Simulating the Earth’s radiation belts: internal acceleration and continuous losses to the magnetopause

In the Earth's radiation belts the flux of relativistic electrons is highly variable, sometimes changing by orders of magnitude within a few hours. Since energetic electrons can damage satellites it is important to understand the processes driving these changes and, ultimately, to develop forecasts of the energetic electron population. One approach is to use 3-dimensional diffusion models, based on a Fokker-Planck equation. Here we describe a model where the phase-space density is set to zero at the outer L* boundary, simulating losses to the magnetopause, using recently published chorus diffusion coefficients for 1.5 ≤ L* ≤ 10. The value of the phase-space density on the minimum energy boundary is determined from a recently published, solar wind dependent, statistical model. Our simulations show that an outer radiation belt can be created by local acceleration of electrons from a very soft energy spectrum without the need for a source of electrons from inward radial transport. The location in L* of the peaks in flux for these steady state simulations is energy dependent and moves Earthward with increasing energy. Comparisons between the model and data from the CRRES satellite are shown; flux drop-outs are reproduced in the model by the increased outward radial diffusion that occurs during storms. Including the inward movement of the magnetopause in the model has little additional effect on the results. Finally, the location of the low energy boundary is shown to be important for accurate modelling of observations

Quasi-linear simulations of inner radiation belt electron pitch angle and energy distributions

“Peculiar” or “butterfly” electron pitch angle distributions (PADs), with minima near 90°, have recently been observed in the inner radiation belt. These electrons are traditionally treated by pure pitch angle diffusion, driven by plasmaspheric hiss, lightning-generated whistlers, and VLF transmitter signals. Since this leads to monotonic PADs, energy diffusion by magnetosonic waves has been proposed to account for the observations. We show that the observed PADs arise readily from two-dimensional diffusion at L = 2, with or without magnetosonic waves. It is necessary to include cross diffusion, which accounts for the relationship between pitch angle and energy changes. The distribution of flux with energy is also in good agreement with observations between 200 keV and 1 MeV, dropping to very low levels at higher energy. Thus, at this location radial diffusion may be negligible at subrelativistic as well as ultrarelativistic energy

The origin of Jupiter's outer radiation belt

The intense inner radiation belt at Jupiter (>50 MeV at 1.5 RJ) is generally accepted to be created by radial diffusion of electrons from further away from the planet. However, this requires a source with energies that exceed 1 MeV outside the orbit of the moon Io at 5.9 RJ, which has never been explained satisfactorily. Here we test the hypothesis that this source population could be formed from a very soft energy spectrum, by particle injection processes and resonant electron acceleration via whistler mode chorus waves. We use the British Antarctic Survey Radiation Belt Model to calculate the change in the electron flux between 6.5 and 15 RJ; these are the first simulations at Jupiter combining wave particle interactions and radial diffusion. The resulting electron flux at 100 keV and 1 MeV lies very close to the Galileo Interim Radiation Electron model spectrum after 1 and 10 days, respectively. The primary driver for the increase in the flux is cyclotron resonant acceleration by chorus waves. A peak in phase space density forms such that inside L≈9 radial diffusion transports electrons toward Jupiter, but outside L≈9 radial diffusion acts away from the planet. The results are insensitive to the softness of the initial energy spectrum but do depend on the value of the flux at the minimum energy boundary. We conclude by suggesting that the source population for the inner radiation belt at Jupiter could indeed be formed by wave-particle interactions

Effects of VLF transmitter waves on the inner belt and slot region

Signals from very low frequency (VLF) transmitters can leak from the Earth‐ionosphere wave guide into the inner magnetosphere, where they propagate in the whistler mode and contribute to electron dynamics in the inner radiation belt and slot region. Observations show that the waves from each VLF transmitter are highly localized, peaking on the nightside in the vicinity of the transmitter. In this study we use ∼5 years of Van Allen Probes observations to construct global statistical models of the bounce‐averaged pitch angle diffusion coefficients for each individual VLF transmitter, as a function of L*, magnetic local time (MLT), and geographic longitude. We construct a 1‐D pitch angle diffusion model with implicit longitude and MLT dependence to show that VLF transmitter waves weakly scatter electrons into the drift loss cone. We find that global averages of the wave power, determined by averaging the wave power over MLT and longitude, capture the long‐term dynamics of the loss process, despite the highly localized nature of the waves in space. We use our new model to assess the role of VLF transmitter waves, hiss waves, and Coulomb collisions on electron loss in the inner radiation belt and slot region. At moderate relativistic energies, E∼500 keV, waves from VLF transmitters reduce electron lifetimes by an order of magnitude or more, down to the order of 200 days near the outer edge of the inner radiation belt. However, VLF transmitter waves are ineffective at removing multi–megaelectron volt electrons from either the inner radiation belt or slot region

A simple technique for flat osmicating and flat embedding of immunolabelled vibratome sections of the rat spinal cord for light and electron microscopy

We describe here a simple technique for flat-osmicating and flat-embedding of immunolabelled vibratome sections. The technique is particularly useful for large specimens such as whole cross-sections of rat spinal cord. After the vibratome section has been flat-osmicated on a flat surface under a glass cover slip, it is dehydrated and then embedded by placing it in a small drop of epoxy resin on a flat base of polypropylene plastic and overlaying a small square piece of cellulose acetate cut from heat-resistant overhead projector transparency film for photocopying. The thin layer of resin containing the flat-embedded vibratome section is then separated from the base and glued onto the flat end of a pre-polymerised blank block of resin. The method produces flat-embedded vibratome sections and thus allows serial large uniformly labelled semithin and ultrathin sections to be obtained of the whole cross-section of the rat spinal cord. This facilitates the observation and quantification of labelled cells in the specimen. Because of its simplicity the technique also allows one worker to process more than 100 vibratome sections at the one time

Electron losses from the radiation belts caused by EMIC waves

Electromagnetic 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 - 18 MLT. To determine the electron loss EMIC diffusion rates were included in the BAS 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

A 30-year simulation of the outer electron radiation belt

As society becomes more reliant on satellite technology, it is becoming increasingly important to understand the radiation environment throughout the Van Allen radiation belts. Historically most satellites have operated in low Earth orbit or geostationary orbit (GEO), but there are now over 100 satellites in medium Earth orbit (MEO). Additionally, satellites using electric orbit raising to reach GEO may spend hundreds of days on orbits that pass through the heart of the radiation belts. There is little long‐term data on the high‐energy electron flux, responsible for internal charging in satellites, available for MEO. Here we simulate the electron flux between the outer edge of the inner belt and GEO for 30 years. We present a method that converts the >2‐MeV flux measured at GEO by the Geostationary Operational Environmental Satellites spacecraft into a differential flux spectrum to provide an outer boundary condition. The resulting simulation is validated using independent measurements made by the Galileo In‐Orbit Validation Element‐B spacecraft; correlation coefficients are in the range 0.72 to 0.88, and skill scores are between 0.6 and 0.8 for a range of L∗ and energies. The results show a clear solar cycle variation and filling of the slot region during active conditions and that the worst case spectrum overlaps that derived independently for the limiting extreme event. The simulation provides a resource that can be used by satellite designers to understand the MEO environment, by space insurers to help resolve the cause of anomalies and by satellite operators to plan for the environmental extremes

Electron acceleration at Jupiter: input from cyclotron-resonant interaction with whistler-mode chorus waves

Jupiter has the most intense radiation belts of all the outer planets. It is not yet known how electrons can be accelerated to energies of 10 MeV or more. It has been suggested that cyclotron-resonant wave-particle interactions by chorus waves could accelerate electrons to a few MeV near the orbit of Io. Here we use the chorus wave intensities observed by the Galileo spacecraft to calculate the changes in electron flux as a result of pitch angle and energy diffusion. We show that, when the bandwidth of the waves and its variation with L are taken into account, pitch angle and energy diffusion due to chorus waves is a factor of 8 larger at L-shells greater than 10 than previously shown. We have used the latitudinal wave intensity profile from Galileo data to model the time evolution of the electron flux using the British Antarctic Survey Radiation Belt (BAS) model. This profile confines intense chorus waves near the magnetic equator with a peak intensity at ∼5° latitude. Electron fluxes in the BAS model increase by an order of magnitude for energies around 3 MeV. Extending our results to L = 14 shows that cyclotron-resonant interactions with chorus waves are equally important for electron acceleration beyond L = 10. These results suggest that there is significant electron acceleration by cyclotron-resonant interactions at Jupiter contributing to the creation of Jupiter's radiation belts and also increasing the range of L-shells over which this mechanism should be considered

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 3,536 power spectra for upper and lower band chorus for 1.5 ≤ L∗ ≤ 10, MLT, magnetic latitude 0o ≤ |λm| ≤ 60o 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 09:00 MLT. Energy diffusion extends to a few MeV at large pitch angles > 60o and at high energies exceeds pitch angle diffusion at the loss cone. Most electron diffusion occurs close to the geomagnetic equator (< 12o). Pitch angle diffusion rates for lower band chorus increase with L∗ and are significant at L∗ = 8 even for low levels of geomagnetic activitywhile 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 keV near the loss cone up to several MeV at large pitch angles indicating loss at low energies and net acceleration at high energies

Quantifying hiss-driven energetic electron precipitation: A detailed conjunction event analysis

Abstract We analyze a conjunction event between the Van Allen Probes and the low-altitude Polar Orbiting Environmental Satellite (POES) to quantify hiss-driven energetic electron precipitation. A physics-based technique based on quasi-linear diffusion theory is used to estimate the ratio of precipitated and trapped electron fluxes (R), which could be measured by the two-directional POES particle detectors, using wave and plasma parameters observed by the Van Allen Probes. The remarkable agreement between modeling and observations suggests that this technique is applicable for quantifying hiss-driven electron scattering near the bounce loss cone. More importantly, R in the 100-300 keV energy channel measured by multiple POES satellites over a broad L magnetic local time region can potentially provide the spatiotemporal evolution of global hiss wave intensity, which is essential in evaluating radiation belt electron dynamics, but cannot be obtained by in situ equatorial satellites alone. Key Points Measured and calculated hiss Bw from POES electron measurements agree well Electron ratio measured by POES is able to estimate hiss wave intensity This technique can be used to provide global hiss wave distributio