pitch angle homogeneous outer belt is explained by the diffusion coefficients that are roughly constant for alpha(0) similar to <60 degrees, E > 100 keV, 3.5 < L < L-pp similar to 6. Thus, observed unidirectional flux decays can be used to estimate local pitch angle diffusion rates in that region. Top-hat distributions are computed and observed at L similar to 3-3.5 and E = 100-300 keV.},
  language  = {en}
}