Equatorial Pitch Angle Distributions Research Articles

The Response of Electron Pitch Angle Distributions to the Upper Limit on Stably Trapped Particles

AbstractWe use Van Allen Probes electron data during 70 geomagnetic storms to examine the response of equatorial pitch angle distributions (PADs) at L* = 4.0–4.5 to a theoretical upper limit on stably trapped particle fluxes. Of the energies examined, 54 and 108 keV electron PADs isotropize to a previously assumed level within 6 hr of reaching the limit, near‐identically across all 70 storms, consistent with rapid pitch angle scattering due to chorus wave interactions. In around 30% of events, 54 keV electrons completely exceed the KP limit, before being quickly subdued. 470 and 749 keV PADs show clear indications of an upper limit, though less aligned with the calculated limit used here. The consistency of an absolute upper limit shown across all events demonstrates the importance of this phenomena in both the limiting effect on electron flux and consistently influencing electron PAD evolution during geomagnetic storms. These results also highlight the need for further investigation, particularly related to the limiting of higher energy electrons.

Proton Equatorial Pitch Angle Distributions in Jupiter's Inner Magnetosphere

AbstractWe use data from the plasma and energetic particle instruments on the Juno spacecraft, JADE and JEDI, to study the equatorial pitch angle distributions of energetic protons within Jupiter's inner magnetosphere during Juno's prime mission from 2016 to 2021. Averaging over all observations made by Juno within M‐shell bins between M = 6 and M = 30, we find protons at energies between 10 and 50 keV are predominantly field‐aligned at all M‐shells. In contrast, those at energies above 200 keV transition from being predominantly field‐aligned at M = 20 to having pancake‐like distributions at M < 10. We find the observed distributions are consistent either with charge exchange of protons with neutral toroidal clouds, or with adiabatic acceleration of protons originating from Jupiter that are transported inward from the middle magnetosphere.

An Empirical Model of the Equatorial Electron Pitch Angle Distributions in Earth's Outer Radiation Belt

AbstractIn 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.

Statistical investigation on equatorial pitch angle distribution of energetic electrons in Earth’s outer radiation belt during CME- and CIR-driven storms

We present a statistical investigation (September 2012 - September 2017) of pitch angle distribution (PAD) of energetic electrons (∼30 keV - 1 MeV) in the outer radiation belt (L ≥ 3) during CME- and CIR-driven geomagnetic storms using Van Allen Probe measurements. We selected geomagnetic storms based on minimum of SYM-H being less than -50 nT and classified the storms according to their drivers. Thus, we obtained 23 CME- and 24 CIR-driven storms. During the storm intervals, pitch angle resolved electron flux measurements are obtained from the MagEIS instrument on-board Van Allen Probe-A spacecraft. We assume symmetric pitch angle distributions around 90° pitch angle and fit the observed PADs with Legendre polynomials after propagating them to the magnetic equator. Legendre coefficients c2 and c4, and the ratio R = |c2/c4| are used to categorize the different PAD types. To resolve the spatio-temporal distribution of PADs, these coefficients are binned in 5 L-shell bins, 12 MLT bins for seven energy channels and four storm phases. We found that several hundreds of keV electrons exhibit clear dependence on local time, storm phases and storm drivers, with increased anisotropy for CME-driven storms during main and early recovery phases. On the contrary, we found that tens of keV electrons do not exhibit significant dependence on these parameters. We have discussed the different physical mechanisms responsible for the observed MLT dependent PADs and found drift-shell splitting to be the major contributor.

Storm-Time Evolution of the Equatorial Electron Pitch Angle Distributions in Earth’s Outer Radiation Belt

In this study we analyze the storm-time evolution of equatorial electron pitch angle distributions (PADs) in the outer radiation belt region using observations from the Magnetic Electron Ion Spectrometer (MagEIS) instrument aboard the Van Allen Probes in 2012–2019. The PADs are approximated using a sum of the first, third and fifth sine harmonics. Different combinations of the respective coefficients refer to the main PAD shapes within the outer radiation belt, namely the pancake, flat-top, butterfly and cap PADs. We conduct a superposed epoch analysis of 129 geomagnetic storms and analyze the PAD evolution for day and night MLT sectors. PAD shapes exhibit a strong energy-dependent response. At energies of tens of keV, the PADs exhibit little variation throughout geomagnetic storms. Cap PADs are mainly observed at energies<300 keV, and their extent in L shrinks with increasing energy. The cap distributions transform into the pancake PADs around the main phase of the storm on the nightside, and then come back to their original shapes during the recovery phase. At higher energies on the dayside, the PADs are mainly pancake during pre-storm conditions and become more anisotropic during the main phase. The quiet-time butterfly PADs can be observed on the nightside at L>5.6. During the main phase, butterfly PADs have stronger 90°-minima and can be observed at lower L-shells (down to L = 5), then transitioning into flat-top PADs at L ∼ 4.5 – 5 and pancake PADs at L<4.5. The resulting PAD coefficients for different energies, locations and storm epochs can be used to test the wave models and physics-based radiation belt codes in terms of pitch angle distributions.

Statistical Characteristics of Energetic Electron Pitch Angle Distributions in the Van Allen Probe Era: 1. Butterfly Distributions With Flux Peaks at Preferred Pitch Angles

AbstractWe present a statistical study on the properties of equatorial electron pitch angle distributions (PADs) in the Earth's outer radiation belt, for the first time based on particle measurements from the entire Van Allen Probes mission. A detailed selection criteria is used to identify intervals when flux measurements at energies from 0.2 to 3.4 MeV are available across a wide range of pitch angles close to the geomagnetic equatorial plane. To better characterize the shape of each pitch angle distribution, the flux data is fitted to functions of the equatorial pitch angle based on Legendre polynomials. Using this technique, we show that the shape of the PADs strongly depends on the particle's energy, location and geomagnetic activity. These results are used to identify the dominant physical processes responsible for creating PADs with different shapes. The results presented here mainly focus on the occurrence statistics and properties of butterfly PADs. Significantly, we find clear evidence that butterfly PADs have a peak flux that preferentially occurs at two distinct and discrete equatorial pitch angles, either 35° ± 5° or 65° ± 5°. Energy, L‐shell and magnetic local time variations indicate that the flux peaks at equatorial pitch angles ∼35° appear consistent with magnetopause shadowing, whilst those peaking at ∼65° may be associated with wave‐particle interactions. We also show that the flux at low and high pitch angles, for both butterfly and nonbutterfly PADs, remains remarkably well correlated even as the flux intensity varies by four orders of magnitude.

Energetic Electron Distributions Near the Magnetic Equator in the Jovian Plasma Sheet and Outer Radiation Belt Using Juno Observations

AbstractWe present the average distribution of energetic electrons in Jupiter's plasma sheet and outer radiation belt near the magnetic equator during Juno's first 29 orbits. Juno observed a clear decrease of magnetic field amplitude and enhancement of energetic electron fluxes over 0.1–1,000 keV energies when traveling through the plasma sheet. In the radiation belts, Juno observed pancake‐shaped electron distributions with high fluxes at ∼90° pitch angle and whistler‐mode waves. Our survey indicates that the statistical electron flux at each energy tends to increase from to . The equatorial pitch angle distributions are isotropic or field‐aligned in the plasma sheet and gradually become pancake‐shaped at . The electron phase space density gradients at MeV/G are relatively small at and become positive over , suggesting the dominant role of adiabatic radial transport at higher shells, and the possible loss processes at lower shells.

Equatorial Pitch Angle Distributions of 1–50 keV Electrons in Earth's Inner Magnetosphere: An Empirical Model Based on the Van Allen Probes Observations

AbstractUsing 7 years of data from the Helium, Oxygen, Proton, and Electron instrument on the Van Allen Probes, equatorial pitch angle distributions (PADs) of 1–50 keV electrons in Earth's inner magnetosphere are investigated statistically. An empirical model of electron equatorial PADs as a function of radial distance, magnetic local time, geomagnetic activity, and electron energy is constructed using the method of Legendre polynomial fitting. Model results show that most equatorial PADs of 1–10s of keV electrons in Earth's inner magnetosphere are pancake PADs, and the lack of butterfly PADs is likely due to their relatively flat or positive flux radial gradients at higher altitudes. During geomagnetically quiet times, more anisotropic distributions of 1–10s of keV electrons at dayside than nightside are observed, which could be responsible for moderate chorus wave activities at dayside during quiet times as reported by previous studies. During active times, the anisotropy of 1–10s of keV electrons significantly enhances, consistent with the enhanced chorus wave activity during active times and suggesting the critical role of 1–10s of keV electrons in generating chorus waves in Earth's inner magnetosphere. Different enhanced anisotropy patterns of different energy electrons are also observed during active times: at R > ∼4 RE, keV electrons are more anisotropic at dawn to noon, while 10s of keV electrons have larger anisotropy at midnight to dawn. These differences, combined with the statistical distribution of chorus waves shown in previous studies, suggest the differential roles of electrons with different energies in generating chorus waves with different properties.

Precipitation of Relativistic Electrons Under Resonant Interaction With Electromagnetic Ion Cyclotron Wave Packets

AbstractWe use numerical simulations to study the resonant interaction of relativistic electrons with rising‐frequency electromagnetic ion cyclotron (EMIC) wave packets in the band. We find that precipitating fluxes are formed by quasi‐linear interaction and several nonlinear interaction regimes having opposite effects. In particular, the direct influence of Lorentz force on the particle phase (force bunching) decreases precipitation for particles with low equatorial pitch angles (up to 15–25°) and can even block it completely. Four other nonlinear regimes are possible: nonlinear shift of the resonance point, which can cause pitch angle drift in both directions; phase bunching that slightly increases pitch angle for untrapped particles; directed scattering that strongly decreases pitch angle for untrapped particles; and particle trapping by the wave field that decreases pitch angle. The evolution of the equatorial pitch angle distribution during several passes of particles through the wave packet is studied. The precipitating fluxes are evaluated and compared with theoretical estimates. We show that strong diffusion limit is maintained for a certain range of energies by a wave packet with realistic amplitude and frequency drift. In this case, the quasi‐linear theory strongly underestimates the precipitating flux. With increasing energy, the precipitating fluxes decrease and become close to the quasi‐linear estimates.

An Empirical Model of Radiation Belt Electron Pitch Angle Distributions Based On Van Allen Probes Measurements

AbstractBased on over 4 years of Van Allen Probes measurements, an empirical model of radiation belt electron equatorial pitch angle distribution (PAD) is constructed. The model, developed by fitting electron PADs with Legendre polynomials, provides the statistical PADs as a function of L‐shell (L = 1–6), magnetic local time, electron energy (~30 keV to 5.2 MeV), and geomagnetic activity (represented by the Dst index) and is also the first empirical PAD model in the inner belt and slot region. For megaelectron volt electrons, model results show more significant day‐night PAD asymmetry of electrons with higher energies and during disturbed times, which is caused by geomagnetic field configuration and flux radial gradient changes. Steeper PADs with higher fluxes around 90° pitch angle and lower fluxes at lower pitch angles for higher‐energy electrons and during active times are also present, which could be due to electromagnetic ion cyclotron wave scattering. For hundreds of kiloelectron volt electrons, cap PADs are generally present in the slot region during quiet times and their energy‐dependent features are consistent with hiss wave scattering, while during active times, cap PADs are less significant especially at outer part of slot region, which could be due to the complex energizing and transport processes. The 90°‐minimum PADs are persistently present in the inner belt and appear in the slot region during active times, and minima at 90° pitch angle are more significant for electrons with higher energies, which could be a critical evidence in identifying the underlying physical processes responsible for the formation of 90°‐minimum PADs.

Reply to Comment by Nishimura Et Al.

AbstractNishimura et al. (2010, https://doi.org/10.1126/science.1193186, 2011, https://doi.org/10.1029/2011JA016876, 2013, https://doi.org/10.1029/2012JA018242, and in their comment, hereafter called N18) have suggested that chorus waves interact with equatorial electrons to produce pulsating auroras. We agree that chorus can scatter electrons >10 keV, as do Time Domain Structures (TDSs). Lower‐energy electrons occurring in pulsating auroras cannot be produced by chorus, but such electrons are scattered and accelerated by TDS. TDSs often occur with chorus and have power in their spectra at chorus frequencies. Thus, the absence of power at low frequencies is not evidence that TDSs are absent, as an example shows. Through examination of equatorial electric field waveforms and electron pitch angle distributions measured on the Time History of Events and Macroscale Interactions during Substorms satellites (in place of examining field and particle spectra, as done by Nishimura et al.), we show that chorus cannot produce the field‐aligned electrons associated with pulsating auroras in the Nishimura et al. (2010, https://doi.org/10.1126/science.1193186) events, but TDSs can. Equatorial field‐aligned electron distributions associated with pulsating auroras and created by TDS in the absence of chorus or any other wave at the equator are also shown.

Direct evidence for EMIC wave scattering of relativistic electrons in space

AbstractElectromagnetic ion cyclotron (EMIC) waves have been proposed to cause efficient losses of highly relativistic (>1 MeV) electrons via gyroresonant interactions. Simultaneous observations of EMIC waves and equatorial electron pitch angle distributions, which can be used to directly quantify the EMIC wave scattering effect, are still very limited, however. In the present study, we evaluate the effect of EMIC waves on pitch angle scattering of ultrarelativistic (>1 MeV) electrons during the main phase of a geomagnetic storm, when intense EMIC wave activity was observed in situ (in the plasma plume region with high plasma density) on both Van Allen Probes. EMIC waves captured by Time History of Events and Macroscale Interactions during Substorms (THEMIS) probes and on the ground across the Canadian Array for Real‐time Investigations of Magnetic Activity (CARISMA) are also used to infer their magnetic local time (MLT) coverage. From the observed EMIC wave spectra and local plasma parameters, we compute wave diffusion rates and model the evolution of electron pitch angle distributions. By comparing model results with local observations of pitch angle distributions, we show direct, quantitative evidence of EMIC wave‐driven relativistic electron losses in the Earth's outer radiation belt.

Test‐particle simulation of energetic electron‐H2O elastic collision along Saturn's magnetic field line around Enceladus

AbstractWe examine the variation of energetic electron pitch angle distribution at the magnetic equator and loss rate of precipitated electrons into Saturn's atmosphere through pitch angle scattering due to elastic collisions with neutral H2O along Saturn's magnetic field line around Enceladus. To examine the variation of those, we perform one‐dimensional test‐particle simulation when the co‐rotating electron flux tube passes through the dense H2O region in the vicinity of Enceladus (~6.4 min). We focus on 1 keV as a typical kinetic energy of the electrons in this study. The initial pitch angle distribution is assumed to be isotropic. Results show that the equatorial electron pitch angle distribution near the loss cone (<20° and >160°) decreases with time through pitch angle scattering due to elastic collisions. It is found that the electrons of ~11.4% to the total number of equatorial electrons at the initial condition are lost in ~380 s. The calculated loss time is twice faster than the loss time under the strong diffusion.

Observations of the inner radiation belt: CRAND and trapped solar protons

AbstractMeasurements of inner radiation belt protons have been made by the Van Allen Probes Relativistic Electron‐Proton Telescopes as a function of kinetic energy (24 to 76 MeV), equatorial pitch angle, and magnetic L shell, during late 2013 and early 2014. A probabilistic data analysis method reduces background from contamination by higher‐energy protons. Resulting proton intensities are compared to predictions of a theoretical radiation belt model. Then trapped protons originating both from cosmic ray albedo neutron decay (CRAND) and from trapping of solar protons are evident in the measured distributions. An observed double‐peaked distribution in L is attributed, based on the model comparison, to a gap in the occurrence of solar proton events during the 2007 to 2011 solar minimum. Equatorial pitch angle distributions show that trapped solar protons are confined near the magnetic equator but that CRAND protons can reach low altitudes. Narrow pitch angle distributions near the outer edge of the inner belt are characteristic of proton trapping limits.

REPAD: An empirical model of pitch angle distributions for energetic electrons in the Earth's outer radiation belt

AbstractWe have recently conducted a statistical survey on pitch angle distributions of energetic electrons trapped in the Earth's outer radiation belt, and a new empirical model was developed based upon survey results. This model—relativistic electron pitch angle distribution (REPAD)—aims to present statistical pictures of electron equatorial pitch angle distributions, instead of the absolute flux levels, as a function of energy, L shell, magnetic local time, and magnetic activity. To quantify and facilitate this statistical survey, we use Legendre polynomials to fit long‐term in situ directional fluxes observed near the magnetic equator from three missions: CRRES, Polar, and LANL‐97A. As the first of this kind of model, REPAD covers the whole outer belt region, providing not only the mean and median pitch angle distributions in the area but also error estimates of the average distributions. Preliminary verification and validation results demonstrate the reliable performance of this model. Usage of REPAD is mainly to predict the full pitch angle distribution of fluxes along a given magnetic field line, or even on a given drift shell, based upon one single unidirectional or omnidirectional flux measurement anywhere on that field line. This can be particularly useful for data assimilation, which usually has large tolerance on data errors. In addition, relatively small variations in pitch angle distributions measured at L shell between ~ 4 and 5 justify the assumption of fixed pitch angle distributions at GPS equatorial crossings (L ~ 4.2) used in our previous studies.

Characterising electron butterfly pitch angle distributions in the magnetosphere through observations and simulations

Abstract. The Imaging Electron Spectrometer (IES) on the Polar satellite has measured the average characteristics of the equatorial electron pitch angle distributions (PADs) in the midnight sector as a function of radial distance out to the 9 RE apogee of the Polar satellite. Depressions in the observed fluxes of electrons occur with pitch angles around 90° in the equatorial zone, while the more field-aligned electrons remain largely unchanged. The orbital precessions of the satellite have allowed much of the inner equatorial magnetosphere to be observed. Statistically, butterfly PADs with different shapes are observed selectively in different regions, which can provide insight to their source and possible history. Electron paths of varied pitch angles were modelled using Runge-Kutta approximations of the Lorentz force in a Tsyganenko (T96) simulated magnetosphere. The resulting drift paths suggest that the process of magnetopause shadowing plays a significant role in the loss of these electrons. Case studies of the drifting patterns of electrons with varied pitch angles were simulated from Polar's orbit when a butterfly PAD was observed on 3 October 2002 at an altitude near 9 RE and on 12 September 2000 at an altitude near 6 RE. These two locations represent regions on each side of the boundary of stable trapping. The modelling effort strongly suggests that magnetopause shadowing does play a significant role in the loss of equatorially drifting electrons from the outer regions of the inner magnetosphere.

Latitude distribution of vertically precipitating energetic neutral atoms observed at low altitudes

Earlier modeling work of the latitude distribution of earthward traveling energetic neutral atoms (ENA) originating in the ring current have suggested that an isotropic ring current with an empty loss cone will deposit most ENA away from the magnetic equator, while a ring current with an equatorial pitch angle distribution peaked at 90° will deposit most ENA at the magnetic equator. We present the first direct low altitude measurements of energetic particles at low and equatorial latitudes supporting this model. The evolution from an isotropic ring current to a more anisotropic one is manifested in the latitude distribution of the low altitude energetic particles during a geomagnetic storm. In the growth and main phase of the storm the latitude distribution of the energetic particles is wide and often show secondary peaks away from the equator, while in the recovery phase the latitude distribution narrows and peaks at the magnetic equator.

Relativistic electron drift shell splitting

A survey of equatorial outer radiation belt relativistic electron pitch angle distributions measured on the Polar satellite shows anisotropies that are consistent with the effects of drift shell splitting. Simulations based on the observed radial intensity gradients and on drift shell calculations in a magnetospheric field model show that for low geomagnetic activity levels, the measured average anisotropies are similar to those predicted. With increasing geomagnetic activity the anisotropies do not change as much as is predicted, particularly on the nightside where the pitch angle distributions have local minima in the direction perpendicular to the magnetic field. At a given location and activity level there is substantial variability in the measured anisotropies about their long‐term averages.

Initial ion equatorial pitch angle distributions from medium and high energy neutral atom images obtained by IMAGE

Examples of the extraction of equatorial ion pitch angle distributions from energetic neutral atom images taken by the HENA instrument on June 10, 2000 between 1200 and 1600 UT and MENA on August 12, 2000 at about 1000 UT on board the IMAGE satellite are presented. The extraction is performed using a method of deconvolution that expands the unknown equatorial ion pitch angle distribution in terms of tri‐cubic splines, and then finds the expansion coefficients by requiring that the result fit the data and be as smooth as possible.

Imaging a geomagnetic storm with energetic neutral atoms

The ring current during a geomagnetic storm on May 2, 1986 has been modeled using a bounce averaged kinetic equations for the phase space density of hydrogen ions, considering charge exchange and Coulomb losses along the drift path. The resulting equatorial pitch angle distribution is used to generate data simulating the medium and high energy neutral atom imagers to be flown on IMAGE. A method for deconvolving these images is described and applied to the simulated data. The results show that, when there are sufficient counts, the deconvolved distribution contains the main features of the original source and that the energy spectrum at a specific time as well as the total energy of the ring current as a function of time can be extracted from the energetic neutral atom images.