Electron trapping in shear Alfvén waves that power the aurora

Results from 1D Vlasov drift-kinetic plasma simulations reveal how and where auroral electrons are accelerated along Earth’s geomagnetic field. In the warm plasma sheet, electrons become trapped in shear Alfven waves, preventing immediate wave damping. As waves move to regions with larger vTe=vA, their parallel electric field decreases, and the trapped electrons escape their influence. The resulting electron distribution functions compare favorably with in situ observations, demonstrating for the first time a self-consistent link between Alfven waves and electrons that form aurora

Electron acceleration and parallel electric fields due to kinetic Alfvén waves in plasma with similar thermal and Alfvén speeds

We investigate electron acceleration due to shear Alfven waves in a collissionless plasma for plasma parameters typical of 4–5RE radial distance from the Earth along auroral field lines. Recent observational work has motivated this study, which explores the plasma regime where the thermal velocity of the electrons is similar to the Alfven speed of the plasma, encouraging Landau resonance for electrons in the wave fields. We use a self-consistent kinetic simulation model to follow the evolution of the electrons as they interact with a short-duration wave pulse, which allows us to determine the parallel electric field of the shear Alfven wave due to both electron inertia and electron pressure effects. The simulation demonstrates that electrons can be accelerated to keV energies in a modest amplitude sub-second period wave. We compare the parallel electric field obtained from the simulation with those provided by fluid approximations

Whistler mode wave growth and propagation in the prenoon magnetosphere

Pitch-angle scattering of electrons can limit the stably trapped particle flux in the magnetosphere and precipitate energetic electrons into the ionosphere. Whistler-mode waves generated by a temperature anisotropy can mediate this pitch-angle scattering over a wide range of radial distances and latitudes, but in order to correctly predict the phase-space diffusion, it is important to characterise the whistler-mode wave distributions that result from the instability. We use previously-published observations of number density, pitch-angle anisotropy and phase space density to model the plasma in the quiet pre-noon magnetosphere (defined as periods when AE<100nT). We investigate the global propagation and growth of whistler-mode waves by studying millions of growing ray paths and demonstrate that the wave distribution at any one location is a superposition of many waves at different points along their trajectories and with different histories. We show that for observed electron plasma properties, very few raypaths undergo magnetospheric reflection, most rays grow and decay within 30 degrees of the magnetic equator. The frequency range of the wave distribution at large L can be adequately described by the solutions of the local dispersion relation, but the range of wavenormal angle is different. The wave distribution is asymmetric with respect to the wavenormal angle. The numerical results suggest that it is important to determine the variation of magnetospheric parameters as a function of latitude, as well as local time and L-shell

Accounting for variability in ULF wave radial diffusion models

Many modern outer radiation belt models simulate the long‐time behavior of high‐energy electrons by solving a three‐dimensional Fokker‐Planck equation for the drift‐ and bounce‐averaged electron phase space density that includes radial, pitch‐angle, and energy diffusion. Radial diffusion is an important process, often characterized by a deterministic diffusion coefficient. One widely used parameterization is based on the median of statistical ultralow frequency (ULF) wave power for a particular geomagnetic index Kp. We perform idealized numerical ensemble experiments on radial diffusion, introducing temporal and spatial variability to the diffusion coefficient through stochastic parameterization, constrained by statistical properties of its underlying observations. Our results demonstrate the sensitivity of radial diffusion over a long time period to the full distribution of the radial diffusion coefficient, highlighting that information is lost when only using median ULF wave power. When temporal variability is included, ensembles exhibit greater diffusion with more rapidly varying diffusion coefficients, larger variance of the diffusion coefficients and for distributions with heavier tails. When we introduce spatial variability, the variance in the set of all ensemble solutions increases with larger spatial scales of variability. Our results demonstrate that the variability of diffusion affects the temporal evolution of phase space density in the outer radiation belt. We discuss the need to identify important temporal and length scales to constrain variability in diffusion models. We suggest that the application of stochastic parameterization techniques in the diffusion equation may allow the inclusion of natural variability and uncertainty in modeling of wave‐particle interactions in the inner magnetosphere

Statistics of Solar Wind Electron Breakpoint Energies Using Machine Learning Techniques

Solar wind electron velocity distributions at 1 au consist of a thermal "core" population and two suprathermal populations: "halo" and "strahl". The core and halo are quasi-isotropic, whereas the strahl typically travels radially outwards along the parallel and/or anti-parallel direction with respect to the interplanetary magnetic field. With Cluster-PEACE data, we analyse energy and pitch angle distributions and use machine learning techniques to provide robust classifications of these solar wind populations. Initially, we use unsupervised algorithms to classify halo and strahl differential energy flux distributions to allow us to calculate relative number densities, which are of the same order as previous results. Subsequently, we apply unsupervised algorithms to phase space density distributions over ten years to study the variation of halo and strahl breakpoint energies with solar wind parameters. In our statistical study, we find both halo and strahl suprathermal breakpoint energies display a significant increase with core temperature, with the halo exhibiting a more positive correlation than the strahl. We conclude low energy strahl electrons are scattering into the core at perpendicular pitch angles. This increases the number of Coulomb collisions and extends the perpendicular core population to higher energies, resulting in a larger difference between halo and strahl breakpoint energies at higher core temperatures. Statistically, the locations of both suprathermal breakpoint energies decrease with increasing solar wind speed. In the case of halo breakpoint energy, we observe two distinct profiles above and below 500 km/s. We relate this to the difference in origin of fast and slow solar wind.Comment: Published in Astronomy & Astrophysics, 11 pages, 10 figure

Statistical characterisation of the growth and spatial scales of the substorm onset arc

We present the first multi-event study of the spatial and temporal structuring of the aurora to provide statistical evidence of the near-Earth plasma instability which causes the substorm onset arc. Using data from ground-based auroral imagers, we study repeatable signatures of along-arc auroral beads, which are thought to represent the ionospheric projection of magnetospheric instability in the near-Earth plasma sheet. We show that the growth and spatial scales of these wave-like fluctuations are similar across multiple events, indicating that each sudden auroral brightening has a common explanation. We find statistically that growth rates for auroral beads peak at low wavenumber with the most unstable spatial scales mapping to an azimuthal wavelength λ≈1700 − 2500 km in the equatorial magnetosphere at around 9-12 RE. We compare growth rates and spatial scales with a range of theoretical predictions of magnetotail instabilities, including the cross-field current instability and the shear-flow ballooning instability. We conclude that, although the cross-field current instability can generate similar magnitude of growth rates, the range of unstable wavenumbers indicates that the shear-flow ballooning instability is the most likely explanation for our observations

Random forest model of ultra-low frequency magnetospheric wave power

Models of magnetospheric ultra‐low frequency (ULF) waves can be used to study wave phenomena and to calculate the effect of these waves on the energisation and transport of radiation belt electrons. We present a decision tree ensemble (i.e. a random forest) model of ground‐based ULF wave power spectral density driven by solar wind speed vsw, north‐south component of the interplanetary magnetic field Bz and variance of proton number density var (Np). This model corresponds to four radial locations in the magnetosphere (roughly L~4.21 to 7.94) and spans 1‐15 mHz, with hourly magnetic local time resolution. The decision tree ensembles are easier to use than the previous model generation; they have better coverage, perform better at predicting power and have reduced error due to intelligently chosen bins in parameter space. We outline the difficulties in extracting physics from parameterised models and demonstrate a hypothesis testing framework to iteratively explore finer driving processes. We confirm a regime change for ULF driving about Bz=0. We posit that ULF wave power directly driven by magnetopause perturbations corresponds to a latitude dependent dawn‐dusk asymmetry, which we see with increasing speed. Model uncertainty identifies where the underlying physics is not fully captured; we find that power due to substorms is less well characterised by Bz > 0, with an effect that is seen globally and not just near midnight. The largest uncertainty is seen for the smallest amounts of solar wind driving, suggesting that internal magnetospheric properties may play a significant role in ULF wave occurrence

Capturing uncertainty in magnetospheric ultra-low frequency wave models

We develop and test an empirical model predicting ground-based observations of ultra-low frequency (ULF, 1-20 mHz) wave power across a range of frequencies, latitudes and magnetic local time sectors. This is parameterized by instantaneous solar wind speed $v_{sw}$, variance in proton number density $var(Np)$ and interplanetary southward magnetic field $B_z$. A probabilistic model of ULF wave power will allow us to address uncertainty in radial diffusion coefficients and therefore improve diffusion modeling of radial transport in Earth's outer radiation belt. Our model can be used in two ways to reproduce wave power; by sampling from conditional probability distribution functions or by using the mean (expectation) values. We derive a method for testing the quality of the parameterization and test the ability of the model to reproduce ULF wave power time series. Sampling is a better method for reproducing power over an extended time period as it retains the same overall distribution while mean values are better for predicting the power in a time series. The model predicts each hour in a time series better than the assumption that power persists from the preceding hour. Finally, we review other sources of diffusion coefficient uncertainty. Although this wave model is designed principally for the goal of improved radial diffusion coefficients to include in outer radiation belt diffusion based modeling, we anticipate that our model can also be used to investigate the occurrence of ULF waves throughout the magnetosphere and hence the physics of ULF wave generation and propagation

Accurately characterising the importance of wave-particle interactions in radiation belt dynamics: the pitfalls of statistical wave representations

Wave-particle interactions play a crucial role in energetic particle dynamics in the Earth's radiation belts. However the relative importance of different wave-modes in these dynamics is poorly understood. Typically this is assessed during geomagnetic storms using statistically averaged empirical wave models as a function of geomagnetic activity in advanced radiation belt simulations. However statistical averages poorly characterise extreme events such as geomagnetic storms in that storm-time ULF wave power is typically larger than that derived over a solar cycle and Kp is a poor proxy for storm-time wave power

Optical characterization of the growth and spatial structure of a substorm onset arc

We present a detailed case study of the characteristics of auroral forms that constitute the first ionospheric signatures of substorm expansion phase onset. Analysis of the optical frequency and along-arc (azimuthal) wave number spectra provides the strongest constraint to date on the potential mechanisms and instabilities in the near-Earth magnetosphere that accompany auroral onset and which precede poleward arc expansion and auroral breakup. We evaluate the frequency and growth rates of the auroral forms as a function of azimuthal wave number to determine whether these wave characteristics are consistent with current models of the substorm onset mechanism. We find that the frequency, spatial scales, and growth rates of the auroral forms are most consistent with the cross-field current instability or a ballooning instability, most likely triggered close to the inner edge of the ion plasma sheet. This result is supportive of a near-Earth plasma sheet initiation of the substorm expansion phase. We also present evidence that the frequency and phase characteristics of the auroral undulations may be generated via resonant processes operating along the geomagnetic field. Our observations provide the most powerful constraint to date on the ionospheric manifestation of the physical processes operating during the first few minutes around auroral substorm onset