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 1-4 MeV, dangerous for satellite electronics, and represent attractors for the system dynamics in the presence of sufficiently strong driving by continuous injections of 10-300 keV 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.

A Climatology of Long-Duration High 2-MeV Electron Flux Periods in the Outer Radiation Belt

Since the advent of the Space Age, the importance of understanding and forecasting relativistic electron fluxes in the Earth's radiation belts has been steadily growing due to the threat that such particles pose to satellite electronics. Here, we provide a model of long-duration periods of high time-integrated 2-MeV electron flux deep inside the outer radiation belt, based on the significant correlation obtained in 2001-2017 between time-integrated electron flux measured by satellites and a measure of the preceding time-integrated homogenized aa H geomagnetic index. We show that this correlation is likely due to a stronger cumulative chorus wave-driven acceleration of relativistic electrons and a stronger cumulative inward radial diffusion of such electrons during periods of higher time-integrated geomagnetic activity. Return levels of 2-MeV electron flux are provided based on Extreme Value analysis of time-integrated geomagnetic activity over 1868-2017, in rough agreement with estimates based on 20-year data sets of measured flux. A high correlation is also found between our measure of time-integrated geomagnetic activity averaged over each solar cycle and averaged sunspot numbers, potentially paving the way for forecasts of time-integrated relativistic electron flux during future solar cycles based on predictions of solar activity.

Wave-particle interaction effects in the Van Allen belts

Discovering such structures as the third radiation belt (or "storage ring") has been a major observational achievement of the NASA Radiation Belt Storm Probes program (renamed the "Van Allen Probes" mission in November 2012). A goal of that program was to understand more thoroughly how high-energy electrons are accelerated deep inside the radiation belts-and ultimately lost-due to various wave-particle interactions. Van Allen Probes studies have demonstrated that electrons ranging up to 10 megaelectron volts (MeV) or more can be produced over broad regions of the outer Van Allen zone on timescales as short as a few minutes. The key to such rapid acceleration is the interaction of "seed" populations of ~ 10-200 keV electrons (and subsequently higher energies) with electromagnetic waves in the lower band (whistler-mode) chorus frequency range. Van Allen Probes data show that "source" electrons (in a typical energy range of one to a few tens of keV energy) produced by magnetospheric substorms play a crucial role in feeding free energy into the chorus waves in the outer zone. These chorus waves then, in turn, rapidly heat and accelerate the tens to hundreds of keV seed electrons injected by substorms to much higher energies. Hence, we often see that geomagnetic activity driven by strong solar storms (coronal mass ejections, or CMEs) commonly leads to ultra-relativistic electron production through the intermediary step of waves produced during intense magnetospheric substorms. More generally, wave-particle interactions are of fundamental importance over a broad range of energies and in virtually all regions of the magnetosphere. We provide a summary of many of the wave modes and particle interactions that have been studied in recent times.

From solar sneezing to killer electrons: outer radiation belt response to solar eruptions

Electrons in the outer Van Allen (radiation) belt occasionally reach relativistic energies, turning them into a potential hazard for spacecraft operating in geospace. Such electrons have secured the reputation of satellite killers and play a prominent role in space weather. The flux of these electrons can vary over time scales of years (related to the solar cycle) to minutes (related to sudden storm commencements). Electric fields and plasma waves are the main factors regulating the electron transport, acceleration and loss. Both the fields and the plasma waves are driven directly or indirectly by disturbances originating in the Sun, propagating through interplanetary space and impacting the Earth. This paper reviews our current understanding of the response of outer Van Allen belt electrons to solar eruptions and their interplanetary extensions, i.e. interplanetary coronal mass ejections and high-speed solar wind streams and the associated stream interaction regions. This article is part of the theme issue 'Solar eruptions and their space weather impact'.

Formaldehyde in the Tropical Western Pacific: Chemical sources and sinks, convective transport, and representation in CAM-Chem and the CCMI models

Formaldehyde (HCHO) directly affects the atmospheric oxidative capacity through its effects on HO_x. In remote marine environments, such as the Tropical Western Pacific (TWP), it is particularly important to understand the processes controlling the abundance of HCHO because model output from these regions is used to correct satellite retrievals of HCHO. Here, we have used observations from the CONTRAST field campaign, conducted during January and February 2014, to evaluate our understanding of the processes controlling the distribution of HCHO in the TWP as well as its representation in chemical transport/climate models. Observed HCHO mixing ratios varied from ~500 pptv near the surface to ~75 pptv in the upper troposphere. Recent convective transport of near surface HCHO and its precursors, acetaldehyde and possibly methyl hydroperoxide, increased upper tropospheric HCHO mixing ratios by ~33% (22 pptv); this air contained roughly 60% less NO than more aged air. Output from the CAM-Chem chemistry transport model (2014 meteorology) as well as nine chemistry climate models from the Chemistry-Climate Model Initiative (free-running meteorology) are found to uniformly underestimate HCHO columns derived from in situ observations by between 4 and 50%. This underestimate of HCHO likely results from a near factor of two underestimate of NO in most models, which strongly suggests errors in NO_x emissions inventories and/or in the model chemical mechanisms. Likewise, the lack of oceanic acetaldehyde emissions and potential errors in the model acetaldehyde chemistry lead to additional underestimates in modeled HCHO of up to 75 pptv (~15%) in the lower troposphere.

What effect do substorms have on the content of the radiation belts?

Substorms are fundamental and dynamic processes in the magnetosphere, converting captured solar wind magnetic energy into plasma energy. These substorms have been suggested to be a key driver of energetic electron enhancements in the outer radiation belts. Substorms inject a keV "seed" population into the inner magnetosphere which is subsequently energized through wave-particle interactions up to relativistic energies; however, the extent to which substorms enhance the radiation belts, either directly or indirectly, has never before been quantified. In this study, we examine increases and decreases in the total radiation belt electron content (TRBEC) following substorms and geomagnetically quiet intervals. Our results show that the radiation belts are inherently lossy, shown by a negative median change in TRBEC at all intervals following substorms and quiet intervals. However, there are up to 3 times as many increases in TRBEC following substorm intervals. There is a lag of 1-3 days between the substorm or quiet intervals and their greatest effect on radiation belt content, shown in the difference between the occurrence of increases and losses in TRBEC following substorms and quiet intervals, the mean change in TRBEC following substorms or quiet intervals, and the cross correlation between SuperMAG AL (SML) and TRBEC. However, there is a statistically significant effect on the occurrence of increases and decreases in TRBEC up to a lag of 6 days. Increases in radiation belt content show a significant correlation with SML and SYM-H, but decreases in the radiation belt show no apparent link with magnetospheric activity levels.

Applying the cold plasma dispersion relation to whistler mode chorus waves: EMFISIS wave measurements from the Van Allen Probes

Most theoretical wave models require the power in the wave magnetic field in order to determine the effect of chorus waves on radiation belt electrons. However, researchers typically use the cold plasma dispersion relation to approximate the magnetic wave power when only electric field data are available. In this study, the validity of using the cold plasma dispersion relation in this context is tested using Electric and Magnetic Field Instrument Suite and Integrated Science (EMFISIS) observations of both the electric and magnetic spectral intensities in the chorus wave band (0.1-0.9 fce). Results from this study indicate that the calculated wave intensity is least accurate during periods of enhanced wave activity. For observed wave intensities >10-3 nT2, using the cold plasma dispersion relation results in an underestimate of the wave intensity by a factor of 2 or greater 56% of the time over the full chorus wave band, 60% of the time for lower band chorus, and 59% of the time for upper band chorus. Hence, during active periods, empirical chorus wave models that are reliant on the cold plasma dispersion relation will underestimate chorus wave intensities to a significant degree, thus causing questionable calculation of wave-particle resonance effects on MeV electrons.

Analytic expressions for ULF wave radiation belt radial diffusion coefficients

We present analytic expressions for ULF wave-derived radiation belt radial diffusion coefficients, as a function of L and Kp, which can easily be incorporated into global radiation belt transport models. The diffusion coefficients are derived from statistical representations of ULF wave power, electric field power mapped from ground magnetometer data, and compressional magnetic field power from in situ measurements. We show that the overall electric and magnetic diffusion coefficients are to a good approximation both independent of energy. We present example 1-D radial diffusion results from simulations driven by CRRES-observed time-dependent energy spectra at the outer boundary, under the action of radial diffusion driven by the new ULF wave radial diffusion coefficients and with empirical chorus wave loss terms (as a function of energy, Kp and L). There is excellent agreement between the differential flux produced by the 1-D, Kp-driven, radial diffusion model and CRRES observations of differential electron flux at 0.976 MeV-even though the model does not include the effects of local internal acceleration sources. Our results highlight not only the importance of correct specification of radial diffusion coefficients for developing accurate models but also show significant promise for belt specification based on relatively simple models driven by solar wind parameters such as solar wind speed or geomagnetic indices such as Kp.

KEY POINTS

Analytic expressions for the radial diffusion coefficients are presentedThe coefficients do not dependent on energy or wave m valueThe electric field diffusion coefficient dominates over the magnetic.