Pitch Angle Diffusion Rates Research Articles

Impact of EMIC Waves on Electron Flux Dropouts Measured by GPS Spacecraft: Insights From ELFIN

AbstractAlthough the effects of electromagnetic ion cyclotron (EMIC) waves on the dynamics of the Earth's outer radiation belt have been a topic of intense research for more than 20 years, their influence on rapid dropouts of electron flux has not yet been fully assessed. Here, we make use of contemporaneous measurements on the same ‐shell of trapped electron fluxes at 20,000 km altitude by Global Positioning System (GPS) spacecraft and of trapped and precipitating electron fluxes at 450 km altitude by Electron Losses and Fields Investigation (ELFIN) CubeSats in 2020–2022, to investigate the impact of EMIC wave‐driven electron precipitation on the dynamics of the outer radiation belt below the last closed drift shell of trapped electrons. During six of the seven selected events, the strong 1–2 MeV electron precipitation measured at ELFIN, likely driven by EMIC waves, occurs within 1–2 hr from a dropout of relativistic electron flux at GPS spacecraft. Using quasi‐linear diffusion theory, EMIC wave‐driven pitch angle diffusion rates are inferred from ELFIN measurements, allowing us to quantitatively estimate the corresponding flux drop based on typical spatial and temporal extents of EMIC waves. We find that EMIC wave‐driven electron precipitation alone can account for the observed dropout magnitude at 1.5–3 MeV during all events and that, when dropouts extend down to 0.5 MeV, a fraction of electron loss may sometimes be due to EMIC waves. This suggests that EMIC wave‐driven electron precipitation could modulate dropout magnitude above 1 MeV in the heart of the outer radiation belt.

Modeling the Contribution of Precipitation Loss to a Radiation Belt Electron Dropout Observed by Van Allen Probes

AbstractA drift‐diffusion model is used to simulate the low‐altitude electron distribution, accounting for azimuthal drift, pitch angle diffusion, and atmospheric backscattering effects during a rapid electron dropout event on 21st August 2013, at L = 4.5. Additional external loss effects are introduced during times when the low‐altitude electron distribution cannot be reproduced by diffusion alone. The model utilizes low‐altitude electron count rate data from five POES/MetOp satellites to quantify pitch angle diffusion rates. Low‐altitude data provides critical constraint on the model because it includes the drift loss cone region where the electron distribution in longitude is highly dependent on the balance between azimuthal drift and pitch angle diffusion. Furthermore, a newly derived angular response function for the detectors onboard POES/MetOp is employed to accurately incorporate the bounce loss cone measurements, which have been previously contaminated by electrons from outside the nominal field‐of‐view. While constrained by low‐altitude data, the model also shows reasonable agreement with high‐altitude data. Pitch angle diffusion rates during the event are quantified and are faster at lower energies. Precipitation is determined to account for all of the total loss observed for 450 keV electrons, 88% for 600 keV and 38% for 900 keV. Predictions made in the MeV range are deemed unreliable as the integral energy channels E3 and P6 fail to provide the necessary constraint at relativistic energies.

New Chorus Diffusion Coefficients for Radiation Belt Modeling

AbstractWhistler mode chorus is an important magnetospheric wave emission playing a major role in radiation belt dynamics, where it contributes to both the acceleration and loss of relativistic electrons. In this study we compute bounce and drift averaged chorus diffusion coefficients for 3.0 < L* < 6.0, using the TS04 external magnetic field model, taking into account co‐located near‐equatorial measurements of the wave intensity and fpe/fce, by combining the Van Allen probes measurements with data from a multi‐satellite VLF wave database. The variation of chorus wave normal angle (WNA) with spatial location and fpe/fce is also taken into account. We find that chorus propagating at small WNAs has the dominant contribution to the diffusion rates in most MLT sectors. However, in the region 4 ≤ MLT < 11 high WNAs dominate at intermediate pitch angles. In the region 3 < L* < 4, the bounce and drift averaged pitch angle and energy diffusion rates during active conditions are primarily larger than those in our earlier models by up to a factor of 10 depending on energy and pitch angle. Further out, the results are similar. We find that the bounce and drift averaged energy and pitch angle diffusion rates can be significantly larger than the new model in regions of low , where the differences can be up to a factor of 10 depending on energy and pitch angle.

Extreme Energy Spectra of Relativistic Electron Flux in the Outer Radiation Belt.

Electron diffusion by whistler-mode chorus waves is one of the key processes controlling the dynamics of relativistic electron fluxes in the Earth's radiation belts. It is responsible for the acceleration of sub-relativistic electrons injected from the plasma sheet to relativistic energies as well as for their precipitation and loss into the atmosphere. Based on analytical estimates of chorus wave-driven quasi-linear electron energy and pitch-angle diffusion rates, we provide analytical steady-state solutions to the corresponding Fokker-Planck equation for the relativistic electron distribution and flux. The impact on these steady-state solutions of additional electromagnetic ion cyclotron waves, and of ultralow frequency waves are examined. Such steady-state solutions correspond to hard energy spectra at 1-4MeV, dangerous for satellite electronics, and represent attractors for the system dynamics in the presence of sufficiently strong driving by continuous injections of 10-300keV electrons. Therefore, these analytical steady-state solutions provide a simple means for estimating the most extreme electron energy spectra potentially encountered in the outer radiation belt, despite the great variability of injections and plasma conditions. These analytical steady-state solutions are compared with numerical simulations based on the full Fokker-Planck equation and with relativistic electron flux spectra measured by satellites during one extreme event and three strong events of high time-integrated geomagnetic activity, demonstrating a good agreement.

Resonance broadening effect for relativistic electron interaction with electromagnetic ion cyclotron waves

Relativistic electron scattering by electromagnetic ion cyclotron (EMIC) waves is one of the most effective mechanisms for >1 MeV electron flux depletion in the Earth's radiation belts. Resonant electron interaction with EMIC waves is traditionally described by quasi-linear diffusion equations, although spacecraft observations often report EMIC waves with intensities sufficiently large to trigger nonlinear resonant interaction with electrons. An important consequence of such nonlinear interaction is the resonance broadening effect due to high wave amplitudes. In this study, we quantify this resonance broadening effect in electron pitch-angle diffusion rates. We show that resonance broadening can significantly increase the pitch-angle range of EMIC-scattered electrons. This increase is especially important for ∼1 MeV electrons, where, without the resonance broadening, only those near the loss cone (with low fluxes) can resonate with EMIC waves.

Electron Diffusion by Magnetosonic Waves in the Earth’s Radiation Belts

AbstractWe conduct a global survey of magnetosonic waves and compute the associated bounce‐ and drift‐averaged diffusion coefficients, taking into account colocated measurements of fpe/fce, to assess the role of magnetosonic waves in radiation belt dynamics. The average magnetosonic wave intensities increase with increasing geomagnetic activity and decreasing relative frequency with the majority of the wave power in the range fcp < f < 0.3fLHR during active conditions. In the region 4.0 ≤ L* ≤ 5.0, the bounce‐ and drift‐averaged energy diffusion rates due to magnetosonic waves never exceed those due to whistler mode chorus, suggesting that whistler mode chorus is the dominant mode for electron energization to relativistic energies in this region. Further in, in the region 2.0 ≤ L* ≤ 3.5, the bounce‐ and drift‐averaged pitch angle diffusion rates due to magnetosonic waves can exceed those due to plasmaspheric hiss and very low frequency (VLF) transmitters over energy‐dependent ranges of intermediate pitch angles. We compute electron lifetimes by solving the 1D pitch angle diffusion equation including the effects of plasmaspheric hiss, VLF transmitters, and magnetosonic waves. We find that magnetosonic waves can have a significant effect on electron loss timescales in the slot region reducing the loss timescales during active times from 5.6 to 1.5 days for 500 keV electrons at L* = 2.5 and from 140.4 to 35.7 days for 1 MeV electrons at L* = 2.0.

Statistical Study of Whistler-Mode Waves and Expected Pitch Angle Diffusion Rates During Dispersionless Electron Injections.

Energetic electron injections can generate or amplify electromagnetic waves such as whistler‐mode waves. These waves can resonantly interact with available particles to affect their equatorial pitch angle. This process can be considered as a diffusion that scatters particles into the loss cone. This study investigates whistler‐mode wave generation in conjunction with electron injections using in situ wave measurements by the Time History of Events and Macroscale Interactions during Substorms mission during 2011–2020. We characterize the whistler‐mode wave behavior associated with 733 selected dispersionless electron injections and dipolarizing flux bundles (DFBs). We observe intense wave activity and strong diffusion associated with only the top 5% and 10% of the selected injection events, respectively. We also study the wave activity when there is a sharp rise in the northward component of the magnetic field around the injection time (DFBs). In this case, the generated wave powers increase, and the power change is at least two times greater than non‐DFB injections.

Scattering effect of very low frequency transmitter signals on energetic electrons in Earth’s inner belt and slot region

Whistler mode very low frequency (VLF) waves from man-made ground-based transmitters in a frequency range of 10–30 kHz are mainly used for submarine communication, and they propagate primarily in the Earth-lower ionosphere waveguide and part of their energy can leak into the inner magnetosphere, leading the energetic electrons in inner radiation belt and slot region to precipitate into atmosphere and then affect the energetic electron dynamics in the near-Earth space. The scattering effects of artificial VLF signals from NWC, NAA and DHO38 transmitters on energetic electrons in Earth’s inner belt and slot region are investigated in detail in this work. Based on the quasi-linear theory and the Full Diffusion Code, we calculate the bounce-average pitch angle diffusion coefficients induced by NWC, NAA and DHO38 VLF transmitter signals, for which the resonance harmonics |<i>N</i>| ≤ 10 are considered, respectively. We further implement the one-dimensional Fokker-Planck diffusion simulations by using the available pitch angle diffusion rates to model the dynamic evolutions of energetic electrons caused by the scattering of the VLF transmitter signals in the inner belt and slot region in 200 d. The simulation results indicate that the NWC VLF transmitter signals are dominant in scattering ~100 keV electrons with pitch angles less than 60° at <i>L</i> ≤ 1.8, and the mainly scattered electron energy values increase with <i>L</i>-shell decreasing , from <i>L</i> = 1.8 to <i>L </i>= 1.5, the mainly scattered electron energy increases from 90–120 keV to 550–650 keV. The NAA and DHO38 VLF transmitter signals are important in scattering < 20 keV electrons with pitch angles less than 70° at higher <i>L</i>-shells (2.2 ≤ <i>L</i> ≤ 2.7), from <i>L</i> = 2.2 to <i>L</i> = 2.7, the mainly scattered electron energy decreases from 10–20 keV to several keV. The VLF transmitter signals are found to have a slight influence on the loss of energetic electrons with pitch angles larger than 80°.

The influence of various frequency chorus waves on electron dynamics in radiation belts

Non-adiabatic behaviour induced by the chorus-electron interaction is an important contributor to the radiation belt dynamics, and largely relies on wave frequency distribution. During the geomagnetic storm on August 2, 2016, upper-band, lower-band and extremely low frequency (ELF) chorus waves were simultaneously observed within one orbit period of the Van Allen Probe B. Numerical simulations are performed to investigate the electron evolution by the observed chorus with different frequencies. The results show that various frequency chorus waves have different effects on electron dynamics. For chorus in the range f≈0.3fce−0.7fce, energy diffusion is the dominant process in electron evolutions. For chorus in the range 0.1fce⩽f⩽0.25fce, the pitch angle diffusion tends to be comparable to energy diffusion for Ek>0.5 MeV. For ELF chorus below 0.1fce, the pitch angle diffusion rate is much above the energy diffusion rate, leading to potential scattering losses.

Precipitation Loss of Radiation Belt Electrons by Two‐Band Plasmaspheric Hiss Waves

AbstractA two‐band plasmaspheric hiss consisting of a low‐frequency band (normal hiss with the frequency below 2 kHz) and a high‐frequency band (locally generated hiss with the frequency up to 10 kHz) was observed on 6 January 2014 by the Van Allen Probes (He et al., 2019, https://doi.org/10.1029/2018GL081578). The electron scattering effect driven by this kind of two‐band plasmaspheric hiss is evaluated by the quasi‐linear diffusion simulation for the first time. Realistic wave characteristic parameters of the two‐band plasmaspheric hiss from statistics are adopted for driving our simulation. The pitch angle diffusion rates of the low‐frequency band hiss present a “gap” with minimum magnitude at pitch angle αe ∼ 70°, a condition not favoring the transport of large pitch angle electrons toward the loss cone. However, the diffusion rates of the high‐frequency band hiss have peak values at αe ∼ 70°, filling up for the “gap” of the low‐frequency hiss diffusion rates. The realistic wave‐driven electron PSD evolutions demonstrate that the collaborated effect of the low‐frequency band and high‐frequency band hiss can cause significant precipitation losses of energetic electrons of tens to several hundred keV within 2 days.

Observations and Fokker‐Planck Simulations of the L‐Shell, Energy, and Pitch Angle Structure of Earth's Electron Radiation Belts During Quiet Times

AbstractThe evolution of the radiation belts in L‐shell (L), energy (E), and equatorial pitch angle (α 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, α 0) regions persist through 11 days of hiss wave scattering; the pitch angle‐dependent inner belt core (L ~ <2.2 and E < 700 keV), pitch angle homogeneous outer belt low‐energy core (L > ~5 and E~ < 100 keV), and a distinct pocket of electrons (L ~ [4.5, 5.5] and E ~ [0.7, 2] MeV). The pitch angle homogeneous outer belt is explained by the diffusion coefficients that are roughly constant for α 0 ~ <60°, E > 100 keV, 3.5 < L < L pp ~ 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 ~ 3–3.5 and E = 100–300 keV.

Global Model of Plasmaspheric Hiss From Multiple Satellite Observations

AbstractWe present a global model of plasmaspheric hiss, using data from eight satellites, extending the coverage and improving the statistics of existing models. We use geomagnetic activity dependent templates to separate plasmaspheric hiss from chorus. In the region 22–14 magnetic local time (MLT) the boundary between plasmaspheric hiss and chorus moves to lower values with increasing geomagnetic activity. The average wave intensity of plasmaspheric hiss is largest on the dayside and increases with increasing geomagnetic activity from midnight through dawn to dusk. Plasmaspheric hiss is most intense and spatially extended in the 200 to 500 Hz frequency band during active conditions, 400 750 nT, with an average intensity of 1,128 pT in the region 05–17 MLT from 1.5 . In the prenoon sector, waves in the 100 to 200 Hz frequency band peak near the magnetic equator and decrease in intensity with increasing magnetic latitude, inconsistent with a source from chorus outside the plasmapause, but more consistent with local amplification by substorm‐injected electrons. At higher frequencies the average wave intensities in this sector exhibit two peaks, one near the magnetic equator and one at high latitudes, 45° °, with a minimum at intermediate latitudes, 30° °, consistent with a source from chorus outside the plasmapause. In the premidnight sector, the intensity of plasmaspheric hiss in the frequency range 50 < f < 1,000 Hz decreases with increasing geomagnetic activity. The source of this weak premidnight plasmaspheric hiss is likely to be chorus at larger in the postnoon sector that enters that plasmasphere in the postnoon sector and subsequently propagates eastward in MLT.

VLF waves from ground‐based transmitters observed by the Van Allen Probes: Statistical model and effects on plasmaspheric electrons

AbstractWhistler mode very low frequency (VLF) waves from powerful ground‐based transmitters can resonantly scatter energetic plasmaspheric electrons and precipitate them into the atmosphere. A comprehensive 4 year statistics of Van Allen Probes measurements is carried out to assess their consequences on the dynamics of the inner radiation belt and slot region. Statistical models of the measured wave electric field power and of the inferred full wave magnetic amplitude are provided as a function of L, magnetic local time, season, and Kp over L = 1–3, revealing the localization of VLF wave intensity and its variation with geomagnetic activity over 2012–2016. Since this VLF wave model can be directly used together with existing hiss and lightning‐generated wave models in radiation belt simulation codes, we perform numerical calculations of the corresponding quasi‐linear pitch angle diffusion rates, allowing us to demonstrate the crucial role played by VLF waves from transmitters in energetic electron loss at L < 2.5.

Resonant scattering of central plasma sheet protons by multiband EMIC waves and resultant proton loss timescales

AbstractThis is a companion study to Liang et al. (2014) which reported a “reversed” energy‐latitude dispersion pattern of ion precipitation in that the lower energy ion precipitation extends to lower latitudes than the higher‐energy ion precipitation. Electromagnetic ion cyclotron (EMIC) waves in the central plasma sheet (CPS) have been suggested to account for this reversed‐type ion precipitation. To further investigate the association, we perform a comprehensive study of pitch angle diffusion rates induced by EMIC wave and the resultant proton loss timescales at L = 8–12 around the midnight. Comparing the proton scattering rates in the Earth's dipole field and a more realistic quiet time geomagnetic field constructed from the Tsyganenko 2001 (T01) model, we find that use of a realistic, nondipolar magnetic field model not only decreases the minimum resonant energies of CPS protons but also considerably decreases the limit of strong diffusion and changes the proton pitch angle diffusion rates. Adoption of the T01 model increases EMIC wave diffusion rates at > ~ 60° equatorial pitch angles but decreases them at small equatorial pitch angles. Pitch angle scattering coefficients of 1–10 keV protons due to H+ band EMIC waves can exceed the strong diffusion rate for both geomagnetic field models. While He+ and O+ band EMIC waves can only scatter tens of keV protons efficiently to cause a fully filled loss cone at L > 10, in the T01 magnetic field they can also cause efficient scattering of ~ keV protons in the strong diffusion limit at L > 10. The resultant proton loss timescales by EMIC waves with a nominal amplitude of 0.2 nT vary from a few hours to several days, depending on the wave band and L shell. Overall, the results demonstrate that H+ band EMIC waves, once present, can act as a major contributor to the scattering loss of a few keV protons at lower L shells in the CPS, accounting for the reversed energy‐latitude dispersion pattern of proton precipitation at low energies (~ keV) on the nightside. The pitch angle coverage for H+ band EMIC wave resonant scattering strongly depends on proton energy, L shell, and field model. He+ and O+ band EMIC waves tend to cause efficient scattering loss of protons at higher energies, thereby importantly contributing to the isotropic distribution of higher energy (> ~ 10 keV) protons at higher L shells on the nightside where the geomagnetic field line is highly stretched. Our results also suggest that scattering by H+ band EMIC waves may significantly contribute to the formation of the reversed‐type CPS proton precipitation on the dawnside where both the wave activity and occurrence probability is statistically high.

Estimation of pitch angle diffusion rates and precipitation time scales of electrons due to EMIC waves in a realistic field model

AbstractElectromagnetic ion cyclotron (EMIC) waves are closely related to precipitating loss of relativistic electrons in the radiation belts, and thereby, a model of the radiation belts requires inclusion of the pitch angle diffusion caused by EMIC waves. We estimated the pitch angle diffusion rates and the corresponding precipitation time scales caused by H and He band EMIC waves using the Tsyganenko 04 (T04) magnetic field model at their probable regions in terms of geomagnetic conditions. The results correspond to enhanced pitch angle diffusion rates and reduced precipitation time scales compared to those based on the dipole model, up to several orders of magnitude for storm times. While both the plasma density and the magnetic field strength varied in these calculations, the reduction of the magnetic field strength predicted by the T04 model was found to be the main cause of the enhanced diffusion rates relative to those with the dipole model for the same Li values, where Li is defined from the ionospheric foot points of the field lines. We note that the bounce‐averaged diffusion rates were roughly proportional to the inversion of the equatorial magnetic field strength and thus suggest that scaling the diffusion rates with the magnetic field strength provides a good approximation to account for the effect of the realistic field model in the EMIC wave‐pitch angle diffusion modeling.

Field-aligned chorus wave spectral power in Earth's outer radiation belt

Abstract. Chorus-type whistler waves are one of the most intense electromagnetic waves generated naturally in the magnetosphere. These waves have a substantial impact on the radiation belt dynamics as they are thought to contribute to electron acceleration and losses into the ionosphere through resonant wave–particle interaction. Our study is devoted to the determination of chorus wave power distribution on frequency in a wide range of magnetic latitudes, from 0 to 40°. We use 10 years of magnetic and electric field wave power measured by STAFF-SA onboard Cluster spacecraft to model the initial (equatorial) chorus wave spectral power, as well as PEACE and RAPID measurements to model the properties of energetic electrons (~ 0.1–100 keV) in the outer radiation belt. The dependence of this distribution upon latitude obtained from Cluster STAFF-SA is then consistently reproduced along a certain L-shell range (4 ≤ L ≤ 6.5), employing WHAMP-based ray tracing simulations in hot plasma within a realistic inner magnetospheric model. We show here that, as latitude increases, the chorus peak frequency is globally shifted towards lower frequencies. Making use of our simulations, the peak frequency variations can be explained mostly in terms of wave damping and amplification, but also cross-L propagation. These results are in good agreement with previous studies of chorus wave spectral extent using data from different spacecraft (Cluster, POLAR and THEMIS). The chorus peak frequency variations are then employed to calculate the pitch angle and energy diffusion rates, resulting in more effective pitch angle electron scattering (electron lifetime is halved) but less effective acceleration. These peak frequency parameters can thus be used to improve the accuracy of diffusion coefficient calculations.

Electron losses from the radiation belts caused by EMIC waves

AbstractElectromagnetic Ion Cyclotron (EMIC) waves cause electron loss in the radiation belts by resonating with high‐energy electrons at energies greater than about 500 keV. However, their effectiveness has not been fully quantified. Here we determine the effectiveness of EMIC waves by using wave data from the fluxgate magnetometer on CRRES to calculate bounce‐averaged pitch angle and energy diffusion rates for L*=3.5–7 for five levels of Kp between 12 and 18 MLT. To determine the electron loss, EMIC diffusion rates were included in the British Antarctic Survey Radiation Belt Model together with whistler mode chorus, plasmaspheric hiss, and radial diffusion. By simulating a 100 day period in 1990, we show that EMIC waves caused a significant reduction in the electron flux for energies greater than 2 MeV but only for pitch angles lower than about 60°. The simulations show that the distribution of electrons left behind in space looks like a pancake distribution. Since EMIC waves cannot remove electrons at all pitch angles even at 30 MeV, our results suggest that EMIC waves are unlikely to set an upper limit on the energy of the flux of radiation belt electrons.

Inner belt and slot region electron lifetimes and energization rates based on AKEBONO statistics of whistler waves

Global statistics of the amplitude distributions of hiss, lightning‐generated, and other whistler mode waves from terrestrial VLF transmitters have been obtained from the EXOS‐D (Akebono) satellite in the Earth's plasmasphere and fitted as functions of L and latitude for two geomagnetic activity ranges (Kp<3 and Kp>3). In particular, the present study focuses on the inner zone L∈[1.4,2] where reliable in situ measurements were lacking. Such statistics are critically needed for an accurate assessment of the role and relative dominance of each type of wave in the dynamics of the inner radiation belt. While VLF waves seem to propagate mainly in a ducted mode at L∼1.5–3 for Kp<3, they appear to be substantially unducted during more disturbed periods (Kp>3). Hiss waves are generally the most intense in the inner belt, and lightning‐generated and hiss wave intensities increase with geomagnetic activity. Lightning‐generated wave amplitudes generally peak within 10° of the equator in the region L<2 where magnetosonic wave amplitudes are weak for Kp<3. Based on this statistics, simplified models of each wave type are presented. Quasi‐linear pitch angle and energy diffusion rates of electrons by the full wave model are then calculated. Corresponding electron lifetimes compare well with decay rates of trapped energetic electrons obtained from Solar Anomalous and Magnetospheric Particle Explorer and other satellites at L∈[1.4,2].

Effect of EMIC waves on relativistic and ultrarelativistic electron populations: Ground‐based and Van Allen Probes observations

AbstractWe study the effect of electromagnetic ion cyclotron (EMIC) waves on the loss and pitch angle scattering of relativistic and ultrarelativistic electrons during the recovery phase of a moderate geomagnetic storm on 11 October 2012. The EMIC wave activity was observed in situ on the Van Allen Probes and conjugately on the ground across the Canadian Array for Real‐time Investigations of Magnetic Activity throughout an extended 18 h interval. However, neither enhanced precipitation of >0.7 MeV electrons nor reductions in Van Allen Probe 90° pitch angle ultrarelativistic electron flux were observed. Computed radiation belt electron pitch angle diffusion rates demonstrate that rapid pitch angle diffusion is confined to low pitch angles and cannot reach 90°. For the first time, from both observational and modeling perspectives, we show evidence of EMIC waves triggering ultrarelativistic (~2–8 MeV) electron loss but which is confined to pitch angles below around 45° and not affecting the core distribution.

A new diffusion matrix for whistler mode chorus waves

Global models of the Van Allen radiation belts usually include resonant wave‐particle interactions as a diffusion process, but there is a large uncertainty over the diffusion rates. Here we present a new diffusion matrix for whistler mode chorus waves that can be used in such models. Data from seven satellites are used to construct 3536 power spectra for upper and lower band chorus for 1.5≤L∗≤10 MLT, magnetic latitude 0°≤|λm|≤60° and five levels of Kp. Five density models are also constructed from the data. Gaussian functions are fitted to the spectra and capture typically 90% of the wave power. The frequency maxima of the power spectra vary with L∗ and are typically lower than that used previously. Lower band chorus diffusion increases with geomagnetic activity and is largest between 21:00 and 12:00 MLT. Energy diffusion extends to a few megaelectron volts at large pitch angles >60° and at high energies exceeds pitch angle diffusion at the loss cone. Most electron diffusion occurs close to the geomagnetic equator (<12°). Pitch angle diffusion rates for lower band chorus increase with L∗ and are significant at L∗=8 even for low levels of geomagnetic activity, while upper band chorus is restricted to mainly L∗<6. The combined drift and bounce averaged diffusion rates for upper and lower band chorus extend from a few kiloelectron volts near the loss cone up to several megaelectron volts at large pitch angles indicating loss at low energies and net acceleration at high energies.