Pitch Angle Diffusion Research Articles

Models of Resonant Wave‐Particle Interactions

AbstractRadiation belt electrons are strongly affected by resonant interactions with cyclotron‐resonant waves. For broad band, small amplitude waves the interactions are well described by quasi‐linear diffusion in pitch angle and energy, but coherent, large amplitude waves such as strong whistler mode chorus call for a different treatment. The standard nonlinear framework reduces the problem to that of a classical pendulum. This picture has generally been confirmed by many numerical simulations, but recent studies have uncovered additional, complex behavior, not captured by the pendulum model, for particles with low pitch angle. We show that avoiding a commonly made approximation leads to a more general but still tractable “second fundamental model” Hamiltonian, which involves not one but two regions of phase trapping. We analyze its phase portraits in detail, and perform representative test particle simulations with slowly changing parameters. We find that the trajectories encompass traditional phase bunching and phase trapping as well as additional behavior best understood using the new model.

Empirical Loss Timescales of Slot Region Electrons due to Plasmaspheric Hiss Based on Van Allen Probes Observations

AbstractBased on Van Allen Probes observations, in this study we perform a statistical analysis of the spectral intensities of plasmaspheric hiss at L‐shells of 1.8–3.0 in the slot region. Our results show that slot region hiss power intensifies with a strong day‐night asymmetry as the level of substorm activity or L‐shell increases. Using the statistical spectral profiles of plasmaspheric hiss, we calculate the drift‐ and bounce‐averaged electron pitch angle diffusion coefficients and subsequently obtain the resultant electron loss timescales through 1‐D Fokker‐Planck simulations. We find that slot region electron loss timescales vary significantly from <1 day to several years, showing a strong dependence on electron energy, L‐shell and substorm activity. We also construct an empirical model of slot region electron loss timescales due to scattering by plasmaspheric hiss, which agrees well with the 1‐D simulation results and can be readily used in modeling the dynamics of slot region electrons.

Comparing Electron Precipitation Fluxes Calculated From Pitch Angle Diffusion Coefficients to LEO Satellite Observations

AbstractParticle precipitation is a loss mechanism from the radiation belts whereby particles trapped by the Earth's magnetic field are scattered into the loss cone due to wave‐particle interactions. Energetic electron precipitation creates ozone destroying chemicals which can affect the temperatures of the polar regions, therefore it is crucial to accurately quantify this impact on the Earth's atmosphere. We use bounce‐averaged pitch angle diffusion coefficients for whistler mode chorus waves, plasmaspheric hiss and atmospheric collisions to calculate magnetic local time (MLT) dependent electron precipitation inside the field of view of the Polar Orbiting Environmental Satellites (POES) T0 detector, between 26–30 March 2013. These diffusion coefficients are used in the BAS Radiation Belt Model (BAS‐RBM) and this paper is a first step toward testing the loss in this model via comparison with real world data. We find the best agreement between the calculated and measured T0 precipitation at L* > 5 on the dawnside for the >30 keV electron channel, consistent with precipitation driven by lower band chorus. Additional diffusion is required to explain the flux at higher energies and on the dusk side. The POES T0 detector underestimates electron precipitation as its field of view does not measure the entire loss cone. We demonstrate the potential for utilizing diffusion coefficients to reconstruct precipitating flux over the entire loss cone. Our results show that the total precipitation can exceed that measured by the POES >30 keV electron channel by a factor that typically varies from 1 to 10 for L* = 6, 6.5, and 7.

Reconstruction of the Radiation Belts for Solar Cycles 17–24 (1933–2017)

AbstractWe present a reconstruction of the dynamics of the radiation belts from solar cycles 17 to 24 which allows us to study how radiation belt activity has varied between the different solar cycles. The radiation belt simulations are produced using the Versatile Electron Radiation Belt (VERB)‐3D code. The VERB‐3D code simulations incorporate radial, energy, and pitch angle diffusion to reproduce the radiation belts. Our simulations use the historical measurements of Kp (available since solar cycle 17, i.e., 1933) to model the evolution radiation belt dynamics between L* = 1–6.6. A nonlinear auto regressive network with exogenous inputs (NARX) neural network was trained off GOES 15 measurements (January 2011–March 2014) and used to supply the upper boundary condition (L* = 6.6) over the course of solar cycles 17–24 (i.e., 1933–2017). Comparison of the model with long term observations of the Van Allen Probes and CRRES demonstrates that our model, driven by the NARX boundary, can reconstruct the general evolution of the radiation belt fluxes. Solar cycle 24 (January 2008–2017) has been the least active of the considered solar cycles which resulted in unusually low electron fluxes. Our results show that solar cycle 24 should not be used as a representative solar cycle for developing long term environment models. The developed reconstruction of fluxes can be used to develop or improve empirical models of the radiation belts.

Ring Current Proton Dynamics Driven by Wave-Particle Interactions During a Nonstorm Period

Modeling of pitch angle scattering of ring current protons at interaction with electromagnetic ion cyclotron waves during a nonstorm period was considered very seldom. Therefore it is used correlated observation of enhanced electromagnetic ion cyclotron (EMIC) waves and dynamic evolution of ring current proton flux collected by Cluster satellite near the location L = 4.5 during March 26–27, 2003, a nonstorm period (Dst > –10 nT). Energetic (5–30 keV) proton fluxes are found to drop rapidly (e.g., a half hour) at lower pitch angles, corresponding to intensified EMIC wave activities. As mathematical model is used the non-stationary one-dimensional pitch angle diffusion equation which allows to compute numerically density of phase space or pitch angle distribution of the charged particles in the Earth’s magnetosphere. The model depends on time t, a local pitch angle and several parameters (the mass of a particle, the energy, the McIlwain parameter, the magnetic local time or geomagnetic eastern longitude, the geomagnetic activity index, parameter of the charged particle pitch angle distribution taken for the 90 degrees pitch angle at t = 0, the lifetime due to wave–particle interactions). This model allows numerically to estimate also for different geophysical conditions a lifetime due to wave–particle interactions. It is shown, that EMIC waves can yield decrements in proton flux within 30 minutes, consistent with the observational data. The good consent is received. Comparison of results on full model for the pitch angle range from 0 up to 180 degrees and on the model for the 90 degrees pitch angle is lead. For a perpendicular differential flux of the Earth’s ring current protons very good consent with the maximal relative error approximately 3.23 % is received

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.

Scattering by whistler-mode waves during a quiet period perturbed by substorm activity

We study the dynamics of radiation belt electrons during a 10-day quiet period perturbed by substorm activity and preceding a high-speed stream (HSS), aiming at a global description of the radiation belts in L-shell, L in [2, 6], and energy [0.1, 10] MeV. We combine Van Allen Probes observations and Fokker-Planck numerical simulations of pitch-angle diffusion. The Fokker-Planck model uses event-driven pitch angle diffusion coefficients from whistler-mode waves, built from the wave properties and the ambient plasma density measurements from the Van Allen Probes. We first find this event has some similar characteristics to regular quiet times previously studied; a widely extended plasmasphere within which we observe strong and varying whistler-mode waves. These ambient conditions lead to strong pitch-angle scattering, which contributes to the creation of a wide slot region as well as a significant decay of the outer radiation belts, which are observed and qualitatively well simulated. In addition, we find the substorm activity causes short duration (within ± 4h) decay of the plasma density and a lowering amplitude of the whistler-mode waves within the plasmasphere, both causing opposite effects in terms of pitch angle diffusion. This leads to a diminution of pitch-angle diffusion at the time of the main substorm activity. Conversely, whistler-mode waves become enhanced in the time periods between the substorm injections. All effects cumulated, we find an enhancement of pitch angle diffusion by whistler-mode waves above L~4.7 during the 10-day period. This directly relates to the combination of quietness and substorm activity which allows pitch angle diffusing of up to 1 MeV electrons in the outer belt. Relativistic electrons of 1–2 MeV remain trapped in the outer belt, from L~4.7 to L~5.2, forming, in both the observations and the simulations, a distinct pocket of remnant electrons.

Modeling the Transport of Nonthermal Particles in Flares Using Fokker–Planck Kinetic Theory

Abstract We describe a new approach for modeling the transport of high-energy particles accelerated during flares from the acceleration region in the solar corona until their eventual thermalization in the flare footpoint. Our technique numerically solves the Fokker–Planck equation and includes forces corresponding to Coulomb collisions in a flux loop with nonuniform ionization, synchrotron emission reaction, magnetic mirroring, and a return current electric field. Our solution to the Fokker–Planck equation includes second-order pitch angle and momentum diffusion. It is applicable to particles of arbitrary mass and charge. By tracking the collisions, we predict the bremsstrahlung produced as these particles interact with the ambient stellar atmosphere. This can be compared directly with observations and used to constrain the accelerated particle energy distribution. We have named our numerical code FP and distributed it for general use. We demonstrate its effectiveness in several test cases.

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.

Effects of Polarization Reversal on the Pitch Angle Scattering of Radiation Belt Electrons and Ring Current Protons by EMIC Waves

AbstractIn this study, we investigate the effects of polarization reversal of electromagnetic ion cyclotron (EMIC) waves at the crossover frequencies on computations of bounce‐averaged pitch angle diffusion coefficients of radiation belt electrons and ring current protons. We find that inclusion of polarization reversal can cause significant changes of H+ band‐induced particle diffusion coefficients, while scattering by the He+ band is almost unaffected. Our results show that the pure L‐mode approach, which has been widely implemented in previous studies, tends to underestimate the diffusion coefficients of ultrarelativistic (>4 MeV) electrons and overestimate those of 10–50 and >100 keV protons caused by H+ band EMIC waves. Especially for >100 keV protons, the differences in diffusion coefficients can be larger by an order of magnitude. We confirm that the polarization reversal can contribute importantly to the scattering loss of radiation belt electrons and ring current protons by H+ band EMIC waves.

How whistler mode hiss waves and the plasmasphere drive the quiet decay of radiation belts electrons following a geomagnetic storm

We show how an extended period of quiet solar wind conditions contributes to a quiet state of the plasmasphere that expands up to L ∼ 5.5, which creates the perfect conditions for wave-particle interactions between the radiation belt electrons and whistler-mode hiss waves. The correlation between the hiss waves and the plasma density is direct with hiss wave power increasing with plasma density, while it was generally assumed that these quantities can be specified independently. Whistler-mode hiss waves pitch angle diffuse and ultimately scatter freshly injected electrons into the atmosphere until the slot region is formed between the inner and outer belt and the outer belt is drastically reduced. In this study, we use and combine Van Allen Probes observations and Fokker-Planck numerical simulations. The Fokker-Planck model uses consistent event-driven pitch angle diffusion coefficients from whistler-mode hiss waves. Observations and simulations allow us to reach a global understanding of the variations in the trapped electron population with time, space, energy, and pitch angle that is based on the existing theory of quasi-linear wave-particle interactions. We show, for instance, the outer belt is pitch-angle homogeneous, which is explained by the event-driven diffusion coefficients that are roughly constant for equatorial pitch angle α 0∼<60°, E>100 keV, 3.5<L<Lpp∼6. The impact of this work is to bring an improved understanding of the belt evolution based on the integration of high quality and highly temporally and spatially resolved measurements that are integrated in modern computations. We also propose the event-driven method as an accurate method (within ×2) to predict the electron flux decay after storms.

POES/MEPED Angular Response Functions and the Precipitating Radiation Belt Electron Flux

AbstractAngular response functions are derived for four electron channels and six proton channels of the SEM‐2 MEPED particle telescopes on the POES and MetOp satellites from Geant4 simulations previously used to derive the energy response. They are combined with model electron distributions in energy and pitch angle to show that the vertical 0° telescope, intended to measure precipitating electrons, instead usually measures trapped or quasi‐trapped electrons, except during times of enhanced pitch angle diffusion. A simplified dynamical model of the radiation belt electron distribution near the loss cone, as a function of longitude, energy, and pitch angle, that accounts for pitch angle diffusion, azimuthal drift, and atmospheric backscatter is fit to sample MEPED electron data at L = 4 during times of differing diffusion rates. It is then used to compute precipitating electron flux, as function of energy and longitude, that is lower than would be estimated by assuming that the 0° telescope always measures precipitating electrons.

Perpendicular diffusion of solar energetic particles: When is the diffusion approximation valid?

Multi-spacecraft observations of widespread solar energetic particle (SEP) events indicate that perpendicular (to the mean field) diffusion is an important SEP transport mechanism. However, this is in direct contrast to so-called spike and drop-out events, which indicate very little lateral transport. To better understand these seemingly incongruous observations, we discuss the recent progress made towards understanding and implementing perpendicular diffusion in transport models of SEP electrons. This includes a re-derivation of the relevant focused transport equation, a discussion surrounding the correct form of the pitch-angle dependent perpendicular diffusion coefficient and what turbulence quantities are needed as input, and how models lead to degenerate solutions of the particle intensity. Lastly, we evaluate the validity of a diffusion approach to SEP transport and conclude that it is valid when examining a large number of (an ensemble of) events, but that individual SEP events may exhibit coherent structures related to the magnetic field turbulence at short timescales that cannot be accounted for in this modelling approach.

Ionospheric Signatures of Ring Current Ions Scattered by Magnetosonic Waves

AbstractIn this letter, we present unique conjugated satellite observations of ionospheric signatures of ring current (RC) ions scattered by fast magnetosonic (MS) waves. In the plasmasphere, the Van Allen Probe in situ observed MS waves. At ionospheric altitudes, the NOAA 16 satellite at the footprint of Van Allen Probe simultaneously observed obvious enhancements of mirroring RC ions, but no obvious variations of precipitating RC ions at subauroral latitudes. Theoretical calculations of pitch angle diffusion coefficients for RC ions confirm that observed MS waves can lead to flux enhancements only for mirroring but not for precipitating RC ions, which is in agreement with the observations of NOAA 16. Our result provides a direct link between in situ inner magnetospheric observations of MS waves and conjugated ionospheric observations of flux enhancements for mirroring RC ions caused by MS waves so as to reveal the ionospheric signature of RC ions scattered by MS waves.

Whistler Mode Waves in the Compressional Boundary of Foreshock Transients

AbstractEarth's foreshock is filled with backstreaming particles that can generate a variety of waves and foreshock transients. According to recent studies, these particles can be further accelerated while being scattered by field fluctuations, including waves, inside foreshock transients, contributing to particle acceleration at the parent bow shock. The properties of these waves and how they interact with particles and affect particle acceleration inside foreshock transients are still unclear, however. Here we take the first step to study one important type of these waves, whistler waves. We use Time History of Events and Macroscale Interactions during Substorms (THEMIS) observations and employ multiple case studies to investigate the properties of whistler waves in the compressional boundaries of foreshock transients where THEMIS wave burst mode is triggered. We show that the whistler waves are quasi parallel propagating with bidirectional Poynting vectors, suggesting that they are locally generated. We focus on how they interact with electrons. We show that the diffusion surfaces for these waves in the electron velocity space match the observed electron phase space density distribution contours better when the modeled pitch angle diffusion coefficients from these waves are higher. We also demonstrate that higher‐energy electrons are more likely to be scattered by whistler waves. Our results suggest that whistler waves are important for scattering tens to hundreds of electronvolt electrons inside foreshock transients and elucidate electron dynamics and whistler wave properties in such environments.

Hot Plasma Effects on the Pitch-angle Scattering Rates of Radiation Belt Electrons Due to Plasmaspheric Hiss

Abstract Plasmaspheric hiss is known to be a major contributor to the dynamic losses of Earth’s radiation belt electrons. While previous computation attempts of hiss-driven electron losses are limited to the cold plasma approximation, in this study we find that hot plasma effects will modify the hiss dispersion relation and result in changes in the electron bounce-averaged electron pitch angle diffusion coefficients. Cold plasma approximation tends to overestimate the diffusion coefficients of ≲100 keV electrons by orders of magnitude, while the scattering efficiency of higher energy electrons is not greatly affected. As the L-shell decreases or the parameter decreases (where is the electron gyrofrequency and is the plasma frequency), the decrease of diffusion coefficients of low energy electrons caused by hot plasma effects become more pronounced. It is also shown that both the increase of hot electron abundance and temperature anisotropy can weaken the scattering efficiency of ≲100 keV electrons at almost all pitch angles, while the diffusion coefficients of higher energy electrons decrease at large pitch angles. Our study confirms the importance of including hot plasma effects in evaluations of hiss-driven scattering loss of radiation belt electrons.

Localized Heating of the Martian Topside Ionosphere Through the Combined Effects of Magnetic Pumping by Large‐Scale Magnetosonic Waves and Pitch Angle Diffusion by Whistler Waves

AbstractWe present Mars Atmosphere and Volatile EvolutioN (MAVEN) observations of periodic ( 25 s) large‐scale (hundreds of km) magnetosonic waves propagating into the Martian dayside upper ionosphere. These waves adiabatically modulate the superthermal electron distribution function, and the induced electron temperature anisotropies drive the generation of observed electromagnetic whistler waves. The localized (in altitude) minimum in the ratio pe/ ce provides conditions favorable for the local enhancement of efficient wave‐particle interactions, so that the induced whistlers act back on the superthermal electron population to isotropize the plasma through pitch angle scattering. These wave‐particle interactions break the adiabaticity of the large‐scale magnetosonic wave compressions, leading to local heating of the superthermal electrons during compressive wave “troughs.” Further evidence of this heating is observed as the subsequent phase shift between the observed perpendicular‐to‐parallel superthermal electron temperatures and compressive wave fronts. This heating mechanism may be important at other unmagnetized bodies.

ULF modulation of energetic electron precipitation observed by VLF/LF radio propagation

We investigated the modulation of D-region signatures due to ultra-low-frequency (ULF) waves using very-low-frequency/low-frequency (VLF/LF) radio propagation. Three transmitters from the United States (NLK, NDK, and WWVB) were received at Athabasca (ATHA), Canada. We observed oscillations in intensities and phases on the NDK-ATHA and WWVB-ATHA paths with a period of 3 to 4 minutes, associated with ULF waves during a substorm at 05:25–05:45 UT on 4 June, 2017. This is the first observational report showing clear VLF/LF oscillations in the ULF range. The ground-based H-component magnetic-field variations and Doppler velocity observed by the SuperDARN HF radars showed the same periodic changes as seen in the VLF/LF oscillations, suggesting that energetic electron precipitation (EEP) over the WWVB-ATHA and NDK-ATHA paths was modulated by the ULF waves. Based on ground-based magnetic-field data, we concluded that the ULF wave corresponded to the Pi2 pulsations associated with the substorm, because the propagation direction of the wave was westward (66.4 km/s) from the pre-midnight sector, the magnetic variations at low latitudes were inphase over wide longitudes, and the magnetic variations at ATHA slightly preceded those at low latitudes. A rising-tone chorus emission was observed in the frequency range of 5 kHz to 6 kHz at ATHA during the VLF/LF oscillations. Pitch-angle diffusion by the whistler-mode chorus wave is one possible mechanism accounting for the energetic electron precipitation.

On Energetic Electron Dynamics During Geomagnetic Quiet Times in Earth's Inner Radiation Belt due to Atmospheric Collisional Loss and CRAND as a Source

AbstractTo investigate the role of atmospheric collisions and cosmic ray albedo neutron decay (CRAND) in the dynamics of energetic electrons in the Earth's inner radiation belt during geomagnetic quiet times, a drift‐collision‐source model that includes azimuthal drift, pitch angle diffusion from elastic collision, energy loss from inelastic collision, and a CRAND source is developed. In the model, the bounce‐averaged pitch angle diffusion coefficients and energy loss rates are calculated based on scattering of electrons with neutrals given by the NRLMSISE‐00 model and with ions and electrons given by International Reference Ionosphere (IRI) 2012 model. The electron source rate from CRAND follows the recently developed drift‐source model in Xiang et al. (2019). For 304‐keV quasi‐trapped electrons at L = 1.25, simulation results with CRAND show good agreement with Detection of Electro‐Magnetic Emissions Transmitted from Earthquake Regions satellite observations, confirming that CRAND is the main source for these quasi‐trapped electrons, in contrast to the previous understanding that these quasi‐trapped electrons were formed by wide‐angle scattering of the trapped populations. For trapped electrons, 153, 304, and 509 keV at L &lt; 1.3, the simulation results with only azimuthal drift and atmospheric collisions show a much quicker decrease than observations, while simulation results including a CRAND source are generally comparable to the observations, suggesting that CRAND is an important source of trapped hundreds of kiloelectron‐volt electrons at L &lt; 1.3 during quiet times and provides a baseline for the electron flux even during active times as well. Furthermore, these results suggest that actual radial diffusion rates in the inner belt are lower than previous estimates in which CRAND contributions were not considered.