TY - JOUR A1 - Zhelavskaya, Irina A1 - Spasojevic, M. A1 - Shprits, Yuri A1 - Kurth, William S. T1 - Automated determination of electron density from electric field measurements on the Van Allen Probes spacecraft JF - Journal of geophysical research : Space physics N2 - We present the Neural-network-based Upper hybrid Resonance Determination (NURD) algorithm for automatic inference of the electron number density from plasma wave measurements made on board NASA's Van Allen Probes mission. A feedforward neural network is developed to determine the upper hybrid resonance frequency, fuhr, from electric field measurements, which is then used to calculate the electron number density. In previous missions, the plasma resonance bands were manually identified, and there have been few attempts to do robust, routine automated detections. We describe the design and implementation of the algorithm and perform an initial analysis of the resulting electron number density distribution obtained by applying NURD to 2.5 years of data collected with the Electric and Magnetic Field Instrument Suite and Integrated Science (EMFISIS) instrumentation suite of the Van Allen Probes mission. Densities obtained by NURD are compared to those obtained by another recently developed automated technique and also to an existing empirical plasmasphere and trough density model. KW - Van Allen Probes KW - electron number density KW - neural networks Y1 - 2016 U6 - https://doi.org/10.1002/2015JA022132 SN - 2169-9380 SN - 2169-9402 VL - 121 SP - 4611 EP - 4625 PB - American Geophysical Union CY - Washington ER - TY - JOUR A1 - Boyd, A. J. A1 - Spence, Harlan E. A1 - Huang, Chia-Lin A1 - Reeves, Geoffrey D. A1 - Baker, Daniel N. A1 - Turner, D. L. A1 - Claudepierre, Seth G. A1 - Fennell, Joseph F. A1 - Blake, J. Bernard A1 - Shprits, Yuri T1 - Statistical properties of the radiation belt seed population JF - Journal of geophysical research : Space physics N2 - 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. Y1 - 2016 U6 - https://doi.org/10.1002/2016JA022652 SN - 2169-9380 SN - 2169-9402 VL - 121 SP - 7636 EP - 7646 PB - American Geophysical Union CY - Washington ER - TY - JOUR A1 - Cao, Xing A1 - Shprits, Yuri A1 - Ni, Binbin A1 - Zhelavskaya, Irina T1 - Scattering of Ultra-relativistic Electrons in the Van Allen Radiation Belts Accounting for Hot Plasma Effects JF - Scientific reports N2 - Electron flux in the Earth’s outer radiation belt is highly variable due to a delicate balance between competing acceleration and loss processes. It has been long recognized that Electromagnetic Ion Cyclotron (EMIC) waves may play a crucial role in the loss of radiation belt electrons. Previous theoretical studies proposed that EMIC waves may account for the loss of the relativistic electron population. However, recent observations showed that while EMIC waves are responsible for the significant loss of ultra-relativistic electrons, the relativistic electron population is almost unaffected. In this study, we provide a theoretical explanation for this discrepancy between previous theoretical studies and recent observations. We demonstrate that EMIC waves mainly contribute to the loss of ultra-relativistic electrons. This study significantly improves the current understanding of the electron dynamics in the Earth’s radiation belt and also can help us understand the radiation environments of the exoplanets and outer planets. Y1 - 2017 U6 - https://doi.org/10.1038/s41598-017-17739-7 SN - 2045-2322 VL - 7 PB - Nature Publ. Group CY - London ER - TY - GEN A1 - Shprits, Yuri T1 - Editorial: Topical Collection on the Lomonosov Mission T2 - Space science reviews Y1 - 2017 U6 - https://doi.org/10.1007/s11214-017-0393-1 SN - 0038-6308 SN - 1572-9672 VL - 212 SP - 1685 EP - 1686 PB - Springer CY - Dordrecht ER - TY - GEN A1 - Woodfield, Emma E. A1 - Horne, Richard B. A1 - Glauert, Sarah A. A1 - Menietti, John D. A1 - Shprits, Yuri A1 - Kurth, William S. T1 - Formation of electron radiation belts at Saturn by Z-mode wave acceleration T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - At Saturn electrons are trapped in the planet's magnetic field and accelerated to relativistic energies to form the radiation belts, but how this dramatic increase in electron energy occurs is still unknown. Until now the mechanism of radial diffusion has been assumed but we show here that in-situ acceleration through wave particle interactions, which initial studies dismissed as ineffectual at Saturn, is in fact a vital part of the energetic particle dynamics there. We present evidence from numerical simulations based on Cassini spacecraft data that a particular plasma wave, known as Z-mode, accelerates electrons to MeV energies inside 4 R-S (1 R-S = 60,330 km) through a Doppler shifted cyclotron resonant interaction. Our results show that the Z-mode waves observed are not oblique as previously assumed and are much better accelerators than O-mode waves, resulting in an electron energy spectrum that closely approaches observed values without any transport effects included. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1032 KW - astrophysical plasmas KW - giant planets KW - magnetospheric physics KW - diffusion KW - pitch angle KW - plasma KW - radio KW - region Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-468342 SN - 1866-8372 IS - 1032 ER - TY - JOUR A1 - Zhu, Hui A1 - Shprits, Yuri A1 - Spasojevic, M. A1 - Drozdov, Alexander T1 - 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 JF - Journal of Atmospheric and Solar-Terrestrial Physics N2 - 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. KW - Inner magnetosphere KW - Radiation belts KW - Chorus waves KW - Diffusion coefficients KW - VERB code Y1 - 2019 U6 - https://doi.org/10.1016/j.jastp.2019.105090 SN - 1364-6826 SN - 1879-1824 VL - 193 PB - Elsevier CY - Oxford ER - TY - JOUR A1 - Kim, Kyung-Chan A1 - Shprits, Yuri T1 - Dependence of the amplitude of magnetosonic waves on the solar wind and AE index using Van Allen Probes JF - Journal of geophysical research : Space physics N2 - We present the dependence of the magnetosonic wave amplitudes both outside and inside the plasmapause on the solar wind and AE index using Van Allen Probe-A spacecraft during the time period of 1 October 2012 to 31 December 2015, based on a correlation and regression analysis. Solar wind parameters considered are the southward interplanetary magnetic field (IMF B-S), solar wind number density (N-SW), and bulk speed (V-SW). We find that the wave amplitudes outside (inside) the plasmapause are well correlated with the preceding AE, IMF B-S, and N-SW with time delays, each corresponding to 2-3 h (3-4 h), 4-5 h (3-4 h), and 2-3 h (8-9 h), while the correlation with V-SW is ambiguous both inside and outside the plasmapause. As measured by the correlation coefficient, the IMF B-S is the most influential solar wind parameter that affects the dayside wave amplitudes both outside and inside the plasmapause, while N-SW contributes to enhancing the duskside waves outside the plasmapause. The AE effect on wave amplitudes is comparable to that of IMF B-S. More interestingly, regression with time histories of the solar wind parameters and the AE index preceding the wave measurements outside the plasmapause shows significant dependence on the IMF B-S, N-SW, and AE: the region of peak coefficients is changed with time delay for IMF B-S and AE, while isolated peaks around duskside remain gradually decrease with time for N-SW. In addition, the regression with magnetosonic waves inside the plasmapause shows high coefficients around prenoon sector with preceding IMF B-S and V-SW. KW - magnetosonic equatorial noise KW - solar wind dependence KW - Van Allen Probes Y1 - 2017 U6 - https://doi.org/10.1002/2017JA024094 SN - 2169-9380 SN - 2169-9402 VL - 122 SP - 6022 EP - 6034 PB - American Geophysical Union CY - Washington ER - TY - JOUR A1 - Drozdov, Alexander A1 - Shprits, Yuri A1 - Usanova, Maria E. A1 - Aseev, Nikita A1 - Kellerman, Adam C. A1 - Zhu, H. T1 - EMIC wave parameterization in the long-term VERB code simulation JF - Journal of geophysical research : Space physics N2 - Electromagnetic ion cyclotron (EMIC) waves play an important role in the dynamics of ultrarelativistic electron population in the radiation belts. However, as EMIC waves are very sporadic, developing a parameterization of such wave properties is a challenging task. Currently, there are no dynamic, activity-dependent models of EMIC waves that can be used in the long-term (several months) simulations, which makes the quantitative modeling of the radiation belt dynamics incomplete. In this study, we investigate Kp, Dst, and AE indices, solar wind speed, and dynamic pressure as possible parameters of EMIC wave presence. The EMIC waves are included in the long-term simulations (1year, including different geomagnetic activity) performed with the Versatile Electron Radiation Belt code, and we compare results of the simulation with the Van Allen Probes observations. The comparison shows that modeling with EMIC waves, parameterized by solar wind dynamic pressure, provides a better agreement with the observations among considered parameterizations. The simulation with EMIC waves improves the dynamics of ultrarelativistic fluxes and reproduces the formation of the local minimum in the phase space density profiles. KW - radiation belts KW - VERB code KW - EMIC Y1 - 2017 U6 - https://doi.org/10.1002/2017JA024389 SN - 2169-9380 SN - 2169-9402 VL - 122 SP - 8488 EP - 8501 PB - American Geophysical Union CY - Washington ER - TY - JOUR A1 - Aseev, Nikita A1 - Shprits, Yuri A1 - Drozdov, Alexander A1 - Kellerman, Adam C. A1 - Usanova, Maria E. A1 - Wang, D. A1 - Zhelavskaya, Irina T1 - Signatures of Ultrarelativistic Electron Loss in the Heart of the Outer Radiation Belt Measured by Van Allen Probes JF - Journal of geophysical research : Space physics N2 - Up until recently, signatures of the ultrarelativistic electron loss driven by electromagnetic ion cyclotron (EMIC) waves in the Earth's outer radiation belt have been limited to direct or indirect measurements of electron precipitation or the narrowing of normalized pitch angle distributions in the heart of the belt. In this study, we demonstrate additional observational evidence of ultrarelativistic electron loss that can be driven by resonant interaction with EMIC waves. We analyzed the profiles derived from Van Allen Probe particle data as a function of time and three adiabatic invariants between 9 October and 29 November 2012. New local minimums in the profiles are accompanied by the narrowing of normalized pitch angle distributions and ground‐based detection of EMIC waves. Such a correlation may be indicative of ultrarelativistic electron precipitation into the Earth's atmosphere caused by resonance with EMIC waves. Y1 - 2017 U6 - https://doi.org/10.1002/2017JA024485 SN - 2169-9380 SN - 2169-9402 VL - 122 SP - 10102 EP - 10111 PB - American Geophysical Union CY - Washington ER - TY - JOUR A1 - Drozdov, Alexander A1 - Aseev, Nikita A1 - Effenberger, Frederic A1 - Turner, Drew L. A1 - Saikin, Anthony A1 - Shprits, Yuri T1 - Storm Time Depletions of Multi-MeV Radiation Belt Electrons Observed at Different Pitch Angles JF - Journal of geophysical research : Space physics N2 - During geomagnetic storms, the rapid depletion of the high-energy (several MeV) outer radiation belt electrons is the result of loss to the interplanetary medium through the magnetopause, outward radial diffusion, and loss to the atmosphere due to wave-particle interactions. We have performed a statistical study of 110 storms using pitch angle resolved electron flux measurements from the Van Allen Probes mission and found that inside of the radiation belt (L* = 3 - 5) the number of storms that result in depletion of electrons with equatorial pitch angle alpha(eq) = 30 degrees is higher than number of storms that result in depletion of electrons with equatorial pitch angle alpha(eq) = 75 degrees. We conclude that this result is consistent with electron scattering by whistler and electromagnetic ion cyclotron waves. At the outer edge of the radiation belt (L* >= 5.2) the number of storms that result in depletion is also large (similar to 40-50%), emphasizing the significance of the magnetopause shadowing effect and outward radial transport. Y1 - 2019 U6 - https://doi.org/10.1029/2019JA027332 SN - 2169-9380 SN - 2169-9402 VL - 124 IS - 11 SP - 8943 EP - 8953 PB - American Geophysical Union CY - Washington ER - TY - JOUR A1 - Castillo, Angelica M. A1 - Shprits, Yuri A1 - Ganushkina, Natalia A1 - Drozdov, Alexander A1 - Aseev, Nikita A1 - Wang, Dedong A1 - Dubyagin, Stepan T1 - Simulations of the inner magnetospheric energetic electrons using the IMPTAM-VERB coupled model JF - Journal of Atmospheric and Solar-Terrestrial Physics N2 - In this study, we present initial results of the coupling between the Inner Magnetospheric Particle Transport and Acceleration Model (IMPTAM) and the Versatile Electron Radiation Belt (VERB-3D) code. IMPTAM traces electrons of 10-100 keV energies from the plasma sheet (L = 9 Re) to inner L-shell regions. The flux evolution modeled by IMPTAM is used at the low energy and outer L* computational boundaries of the VERB code (assuming a dipole approximation) to perform radiation belt simulations of energetic electrons. The model was tested on the March 17th, 2013 storm, for a six-day period. Four different simulations were performed and their results compared to satellites observations from Van Allen probes and GOES. The coupled IMPTAM-VERB model reproduces evolution and storm-time features of electron fluxes throughout the studied storm in agreement with the satellite data (within similar to 0.5 orders of magnitude). Including dynamics of the low energy population at L* = 6.6 increases fluxes closer to the heart of the belt and has a strong impact in the VERB simulations at all energies. However, inclusion of magnetopause losses leads to drastic flux decreases even below L* = 3. The dynamics of low energy electrons (max. 10s of keV) do not affect electron fluxes at energies >= 900 keV. Since the IMPTAM-VERB coupled model is only driven by solar wind parameters and the Dst and Kp indexes, it is suitable as a forecasting tool. In this study, we demonstrate that the estimation of electron dynamics with satellite-data-independent models is possible and very accurate. KW - Electron populations KW - Radiation belts KW - IMPTAM KW - VERB Y1 - 2019 U6 - https://doi.org/10.1016/j.jastp.2019.05.014 SN - 1364-6826 SN - 1879-1824 VL - 191 PB - Elsevier CY - Oxford ER - TY - JOUR A1 - Woodfield, Emma E. A1 - Glauert, Saraha A. A1 - Menietti, J. Douglas A1 - Averkamp, Terrance F. A1 - Horne, Richard B. A1 - Shprits, Yuri T1 - Rapid Electron Acceleration in Low‐Density Regions of Saturn's Radiation Belt by Whistler Mode Chorus Waves JF - Geophysical research letters N2 - Electron acceleration at Saturn due to whistler mode chorus waves has previously been assumed to be ineffective; new data closer to the planet show it can be very rapid (factor of 104 flux increase at 1 MeV in 10 days compared to factor of 2). A full survey of chorus waves at Saturn is combined with an improved plasma density model to show that where the plasma frequency falls below the gyrofrequency additional strong resonances are observed favoring electron acceleration. This results in strong chorus acceleration between approximately 2.5 R-S and 5.5 R-S outside which adiabatic transport may dominate. Strong pitch angle dependence results in butterfly pitch angle distributions that flatten over a few days at 100s keV, tens of days at MeV energies which may explain observations of butterfly distributions of MeV electrons near L = 3. Including cross terms in the simulations increases the tendency toward butterfly distributions. Plain Language Summary Radiation belts are hazardous regions found around several of the planets in our Solar System. They consist of very hot, electrically charged particles trapped in the magnetic field of the planet. At Saturn the most important way to heat these particles has for many years been thought to involve the particles drifting closer toward the planet. This paper adds to the emerging idea at Saturn that a different way to heat the particles is also possible where the heating is done by waves, in a similar way to what we find at the Earth. We use recent information from the Cassini spacecraft on the number and location of particles and also of the waves strength and location combined with computer simulations to show that a particular wave called chorus is excellent at heating the particles where the surrounding number of cold particles is low. Y1 - 2019 U6 - https://doi.org/10.1029/2019GL083071 SN - 0094-8276 SN - 1944-8007 VL - 46 IS - 13 SP - 7191 EP - 7198 PB - American Geophysical Union CY - Washington ER - TY - JOUR A1 - Denton, Richard E. A1 - Ofman, L. A1 - Shprits, Yuri A1 - Bortnik, J. A1 - Millan, R. M. A1 - Rodger, C. J. A1 - da Silva, C. L. A1 - Rogers, B. N. A1 - Hudson, M. K. A1 - Liu, K. A1 - Min, K. A1 - Glocer, A. A1 - Komar, C. T1 - Pitch Angle Scattering of Sub-MeV Relativistic Electrons by Electromagnetic Ion Cyclotron Waves JF - Journal of geophysical research : Space physics N2 - Electromagnetic ion cyclotron (EMIC) waves have long been considered to be a significant loss mechanism for relativistic electrons. This has most often been attributed to resonant interactions with the highest amplitude waves. But recent observations have suggested that the dominant energy of electrons precipitated to the atmosphere may often be relatively low, less than 1 MeV, whereas the minimum resonant energy of the highest amplitude waves is often greater than 2 MeV. Here we use relativistic electron test particle simulations in the wavefields of a hybrid code simulation of EMIC waves in dipole geometry in order to show that significant pitch angle scattering can occur due to interaction with low-amplitude short-wavelength EMIC waves. In the case we examined, these waves are in the H band (at frequencies above the He+ gyrofrequency), even though the highest amplitude waves were in the He band frequency range (below the He+ gyrofrequency). We also present wave power distributions for 29 EMIC simulations in straight magnetic field line geometry that show that the high wave number portion of the spectrum is in every case mostly due to the H band waves. Though He band waves are often associated with relativistic electron precipitation, it is possible that the He band waves do not directly scatter the sub-megaelectron volts (sub-MeV) electrons, but that the presence of He band waves is associated with high plasma density which lowers the minimum resonant energy so that these electrons can more easily resonate with the H band waves. KW - electromagnetic ion cyclotron waves KW - EMIC KW - relativistic electron precipitation KW - pitch angle scattering KW - wave particle interaction KW - radiation belts Y1 - 2019 U6 - https://doi.org/10.1029/2018JA026384 SN - 2169-9402 VL - 124 IS - 7 SP - 5610 EP - 5626 PB - American Geophysical Union CY - Washington ER - TY - JOUR A1 - Qin, Murong A1 - Hudson, Mary A1 - Li, Zhao A1 - Millan, Robyn A1 - Shen, Xiaochen A1 - Shprits, Yuri A1 - Woodger, Leslie A1 - Jaynes, Allison A1 - Kletzing, Craig T1 - Investigating loss of relativistic electrons associated with EMIC Waves at low L values on 22 June 2015 JF - Journal of geophysical research : Space physics N2 - In this study, rapid loss of relativistic radiation belt electrons at low L* values (2.4-3.2) during a strong geomagnetic storm on 22 June 2015 is investigated along with five possible loss mechanisms. Both the particle and wave data are obtained from the Van Allen Probes. Duskside H+ band electromagnetic ion cyclotron (EMIC) waves were observed during a rapid decrease of relativistic electrons with energy above 5.2 MeV occurring outside the plasma sphere during extreme magnetopause compression. Lower He+ composition and enriched O+ composition are found compared to typical values assumed in other studies of cyclotron resonant scattering of relativistic electrons by EMIC waves. Quantitative analysis demonstrates that even with the existence of He+ band EMIC waves, it is the H+ band EMIC waves that are likely to cause the depletion at small pitch angles and strong gradients in pitch angle distributions of relativistic electrons with energy above 5.2 MeV at low L values for this event. Very low frequency wave activity at other magnetic local time can be favorable for the loss of relativistic electrons at higher pitch angles. An illustrative calculation that combines the nominal pitch angle scattering rate due to whistler mode chorus at high pitch angles with the H+ band EMIC wave loss rate at low pitch angles produces loss on time scale observed at L = 2.4-3.2. At high L values and lower energies, radial loss to the magnetopause is a viable explanation. Y1 - 2019 U6 - https://doi.org/10.1029/2018JA025726 SN - 2169-9380 SN - 2169-9402 VL - 124 IS - 6 SP - 4022 EP - 4036 PB - American Geophysical Union CY - Washington ER - TY - JOUR A1 - Shprits, Yuri A1 - Vasile, Ruggero A1 - Zhelayskaya, Irina S. T1 - Nowcasting and Predicting the Kp Index Using Historical Values and Real-Time Observations JF - Space Weather: The International Journal of Research and Applications N2 - Current algorithms for the real-time prediction of the Kp index use a combination of models empirically driven by solar wind measurements at the L1 Lagrange point and historical values of the index. In this study, we explore the limitations of this approach, examining the forecast for short and long lead times using measurements at L1 and Kp time series as input to artificial neural networks. We explore the relative efficiency of the solar wind-based predictions, predictions based on recurrence, and predictions based on persistence. Our modeling results show that for short-term forecasts of approximately half a day, the addition of the historical values of Kp to the measured solar wind values provides a barely noticeable improvement. For a longer-term forecast of more than 2 days, predictions can be made using recurrence only, while solar wind measurements provide very little improvement for a forecast with long horizon times. We also examine predictions for disturbed and quiet geomagnetic activity conditions. Our results show that the paucity of historical measurements of the solar wind for high Kp results in a lower accuracy of predictions during disturbed conditions. Rebalancing of input data can help tailor the predictions for more disturbed conditions. KW - Kp index KW - geomagnetic activity KW - empirical prediction KW - solar wind KW - forecast KW - AI Y1 - 2019 U6 - https://doi.org/10.1029/2018SW002141 SN - 1542-7390 VL - 17 IS - 8 SP - 1219 EP - 1229 PB - American Geophysical Union CY - Washington ER - TY - JOUR A1 - Wang, Dedong A1 - Shprits, Yuri T1 - On How High-Latitude Chorus Waves Tip the Balance Between Acceleration and Loss of Relativistic Electrons JF - Geophysical research letters N2 - 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. KW - radiation belts KW - chorus waves KW - high latitude KW - acceleration KW - loss KW - modeling Y1 - 2019 U6 - https://doi.org/10.1029/2019GL082681 SN - 0094-8276 SN - 1944-8007 VL - 46 IS - 14 SP - 7945 EP - 7954 PB - American Geophysical Union CY - Washington ER - TY - JOUR A1 - Aseev, Nikita A1 - Shprits, Yuri A1 - Drozdov, Alexander A1 - Kellerman, Adam C. T1 - Numerical applications of the advective-diffusive codes for the inner magnetosphere JF - Space Weather: The International Journal of Research and Applications N2 - In this study we present analytical solutions for convection and diffusion equations. We gather here the analytical solutions for the one-dimensional convection equation, the two-dimensional convection problem, and the one- and two-dimensional diffusion equations. Using obtained analytical solutions, we test the four-dimensional Versatile Electron Radiation Belt code (the VERB-4D code), which solves the modified Fokker-Planck equation with additional convection terms. The ninth-order upwind numerical scheme for the one-dimensional convection equation shows much more accurate results than the results obtained with the third-order scheme. The universal limiter eliminates unphysical oscillations generated by high-order linear upwind schemes. Decrease in the space step leads to convergence of a numerical solution of the two-dimensional diffusion equation with mixed terms to the analytical solution. We compare the results of the third- and ninth-order schemes applied to magnetospheric convection modeling. The results show significant differences in electron fluxes near geostationary orbit when different numerical schemes are used. KW - advective-diffusive codes KW - inner magnetosphere KW - numerical schemes Y1 - 2016 U6 - https://doi.org/10.1002/2016SW001484 SN - 1542-7390 VL - 14 SP - 993 EP - 1010 PB - American Geophysical Union CY - Washington ER - TY - JOUR A1 - Kim, Kyung-Chan A1 - Shprits, Yuri A1 - Blake, J. Bernard T1 - Fast injection of the relativistic electrons into the inner zone and the formation of the split-zone structure during the Bastille Day storm in July 2000 JF - Journal of geophysical research : Space physics N2 - During the July 2000 geomagnetic storm, known as the Bastille Day storm, Solar, Anomalous, and Magnetospheric Particle Explorer (SAMPEX)/Heavy Ion Large Telescope (HILT) observed a strong injection of similar to 1MeV electrons into the slot region (L similar to 2.5) during the storm main phase. Then, during the following month, electrons were clearly seen diffusing inward down to L=2 and forming a pronounced split structure encompassing a narrow, newly formed slot region around L=3. SAMPEX observations are first compared with electron and proton observations on HEO-3 and NOAA-15 to validate that the observed unusual dynamics was not caused by proton contamination of the SAMPEX instrument. The time-dependent 3-D Versatile Electron Radiation Belt (VERB) simulation of 1MeV electron flux evolution is compared with the SAMPEX/HILT observations. The results show that the VERB code predicts overall time evolution of the observed split structure. The simulated split structure is produced by pitch angle scattering into the Earth atmosphere of similar to 1MeV electrons by plasmaspheric hiss. KW - inner radiation zone and slot region KW - Bastille Day geomagnetic storm KW - 3-D diffusion simulation KW - plasmaspheric hiss Y1 - 2016 U6 - https://doi.org/10.1002/2015JA022072 SN - 2169-9380 SN - 2169-9402 VL - 121 SP - 8329 EP - 8342 PB - American Geophysical Union CY - Washington ER - TY - JOUR A1 - Shprits, Yuri A1 - Drozdov, Alexander A1 - Spasojevic, Maria A1 - Kellerman, Adam C. A1 - Usanova, Maria E. A1 - Engebretson, Mark J. A1 - Agapitov, Oleksiy V. A1 - Zhelavskaya, Irina A1 - Raita, Tero J. A1 - Spence, Harlan E. A1 - Baker, Daniel N. A1 - Zhu, Hui A1 - Aseev, Nikita T1 - Wave-induced loss of ultra-relativistic electrons in the Van Allen radiation belts JF - Nature Communications Y1 - 2016 U6 - https://doi.org/10.1038/ncomms12883 SN - 2041-1723 VL - 7 PB - Nature Publ. Group CY - London ER - TY - JOUR A1 - Wang, Dedong A1 - Shprits, Yuri A1 - Zhelayskaya, Irina S. A1 - Agapitov, Oleksiy A1 - Drozdov, Alexander A1 - Aseev, Nikita T1 - Analytical chorus wave model derived from van Allen Probe Observations JF - Journal of geophysical research : Space physics N2 - Chorus waves play an important role in the dynamic evolution of energetic electrons in the Earth's radiation belts and ring current. Using more than 5 years of Van Allen Probe data, we developed a new analytical model for upper‐band chorus (UBC; 0.5fce < f < fce) and lower‐band chorus (LBC; 0.05fce < f < 0.5fce) waves, where fce is the equatorial electron gyrofrequency. By applying polynomial fits to chorus wave root mean square amplitudes, we developed regression models for LBC and UBC as a function of geomagnetic activity (Kp), L, magnetic latitude (λ), and magnetic local time (MLT). Dependence on Kp is separated from the dependence on λ, L, and MLT as Kp‐scaling law to simplify the calculation of diffusion coefficients and inclusion into particle tracing codes. Frequency models for UBC and LBC are also developed, which depends on MLT and magnetic latitude. This empirical model is valid in all MLTs, magnetic latitude up to 20°, Kp ≤ 6, L‐shell range from 3.5 to 6 for LBC and from 4 to 6 for UBC. The dependence of root mean square amplitudes on L are different for different bands, which implies different energy sources for different wave bands. This analytical chorus wave model is convenient for inclusion in quasi‐linear diffusion calculations of electron scattering rates and particle simulations in the inner magnetosphere, especially for the newly developed four‐dimensional codes, which require significantly improved wave parameterizations. KW - chorus waves KW - radiation belt electrons KW - ring current electrons KW - analytical model KW - wave-particle interactions KW - diffusion coefficients Y1 - 2019 U6 - https://doi.org/10.1029/2018JA026183 SN - 2169-9380 SN - 2169-9402 VL - 124 IS - 2 SP - 1063 EP - 1084 PB - American Geophysical Union CY - Washington ER -