Richard M. Thorne

Relativistic theory of wave‐particle resonant diffusion with application to electron acceleration in the magnetosphere

Resonant diffusion curves for electron cyclotron resonance with field-aligned electromagnetic R mode and L mode electromagnetic ion cyclotron (EMIC) waves are constructed using a fully relativistic treatment. Analytical solutions are derived for the case of a single-ion plasma, and a numerical scheme is developed for the more realistic case of a multi-ion plasma. Diffusion curves are presented, for plasma parameters representative of the Earths magnetosphere at locations both inside and outside the plasmapause. The results obtained indicate minimal electron energy change along the diffusion curves for resonant interaction with L mode waves. Intense storm time EMIC waves are therefore ineffective for electron stochastic acceleration, although these waves could induce rapid pitch angle scattering for ≳ 1 MeV electrons near the duskside plasmapause. In contrast, significant energy change can occur along the diffusion curves for interaction between resonant electrons and whistler (R mode) waves. The energy change is most pronounced in regions of low plasma density. This suggests that whistler mode waves could provide a viable mechanism for electron acceleration from energies near 100 keV to above 1 MeV in the region outside the plasmapause during the recovery phase of geomagnetic storms. A model is proposed to account for the observed variations in the flux and pitch angle distribution of relativistic electrons during geomagnetic storms by combining pitch angle scattering by intense EMIC waves and energy diffusion during cyclotron resonant interaction with whistler mode chorus outside the plasmasphere.

Potential waves for relativistic electron scattering and stochastic acceleration during magnetic storms

The possibility of electron stochastic energization to relativisitic energies (≥ 1 MeV) via resonant wave-particle interactions during a magnetic storm is explored. The minimum electron energy Emin for cyclotron resonant interaction with various electromagnetic waves is calculated for conditions representative of storm-times. Since Emin > 1 MeV for resonance with L-mode ion cyclotron waves, intense stormtime EMIC waves could contribute to relativistic electron loss, but not acceleration. Inside the plasmapause whistler mode waves, and highly oblique magnetosonic waves near the lower hybrid frequency, can resonate with electrons over the important energy range from ∼ 100 keV to ∼ 1 MeV. In low density regions outside the plasmapause, the whistler, RX, LO and Z modes can resonate with electrons over a similar energy range. These waves have the potential to contribute to the stochastic acceleration of electrons up to relativistic energies during magnetic storms.

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.

The modified plasma dispersion function

In the linear theory of waves in a hot plasma if the zeroth‐order velocity distribution function is taken to be Maxwellian, then there arises a special, complex‐valued function of a complex variable ξ=x+iy, namely Z(ξ), known as the plasma dispersion function. In space physics many particle distributions possess a high‐energy tail that can be well modeled by a generalized Lorentzian (or kappa) distribution function containing the spectral index κ. In this paper, as a natural analog to the definition of Z(ξ), a new special function Z*κ(ξ) is defined based on the kappa distribution function. Here, Z*κ(ξ) is called the modified plasma dispersion function. For any positive integral value of κ, Z*κ(ξ) is calculated in closed form as a finite series. General properties, including small‐argument and large‐argument expansions, of Z*κ(ξ) are given, and simple explicit forms are given for Z*1(ξ), Z*2(ξ), ..., Z*6(ξ). A comprehensive set of graphs of the real and imaginary parts of Z*κ(ξ) is presented. It is demonst...

The terrestrial ring current: Origin, formation, and decay

The terrestrial ring current is an electric current flowing toroidally around the Earth, centered at the equatorial plane and at altitudes of ;10,000 - 60,000 km. Changes in this current are responsible for global decreases in the Earths surface magnetic field, which are known as geomagnetic storms. Intense geomagnetic storms have severe effects on technological systems, such as disturbances or even permanent damage to tele- communication and navigation satellites, telecommuni- cation cables, and power grids. The main carriers of the storm ring current are positive ions, with energies from ;1 keV to a few hundred keV, which are trapped by the geomagnetic field and undergo an azimuthal drift. The ring current is formed by the injection of ions originating in the solar wind and the terrestrial ionosphere. The injection process involves electric fields, associated with enhanced magnetospheric convection and/or magneto- spheric substorms. The quiescent ring current is carried mainly by protons of predominantly solar wind origin, while geospace activity tends to increase the abundance (both absolute and relative) of O 1 ions, which are of ionospheric origin. During intense magnetic storms, the O 1 abundance increases dramatically, resulting in a rapid intensification of the ring current and an O 1 dominance around storm maximum. This compositional change affects, among other processes, the decay of the ring current through the species- and energy-dependent charge exchange and wave-particle scattering loss. En- ergetic neutral atoms, products of charge exchange, en- able global imaging of the ring current and are the most promising diagnostic tool of ring current evolution. This review will cover the origin of ring current particles, their transport and acceleration, the effects of composi- tional variations in the ring current, the effects of sub- storms on ring current growth, and the dynamics of ring current decay with an emphasis on the process of charge exchange and the potential for wave scattering loss.

Electron scattering loss in Earth's inner magnetosphere: 1. Dominant physical processes

Pitch angle diffusion rates due to Coulomb collisions and resonant interactions with plasmaspheric hiss, lightning-induced whistlers and anthropogenic VLF transmissions are computed for inner magnetospheric electrons. The bounce-averaged, quasi-linear pitch angle diffusion coefficients are input into a pure pitch angle diffusion equation to obtain L and energy dependent equilibrium distribution functions and precipitation lifetimes. The relative effects of each scattering mechanism are considered as a function of electron energy and L shell. Model calculations accurately describe the enhanced loss rates in the slot region, as well as reduced scattering in the heavily populated inner radiation belt. Predicted electron distribution function calculations in the slot region display a characteristic “top hat” distribution which is supported by observations. Inner zone electron lifetimes based on observed decay rates of the Starfish electron population are in approximate agreement with model predictions.

Statistical analysis of relativistic electron energies for cyclotron resonance with EMIC waves observed on CRRES

Electromagnetic ion cyclotron (EMIC) waves which propagate at frequencies below the proton gyrofrequency can undergo cyclotron resonant interactions with relativistic electrons in the outer radiation belt and cause pitch-angle scattering and electron loss to the atmosphere. Typical storm-time wave amplitudes of 1-10 nT cause strong diffusion scattering which may lead to significant relativistic electron loss at energies above the minimum energy for resonance, E-min. A statistical analysis of over 800 EMIC wave events observed on the CRRES spacecraft is performed to establish whether scattering can occur at geophysically interesting energies (less than or equal to2 MeV). While E-min is well above 2 MeV for the majority of these events, it can fall below 2 MeV in localized regions of high plasma density and/or low magnetic field (f(pe)/f(ce,eq) > 10) for wave frequencies just below the hydrogen or helium ion gyrofrequencies. These lower energy scattering events, which are mainly associated with resonant L-mode waves, are found within the magnetic local time range 1300 4.5. The average wave spectral intensity of these events (4-5 nT(2)/Hz) is sufficient to cause strong diffusion scattering. The spatial confinement of these events, together with the limited set of these waves that resonate with less than or equal to2 MeV electrons, suggest that these electrons are only subject to strong scattering over a small fraction of their drift orbit. Consequently, drift-averaged scattering lifetimes are expected to lie in the range of several hours to a day. EMIC wave scattering should therefore significantly affect relativistic electron dynamics during a storm. The waves that resonate with the similar toMeV electrons are produced by low-energy (similar tokeV) ring current protons, which are expected to be injected into the inner magnetosphere during enhanced convection events.

Rapid local acceleration of relativistic radiation-belt electrons by magnetospheric chorus.

Recent analysis of satellite data obtained during the 9 October 2012 geomagnetic storm identified the development of peaks in electron phase space density, which are compelling evidence for local electron acceleration in the heart of the outer radiation belt, but are inconsistent with acceleration by inward radial diffusive transport. However, the precise physical mechanism responsible for the acceleration on 9 October was not identified. Previous modelling has indicated that a magnetospheric electromagnetic emission known as chorus could be a potential candidate for local electron acceleration, but a definitive resolution of the importance of chorus for radiation-belt acceleration was not possible because of limitations in the energy range and resolution of previous electron observations and the lack of a dynamic global wave model. Here we report high-resolution electron observations obtained during the 9 October storm and demonstrate, using a two-dimensional simulation performed with a recently developed time-varying data-driven model, that chorus scattering explains the temporal evolution of both the energy and angular distribution of the observed relativistic electron flux increase. Our detailed modelling demonstrates the remarkable efficiency of wave acceleration in the Earth’s outer radiation belt, and the results presented have potential application to Jupiter, Saturn and other magnetized astrophysical objects.

Electron Acceleration in the Heart of the Van Allen Radiation Belts

Local Acceleration How the electrons trapped in Earth-encircling Van Allen radiation belts get accelerated has been debated since their discovery in 1958. Reeves et al. (p. 991, published online 25 July) used data from the Van Allen Radiation Belt Storm Probes, launched by NASA on 30 August 2012, to discover that radiation belt electrons are accelerated locally by wave-particle interactions, rather than by radial transport from regions of weaker to stronger magnetic fields. Satellite observations provide evidence for local relativistic electron acceleration in Earth’s radiation belts. The Van Allen radiation belts contain ultrarelativistic electrons trapped in Earth’s magnetic field. Since their discovery in 1958, a fundamental unanswered question has been how electrons can be accelerated to such high energies. Two classes of processes have been proposed: transport and acceleration of electrons from a source population located outside the radiation belts (radial acceleration) or acceleration of lower-energy electrons to relativistic energies in situ in the heart of the radiation belts (local acceleration). We report measurements from NASA’s Van Allen Radiation Belt Storm Probes that clearly distinguish between the two types of acceleration. The observed radial profiles of phase space density are characteristic of local acceleration in the heart of the radiation belts and are inconsistent with a predominantly radial acceleration process.

Scattering by chorus waves as the dominant cause of diffuse auroral precipitation

Earth’s diffuse aurora occurs over a broad latitude range and is primarily caused by the precipitation of low-energy (0.1–30-keV) electrons originating in the central plasma sheet, which is the source region for hot electrons in the nightside outer magnetosphere. Although generally not visible, the diffuse auroral precipitation provides the main source of energy for the high-latitude nightside upper atmosphere, leading to enhanced ionization and chemical changes. Previous theoretical studies have indicated that two distinct classes of magnetospheric plasma wave, electrostatic electron cyclotron harmonic waves and whistler-mode chorus waves, could be responsible for the electron scattering that leads to diffuse auroral precipitation, but it has hitherto not been possible to determine which is the more important. Here we report an analysis of satellite wave data and Fokker–Planck diffusion calculations which reveals that scattering by chorus is the dominant cause of the most intense diffuse auroral precipitation. This resolves a long-standing controversy. Furthermore, scattering by chorus can remove most electrons as they drift around Earth’s magnetosphere, leading to the development of observed pancake distributions, and can account for the global morphology of the diffuse aurora.