@misc{SadovnichiiPanasyukAmelyushkinetal.2017, author = {Sadovnichii, V. A. and Panasyuk, M. I. and Amelyushkin, A. M. and Benghin, V. V. and Garipov, G. K. and Kalegaev, V. V. and Klimov, P. A. and Khrenov, B. A. and Petrov, V. L. and Sharakin, S. A. and Shirokov, A. V. and Svertilov, S. I. and Zotov, M. Y. and Yashin, I. V. and Gorbovskoy, E. S. and Lipunov, V. M. and Park, I. H. and Lee, J. and Jeong, S. and Kim, M. B. and Jeong, H. M. and Shprits, Yuri Y. and Angelopoulos, V. and Russell, C. T. and Runov, A. and Turner, D. and Strangeway, R. J. and Caron, R. and Biktemerova, S. and Grinyuk, A. and Lavrova, M. and Tkachev, L. and Tkachenko, A. and Martinez, O. and Salazar, H. and Ponce, E.}, title = {"Lomonosov" satellite-space observatory to study extreme phenomena in space}, series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, number = {959}, issn = {1866-8372}, doi = {10.25932/publishup-42818}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-428185}, pages = {1705 -- 1738}, year = {2017}, abstract = {The "Lomonosov" space project is lead by Lomonosov Moscow State University in collaboration with the following key partners: Joint Institute for Nuclear Research, Russia, University of California, Los Angeles (USA), University of Pueblo (Mexico), Sungkyunkwan University (Republic of Korea) and with Russian space industry organi-zations to study some of extreme phenomena in space related to astrophysics, astroparticle physics, space physics, and space biology. The primary goals of this experiment are to study: -Ultra-high energy cosmic rays (UHECR) in the energy range of the Greizen-ZatsepinKuzmin (GZK) cutoff; -Ultraviolet (UV) transient luminous events in the upper atmosphere; -Multi-wavelength study of gamma-ray bursts in visible, UV, gamma, and X-rays; -Energetic trapped and precipitated radiation (electrons and protons) at low-Earth orbit (LEO) in connection with global geomagnetic disturbances; -Multicomponent radiation doses along the orbit of spacecraft under different geomagnetic conditions and testing of space segments of optical observations of space-debris and other space objects; -Instrumental vestibular-sensor conflict of zero-gravity phenomena during space flight. This paper is directed towards the general description of both scientific goals of the project and scientific equipment on board the satellite. The following papers of this issue are devoted to detailed descriptions of scientific instruments.}, language = {en} } @misc{SadovnichiiPanasyukAmelyushkinetal.2017, author = {Sadovnichii, V. A. and Panasyuk, M. I. and Amelyushkin, A. M. and Bogomolov, V. V. and Benghin, V. V. and Garipov, G. K. and Kalegaev, V. V. and Klimov, P. A. and Khrenov, B. A. and Petrov, V. L. and Sharakin, S. A. and Shirokov, A. V. and Svertilov, S. I. and Zotov, M. Y. and Yashin, I. V. and Gorbovskoy, E. S. and Lipunov, V. M. and Park, I. H. and Lee, J. and Jeong, S. and Kim, M. B. and Jeong, H. M. and Shprits, Yuri Y. and Angelopoulos, V. and Russell, C. T. and Runov, A. and Turner, D. and Strangeway, R. J. and Caron, R. and Biktemerova, S. and Grinyuk, A. and Lavrova, M. and Tkachev, L. and Tkachenko, A. and Martinez, O. and Salazar, H. and Ponce, E.}, title = {"Lomonosov" Satellite-Space Observatory to Study Extreme Phenomena in Space}, series = {Space science reviews}, volume = {212}, journal = {Space science reviews}, publisher = {Springer}, address = {Dordrecht}, issn = {0038-6308}, doi = {10.1007/s11214-017-0425-x}, pages = {1705 -- 1738}, year = {2017}, abstract = {The "Lomonosov" space project is lead by Lomonosov Moscow State University in collaboration with the following key partners: Joint Institute for Nuclear Research, Russia, University of California, Los Angeles (USA), University of Pueblo (Mexico), Sungkyunkwan University (Republic of Korea) and with Russian space industry organi-zations to study some of extreme phenomena in space related to astrophysics, astroparticle physics, space physics, and space biology. The primary goals of this experiment are to study: -Ultra-high energy cosmic rays (UHECR) in the energy range of the Greizen-ZatsepinKuzmin (GZK) cutoff; -Ultraviolet (UV) transient luminous events in the upper atmosphere; -Multi-wavelength study of gamma-ray bursts in visible, UV, gamma, and X-rays; -Energetic trapped and precipitated radiation (electrons and protons) at low-Earth orbit (LEO) in connection with global geomagnetic disturbances; -Multicomponent radiation doses along the orbit of spacecraft under different geomagnetic conditions and testing of space segments of optical observations of space-debris and other space objects; -Instrumental vestibular-sensor conflict of zero-gravity phenomena during space flight. This paper is directed towards the general description of both scientific goals of the project and scientific equipment on board the satellite. The following papers of this issue are devoted to detailed descriptions of scientific instruments.}, 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 Cervantes Villa, Juan Sebastian 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} } @article{LongNiCaoetal.2022, author = {Long, Minyi and Ni, Binbin and Cao, Xing and Gu, Xudong and Kollmann, Peter and Luo, Qiong and Zhou, Ruoxian and Guo, Yingjie and Guo, Deyu and Shprits, Yuri Y.}, title = {Losses of radiation belt energetic particles by encounters with four of the inner Moons of Jupiter}, series = {Journal of geophysical research, Planets}, volume = {127}, journal = {Journal of geophysical research, Planets}, number = {2}, publisher = {American Geophysical Union}, address = {Washington}, issn = {2169-9097}, doi = {10.1029/2021JE007050}, pages = {13}, year = {2022}, abstract = {Based on an improved model of the moon absorption of Jovian radiation belt particles, we investigate quantitatively and comprehensively the absorption probabilities and particle lifetimes due to encounters with four of the inner moons of Jupiter (Amalthea, Thebe, Io, and Europa) inside L < 10. Our results demonstrate that the resultant average lifetimes of energetic protons and electrons vary dramatically between similar to 0.1 days and well above 1,000 days, showing a strong dependence on the particle equatorial pitch angle, kinetic energy and moon orbit. The average lifetimes of energetic protons and electrons against moon absorption are shortest for Io (i.e., similar to 0.1-10 days) and longest for Thebe (i.e., up to thousands of days), with the lifetimes in between for Europa and Amalthea. Due to the diploe tilt angle absorption effect, the average lifetimes of energetic protons and electrons vary markedly below and above alpha eq \${\alpha }_{\mathrm{e}\mathrm{q}}\$ = 67 degrees. Overall, the average electron lifetimes exhibit weak pitch angle dependence, but the average proton lifetimes are strongly dependent on equatorial pitch angle. The average lifetimes of energetic protons decrease monotonically and substantially with the kinetic energy, but the average lifetimes of energetic electrons are roughly constant at energies 5MeV electrons. The most crucial differences introduced by the hot plasma effects occur for >3MeV electron scattering rates by He+ band EMIC waves. Mainly due to the changes of resonant frequency and wave group velocity when the hot protons are included, the difference in scattering rates can be up to an order of magnitude, showing a strong dependence on both electron energy and equatorial pitch angle. Our study confirms the importance of including hot plasma effects in modeling the scattering of ultra-relativistic radiation belt electrons by EMIC waves.}, language = {en} } @misc{SmirnovKronbergDalyetal.2020, author = {Smirnov, Artem G. and Kronberg, Elena A. and Daly, Patrick W. and Aseev, Nikita and Shprits, Yuri Y. and Kellerman, Adam C.}, title = {Adiabatic Invariants Calculations for Cluster Mission: A Long-Term Product for Radiation Belts Studies}, series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, number = {2}, issn = {1866-8372}, doi = {10.25932/publishup-52391}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-523915}, pages = {14}, year = {2020}, abstract = {The Cluster mission has produced a large data set of electron flux measurements in the Earth's magnetosphere since its launch in late 2000. Electron fluxes are measured using Research with Adaptive Particle Imaging Detector (RAPID)/Imaging Electron Spectrometer (IES) detector as a function of energy, pitch angle, spacecraft position, and time. However, no adiabatic invariants have been calculated for Cluster so far. In this paper we present a step-by-step guide to calculations of adiabatic invariants and conversion of the electron flux to phase space density (PSD) in these coordinates. The electron flux is measured in two RAPID/IES energy channels providing pitch angle distribution at energies 39.2-50.5 and 68.1-94.5 keV in nominal mode since 2004. A fitting method allows to expand the conversion of the differential fluxes to the range from 40 to 150 keV. Best data coverage for phase space density in adiabatic invariant coordinates can be obtained for values of second adiabatic invariant, K, similar to 10(2), and values of the first adiabatic invariant mu in the range approximate to 5-20 MeV/G. Furthermore, we describe the production of a new data product "LSTAR," equivalent to the third adiabatic invariant, available through the Cluster Science Archive for years 2001-2018 with 1-min resolution. The produced data set adds to the availability of observations in Earth's radiation belts region and can be used for long-term statistical purposes.}, language = {en} } @article{SmirnovShpritsAllisonetal.2022, author = {Smirnov, Artem and Shprits, Yuri Y. and Allison, Hayley and Aseev, Nikita and Drozdov, Alexander and Kollmann, Peter and Wang, Dedong and Saikin, Anthony}, title = {An empirical model of the equatorial electron pitch angle distributions in earth's outer radiation belt}, series = {Space Weather: the International Journal of Research and Applications}, volume = {20}, journal = {Space Weather: the International Journal of Research and Applications}, number = {9}, publisher = {American Geophysical Union}, address = {Washington, DC}, issn = {1542-7390}, doi = {10.1029/2022SW003053}, pages = {17}, year = {2022}, abstract = {In this study, we present an empirical model of the equatorial electron pitch angle distributions (PADs) in the outer radiation belt based on the full data set collected by the Magnetic Electron Ion Spectrometer (MagEIS) instrument onboard the Van Allen Probes in 2012-2019. The PADs are fitted with a combination of the first, third and fifth sine harmonics. The resulting equation resolves all PAD types found in the outer radiation belt (pancake, flat-top, butterfly and cap PADs) and can be analytically integrated to derive omnidirectional flux. We introduce a two-step modeling procedure that for the first time ensures a continuous dependence on L, magnetic local time and activity, parametrized by the solar wind dynamic pressure. We propose two methods to reconstruct equatorial electron flux using the model. The first approach requires two uni-directional flux observations and is applicable to low-PA data. The second method can be used to reconstruct the full equatorial PADs from a single uni- or omnidirectional measurement at off-equatorial latitudes. The model can be used for converting the long-term data sets of electron fluxes to phase space density in terms of adiabatic invariants, for physics-based modeling in the form of boundary conditions, and for data assimilation purposes.}, language = {en} } @article{ZhuShpritsSpasojevicetal.2019, author = {Zhu, Hui and Shprits, Yuri Y. and Spasojevic, M. and Drozdov, Alexander}, title = {New hiss and chorus waves diffusion coefficient parameterizations from the Van Allen Probes and their effect on long-term relativistic electron radiation-belt VERB simulations}, series = {Journal of Atmospheric and Solar-Terrestrial Physics}, volume = {193}, journal = {Journal of Atmospheric and Solar-Terrestrial Physics}, publisher = {Elsevier}, address = {Oxford}, issn = {1364-6826}, doi = {10.1016/j.jastp.2019.105090}, pages = {13}, year = {2019}, abstract = {New wave frequency and amplitude models for the nightside and dayside chorus waves are built based on measurements from the Electric and Magnetic Field Instrument Suite and Integrated Science (EMFISIS) instrument onboard the Van Allen Probes. The corresponding 3D diffusion coefficients are systematically obtained. Compared with previous commonly-used (typical) parameterizations, the new parameterizations result in differences in diffusion rates that depend on the energy and pitch angle. Furthermore, one-year 3D diffusive simulations are performed using the Versatile Electron Radiation Belt (VERB) code. Both typical and new wave parameterizations simulation results are in a good agreement with observations at 0.9 MeV. However, the new parameterizations for nightside chorus better reproduce the observed electron fluxes. These parameterizations will be incorporated into future modeling efforts.}, language = {en} } @article{ShpritsDrozdovSpasojevicetal.2016, author = {Shprits, Yuri Y. and Drozdov, Alexander and Spasojevic, Maria and Kellerman, Adam C. and Usanova, Maria E. and Engebretson, Mark J. and Agapitov, Oleksiy V. and Zhelavskaya, Irina and Raita, Tero J. and Spence, Harlan E. and Baker, Daniel N. and Zhu, Hui and Aseev, Nikita}, title = {Wave-induced loss of ultra-relativistic electrons in the Van Allen radiation belts}, series = {Nature Communications}, volume = {7}, journal = {Nature Communications}, publisher = {Nature Publ. Group}, address = {London}, issn = {2041-1723}, doi = {10.1038/ncomms12883}, pages = {7}, year = {2016}, language = {en} } @article{WangShprits2019, author = {Wang, Dedong and Shprits, Yuri Y.}, title = {On How High-Latitude Chorus Waves Tip the Balance Between Acceleration and Loss of Relativistic Electrons}, series = {Geophysical research letters}, volume = {46}, journal = {Geophysical research letters}, number = {14}, publisher = {American Geophysical Union}, address = {Washington}, issn = {0094-8276}, doi = {10.1029/2019GL082681}, pages = {7945 -- 7954}, year = {2019}, abstract = {Modeling and observations have shown that energy diffusion by chorus waves is an important source of acceleration of electrons to relativistic energies. By performing long-term simulations using the three-dimensional Versatile Electron Radiation Belt code, in this study, we test how the latitudinal dependence of chorus waves can affect the dynamics of the radiation belt electrons. Results show that the variability of chorus waves at high latitudes is critical for modeling of megaelectron volt (MeV) electrons. We show that, depending on the latitudinal distribution of chorus waves under different geomagnetic conditions, they cannot only produce a net acceleration but also a net loss of MeV electrons. Decrease in high-latitude chorus waves can tip the balance between acceleration and loss toward acceleration, or alternatively, the increase in high-latitude waves can result in a net loss of MeV electrons. Variations in high-latitude chorus may account for some of the variability of MeV electrons.}, language = {en} } @article{LandisSaikinZhelavskayaetal.2022, author = {Landis, Daji August and Saikin, Anthony and Zhelavskaya, Irina and Drozdov, Alexander and Aseev, Nikita and Shprits, Yuri Y. and Pfitzer, Maximilian F. and Smirnov, Artem G.}, title = {NARX Neural Network Derivations of the Outer Boundary Radiation Belt Electron Flux}, series = {Space Weather: the international journal of research and applications}, volume = {20}, journal = {Space Weather: the international journal of research and applications}, number = {5}, publisher = {American Geophysical Union}, address = {Washington}, issn = {1542-7390}, doi = {10.1029/2021SW002774}, pages = {18}, year = {2022}, abstract = {We present two new empirical models of radiation belt electron flux at geostationary orbit. GOES-15 measurements of 0.8 MeV electrons were used to train a Nonlinear Autoregressive with Exogenous input (NARX) neural network for both modeling GOES-15 flux values and an upper boundary condition scaling factor (BF). The GOES-15 flux model utilizes an input and feedback delay of 2 and 2 time steps (i.e., 5 min time steps) with the most efficient number of hidden layers set to 10. Magnetic local time, Dst, Kp, solar wind dynamic pressure, AE, and solar wind velocity were found to perform as predicative indicators of GOES-15 flux and therefore were used as the exogenous inputs. The NARX-derived upper boundary condition scaling factor was used in conjunction with the Versatile Electron Radiation Belt (VERB) code to produce reconstructions of the radiation belts during the period of July-November 1990, independent of in-situ observations. Here, Kp was chosen as the sole exogenous input to be more compatible with the VERB code. This Combined Release and Radiation Effects Satellite-era reconstruction showcases the potential to use these neural network-derived boundary conditions as a method of hindcasting the historical radiation belts. This study serves as a companion paper to another recently published study on reconstructing the radiation belts during Solar Cycles 17-24 (Saikin et al., 2021, ), for which the results featured in this paper were used.}, language = {en} } @article{InceogluShpritsHeinemannetal.2022, author = {Inceoglu, Fadil and Shprits, Yuri Y. and Heinemann, Stephan G. and Bianco, Stefano}, title = {Identification of coronal holes on AIA/SDO images using unsupervised machine learning}, series = {The astrophysical journal : an international review of spectroscopy and astronomical physics}, volume = {930}, journal = {The astrophysical journal : an international review of spectroscopy and astronomical physics}, number = {2}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1538-4357}, doi = {10.3847/1538-4357/ac5f43}, pages = {11}, year = {2022}, abstract = {Through its magnetic activity, the Sun governs the conditions in Earth's vicinity, creating space weather events, which have drastic effects on our space- and ground-based technology. One of the most important solar magnetic features creating the space weather is the solar wind that originates from the coronal holes (CHs). The identification of the CHs on the Sun as one of the source regions of the solar wind is therefore crucial to achieve predictive capabilities. In this study, we used an unsupervised machine-learning method, k-means, to pixel-wise cluster the passband images of the Sun taken by the Atmospheric Imaging Assembly on the Solar Dynamics Observatory in 171, 193, and 211 angstrom in different combinations. Our results show that the pixel-wise k-means clustering together with systematic pre- and postprocessing steps provides compatible results with those from complex methods, such as convolutional neural networks. More importantly, our study shows that there is a need for a CH database where a consensus about the CH boundaries is reached by observers independently. This database then can be used as the "ground truth," when using a supervised method or just to evaluate the goodness of the models.}, language = {en} } @article{ShpritsAllisonWangetal.2022, author = {Shprits, Yuri Y. and Allison, Hayley J. and Wang, Dedong and Drozdov, Alexander and Szabo-Roberts, Matyas and Zhelavskaya, Irina and Vasile, Ruggero}, title = {A new population of ultra-relativistic electrons in the outer radiation zone}, series = {Journal of geophysical research : Space physics}, volume = {127}, journal = {Journal of geophysical research : Space physics}, number = {5}, publisher = {American Geophysical Union}, address = {Washington}, issn = {2169-9380}, doi = {10.1029/2021JA030214}, pages = {34}, year = {2022}, abstract = {Van Allen Probes measurements revealed the presence of the most unusual structures in the ultra-relativistic radiation belts. Detailed modeling, analysis of pitch angle distributions, analysis of the difference between relativistic and ultra-realistic electron evolution, along with theoretical studies of the scattering and wave growth, all indicate that electromagnetic ion cyclotron (EMIC) waves can produce a very efficient loss of the ultra-relativistic electrons in the heart of the radiation belts. Moreover, a detailed analysis of the profiles of phase space densities provides direct evidence for localized loss by EMIC waves. The evolution of multi-MeV fluxes shows dramatic and very sudden enhancements of electrons for selected storms. Analysis of phase space density profiles reveals that growing peaks at different values of the first invariant are formed at approximately the same radial distance from the Earth and show the sequential formation of the peaks from lower to higher energies, indicating that local energy diffusion is the dominant source of the acceleration from MeV to multi-MeV energies. Further simultaneous analysis of the background density and ultra-relativistic electron fluxes shows that the acceleration to multi-MeV energies only occurs when plasma density is significantly depleted outside of the plasmasphere, which is consistent with the modeling of acceleration due to chorus waves.}, language = {en} } @article{DrozdovAllisonShpritsetal.2022, author = {Drozdov, Alexander and Allison, Hayley J. and Shprits, Yuri Y. and Usanova, Maria E. and Saikin, Anthony and Wang, Dedong}, title = {Depletions of Multi-MeV Electrons and their association to Minima in Phase Space Density}, series = {Geophysical research letters}, volume = {49}, journal = {Geophysical research letters}, number = {8}, publisher = {American Geophysical Union}, address = {Washington}, issn = {0094-8276}, doi = {10.1029/2021GL097620}, pages = {11}, year = {2022}, abstract = {Fast-localized electron loss, resulting from interactions with electromagnetic ion cyclotron (EMIC) waves, can produce deepening minima in phase space density (PSD) radial profiles. Here, we perform a statistical analysis of local PSD minima to quantify how readily these are associated with radiation belt depletions. The statistics of PSD minima observed over a year are compared to the Versatile Electron Radiation Belts (VERB) simulations, both including and excluding EMIC waves. The observed minima distribution can only be achieved in the simulation including EMIC waves, indicating their importance in the dynamics of the radiation belts. By analyzing electron flux depletions in conjunction with the observed PSD minima, we show that, in the heart of the outer radiation belt (L* < 5), on average, 53\% of multi-MeV electron depletions are associated with PSD minima, demonstrating that fast localized loss by interactions with EMIC waves are a common and crucial process for ultra-relativistic electron populations.}, language = {en} } @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} }