Sarah A. Glauert

Wave acceleration of electrons in the Van Allen radiation belts

The Van Allen radiation belts are two regions encircling the Earth in which energetic charged particles are trapped inside the Earths magnetic field. Their properties vary according to solar activity and they represent a hazard to satellites and humans in space. An important challenge has been to explain how the charged particles within these belts are accelerated to very high energies of several million electron volts. Here we show, on the basis of the analysis of a rare event where the outer radiation belt was depleted and then re-formed closer to the Earth, that the long established theory of acceleration by radial diffusion is inadequate; the electrons are accelerated more effectively by electromagnetic waves at frequencies of a few kilohertz. Wave acceleration can increase the electron flux by more than three orders of magnitude over the observed timescale of one to two days, more than sufficient to explain the new radiation belt. Wave acceleration could also be important for Jupiter, Saturn and other astrophysical objects with magnetic fields.

Resonant diffusion of radiation belt electrons by whistler-mode chorus

We present the first relativistic electron pitch-angle and momentum diffusion rates for scattering by whistler-mode waves in the low density regieme. Diffusion rates are strongly dependent on the ratio between the electron plasma and gyro-frequencies ωpe/Ωe. For conditions typical of storm times, diffusion rates at a few MeV increase by more than 3 orders of magnitude as ωpe/Ωe is reduced from 10 to 1.5. Diffusion rates are extremely sensitive to energy and become ineffective above 3 MeV. At energies below 100 keV pitch-angle diffusion approaches strong diffusion loss to the atmosphere, while loss at higher energies is much weaker. For storm-time whistler-mode chorus amplitudes near 100 pT, and ωpe/Ωe ≤ 2.5, acceleration timescales can be less than a day at 1 MeV. This indicates that chorus diffusion could provide an important mechanism for local acceleration during the recovery phase of storms outside the plasmapause.

Energetic Outer Zone Electron Loss Timescales During Low Geomagnetic Activity

Following enhanced magnetic activity the fluxes of energetic electrons in the Earths outer radiation belt gradually decay to quiet-time levels. We use CRRES observations to estimate the energetic electron loss timescales and to identify the principal loss mechanisms. Gradual loss of energetic electrons in the region 3.0 ≤ L ≤ 5.0 occurs during quiet periods (Kp 7), indicating that the decay takes place in the plasmasphere. We compute loss timescales for pitch-angle scattering by plasmaspheric hiss using the PADIE code with wave properties based on CRRES observations. The resulting timescales suggest that pitch angle scattering by plasmaspheric hiss propagating at small or intermediate wave normal angles is responsible for electron loss over a wide range of energies and L shells. The region where hiss dominates loss is energy-dependent, ranging from 3.5 ≤ L ≤ 5.0 at 214 keV to 3.0 ≤ L ≤ 4.0 at 1.09 MeV. Plasmaspheric hiss at large wave normal angles does not contribute significantly to the loss rates. At E = 1.09 MeV the loss timescales are overestimated by a factor of ∼5 for 4.5 ≤ L ≤ 5.0. We suggest that resonant wave-particle interactions with EMIC waves, which become important at MeV energies for larger L (L > ∼4.5), may play a significant role in this region.

Acceleration mechanism responsible for the formation of the new radiation belt during the 2003 Halloween solar storm

Observations of the relativistic electron flux increases during the first days of November, 2003 are compared to model simulations of two leading mechanisms for electron acceleration. It is demonstrated that radial diffusion driven by ULF waves cannot explain the formation of the new radiation belt in the slot region and instead predicts a decay of fluxes during the recovery phase of the October 31st storm. Compression of the plasmasphere during the main phases of the storm created preferential conditions for local acceleration during interactions with VLF chorus. Local acceleration of electrons at L = 3 is modelled with a 2-D pitch-angle, energy diffusion code. We show that the energy diffusion driven by whistler mode waves can explain the gradual build up of fluxes to energies exceeding 3 MeV in a new radiation belt which is formed in the slot region normally devoid of high energy electrons.

Three-dimensional electron radiation belt simulations using the BAS Radiation Belt Model with new diffusion models for chorus, plasmaspheric hiss, and lightning-generated whistlers

The flux of relativistic electrons in the Earths radiation belts is highly variable and can change by orders of magnitude on timescales of a few hours. Understanding the drivers for these changes is important as energetic electrons can damage satellites. We present results from a new code, the British Antarctic Survey (BAS) Radiation Belt model, which solves a 3-D Fokker-Planck equation, following a similar approach to the Versatile Electron Radiation Belt (VERB) code, incorporating the effects of radial diffusion, wave-particle interactions, and collisions. Whistler mode chorus waves, plasmaspheric hiss, and lightning-generated whistlers (LGW) are modeled using new diffusion coefficients, calculated by the Pitch Angle and Energy Diffusion of Ions and Electrons (PADIE) code, with new wave models based on satellite data that have been parameterized by both the AE and Kp indices. The model for plasmaspheric hiss and LGW includes variation in the wave-normal angle distribution of the waves with latitude. Simulations of 100 days from the CRRES mission demonstrate that the inclusion of chorus waves in the model is needed to reproduce the observed increase in MeV flux during disturbed conditions. The model reproduces the variation of the radiation belts best when AE, rather than Kp, is used to determine the diffusion rates. Losses due to plasmaspheric hiss depend critically on the the wave-normal angle distribution; a model where the peak of the wave-normal angle distribution depends on latitude best reproduces the observed decay rates. Higher frequency waves (∼1–2 kHz) only make a significant contribution to losses for L∗<3 and the highest frequencies (2–5 kHz), representing LGW, have a limited effect on MeV electrons for 2

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 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.

Interaction of Emic Waves With Thermal Plasma and Radiation Belt Particles

Electromagnetic ion cyclotron (EMIC) waves are excited during the enhanced convective injection of plasmasheet ions into the inner magnetosphere. Waves grow rapidly near the magnetic equatorial plane reaching amplitudes up to 10 nT. Such intense waves induce scattering of cyclotron resonant ions at a rate comparable to the strong diffusion limit, causing rapid ion precipitation into the atmosphere in localized regions where the waves are present. The waves also resonate with relativistic electrons at energies typically above 0.5 MeV Such scattering, which could provide a major loss process for relativistic outer zone electrons during the main phase of a magnetic storm, is confined to high-density regions just inside the plasmapause or within dayside drainage plumes. As EMIC waves propagate to higher latitude, their wave normal angle becomes highly oblique. This allows Landau resonant interaction with thermal electrons, which can heat the electron population in the outer plasmasphere to several eV, contributing to the heat flux that drives Stable Auroral Red (SAR) arcs. During the propagation to higher latitude, EMIC waves can also experience cyclotron resonant damping by heavy thermal ions, leading to ion conic distributions, which are observed near the equator.

The Influence of Wave‐Particle Interactions on Relativistic Electron Dynamics During Storms

Vibratory thrust is generated by a rotating crankshaft and controlled orbital movement of a single weight pivoted to the crankpin of the crankshaft. As the crankshaft rotates the center of gravity of the weight moves back and forth on a vector through the crankshaft axis. The direction of the vector is adjustable within a substantial angular range about the crankshaft axis.

Modeling the effects of radial diffusion and plasmaspheric hiss on outer radiation belt electrons

We simulate the behaviour of relativistic (976 keV) electrons in the outer radiation belt (3 ≤ L ≤ 7) during the first half of the CRRES mission. We use a 1d radial diffusion model with losses due to pitch-angle scattering by plasmaspheric hiss expressed through the electron lifetime calculated using the PADIE code driven by a global K p -dependent model of plasmaspheric hiss intensity and f pe /f ce . We use a time and energy-dependent outer boundary derived from observations. The model reproduces flux variations to within an order of magnitude for L ≤ 4 suggesting hiss is the dominant cause of electron losses in the plasmasphere near the equator. At L = 5 the model reproduces significant variations but underestimates the size of the variability. We find that during magnetic storms hiss can cause significant losses for L ≤ 6 due to its presence in plumes. Wave acceleration is partially represented by the boundary conditions.

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.