ULF Waves above the Nightside Auroral Oval during Substorm Onset

This chapter reviews historical ground-based observations of ultra-low-frequency (ULF) waves tied to substorms, and highlights new research linking these ULF waves explicitly to substorm onset itself. There are several robust methods that can be used to determine the characteristics of a nonstationary time series such as the ULF magnetic field traces observed in the auroral zone during substorms. These include the pure state filter, the Hilbert-Huang transform, and wavelet analysis. The first indication of a substorm is a sudden brightening of one of the quiet arcs lying in the midnight sector of the oval. The chapter focuses on the properties of ULF waves that are seen in two-dimensional images of auroral intensity near substorm expansion phase onset. It also discusses a wider range of magnetotail instabilities that could be responsible for the azimuthally structured auroral forms at substorm onset

Statistical Characterization of the Dynamic Near‐Earth Plasma Sheet Relative to Ultra‐Low Frequency (ULF) Wave Growth at Substorm Onset

Magnetospheric substorms are a complex phenomenon. During the initial stages of a substorm a variety of important processes occur in near-Earth space within a span of several minutes. The relative timing and links between these processes are critical to understanding how, where and when substorms may occur. One of the first observed signatures at substorm onset is the exponential increase in ULF (Ultra-Low Frequency) wave power in the near-Earth magnetotail (e.g., −7.5 ≤ XGSM ≤ −12.5 RE). We use the Time History of Events and Macroscale Interactions during Substorms spacecraft to examine the conditions in the magnetotail plasma sheet before, during and after local ULF wave growth. Prior to the ULF wave growth, the magnetotail stretches with convectional flows dominating. We then find strong earthward and azimuthal flows that peak at a similar time to the peak ULF wave power. These flows are found to be faster in the mid-tail (−10 ≤ XGSM ≤ −12.5 RE) than the near-tail (−7.5 ≤ XGSM ≤ −10 RE). Examining the local plasma energy density (magnetic, thermal and kinetic), we find no statistical decrease that could explain the exponentially growing ULF waves, in fact the local energy density is found to increase. This suggests that there may be an injection of energy from elsewhere in the magnetotail. Following the peak ULF wave power the tail is seen to dipolarize, and the local energy density is enhanced

Statistical azimuthal structuring of the substorm onset arc: Implications for the onset mechanism

The onset of an auroral substorm is generally thought to occur on a quiet, homogeneous auroral arc. We present a statistical study of independently selected substorm onset arcs and find that over 90% of the arcs studied have resolvable characteristic spatial scales in the form of auroral beads. We find that the vast majority (~88%) of auroral beads have small amplitudes relative to the background, making them invisible without quantitative analysis. This confirms that auroral beads are highly likely to be ubiquitous to all onset arcs, rather than a special case phenomena as previously thought. Moreover, as these auroral beads grow exponentially through onset, we conclude that a magnetospheric plasma instability is fundamental to substorm onset itself

Forecasting GOES 15 >2 MeV Electron Fluxes From Solar Wind Data and Geomagnetic Indices

The flux of > 2 MeV electrons at geosynchronous orbit is used by space weather forecasters as a key indicator of enhanced risk of damage to spacecraft in low, medium or geosynchronous Earth orbits. We present a methodology that uses the amount of time a single input dataset (solar wind data or geomagnetic indices) exceeds a given threshold to produce deterministic and probabilistic forecasts of the > 2 MeV flux at GEO exceeding 1000 or 10000 cm ‐2 s ‐1 sr ‐1 within up to 10 days. By comparing our forecasts with measured fluxes from GOES 15 between 2014 and 2016, we determine the optimum forecast thresholds for deterministic and probabilistic forecasts by maximising the ROC and Brier Skill Scores respectively. The training dataset gives peak ROC scores of 0.71 to 0.87 and peak Brier Skill Scores of ‐0.03 to 0.32. Forecasts from AL give the highest skill scores for forecasts of up to 6‐days. AL, solar wind pressure or SYM‐H give the highest skill scores over 7‐10 days. Hit rates range over 56‐89% with false alarm rates of 11‐53%. Applied to 2012, 2013 and 2017, our best forecasts have hit rates of 56‐83% and false alarm rates of 10‐20%. Further tuning of the forecasts may improve these. Our hit rates are comparable to those from operational fluence forecasts, that incorporate fluence measurements, but our false alarm rates are higher. This proof‐of‐concept shows that the geosynchronous electron flux can be forecast with a degree of success without incorporating a persistence element into the forecasts

Control of ULF Wave Accessibility to the Inner Magnetosphere by the Convection of Plasma Density

During periods of storm activity and enhanced convection, the plasma density in the afternoon sector of the magnetosphere is highly dynamic due to the development of plasmaspheric drainage plume (PDP) structure. This significantly affects the local Alfvén speed and alters the propagation of ULF waves launched from the magnetopause. Therefore, it can be expected that the accessibility of ULF wave power for radiation belt energization is sensitively dependent on the recent history of magnetospheric convection and the stage of development of the PDP. This is investigated using a 3-D model for ULF waves within the magnetosphere in which the plasma density distribution is evolved using an advection model for cold plasma, driven by a (VollandStern) convection electrostatic field (resulting in PDP structure). The wave model includes magnetic field day/night asymmetry and extends to a paraboloid dayside magnetopause, from which ULF waves are launched at various stages during the PDP development. We find that the plume structure significantly alters the field line resonance location, and the turning point for MHD fast waves, introducing strong asymmetry in the ULF wave distribution across the noon meridian. Moreover, the density enhancement within the PDP creates a waveguide or local cavity for MHD fast waves, such that eigenmodes formed allow the penetration of ULF wave power to much lower L within the plume than outside, providing an avenue for electron energization

Variability of Quasilinear Diffusion Coefficients for Plasmaspheric Hiss

In the outer radiation belt, the acceleration and loss of high‐energy electrons is largely controlled by wave‐particle interactions. Quasilinear diffusion coefficients are an efficient way to capture the small‐scale physics of wave‐particle interactions due to magnetospheric wave modes such as plasmaspheric hiss. The strength of quasilinear diffusion coefficients as a function of energy and pitch angle depends on both wave parameters and plasma parameters such as ambient magnetic field strength, plasma number density, and composition. For plasmaspheric hiss in the magnetosphere, observations indicate large variations in the wave intensity and wave normal angle, but less is known about the simultaneous variability of the magnetic field and number density. We use in situ measurements from the Van Allen Probe mission to demonstrate the variability of selected factors that control the size and shape of pitch angle diffusion coefficients: wave intensity, magnetic field strength, and electron number density. We then compare with the variability of diffusion coefficients calculated individually from colocated and simultaneous groups of measurements. We show that the distribution of the plasmaspheric hiss diffusion coefficients is highly non‐Gaussian with large variance and that the distributions themselves vary strongly across the three phase space bins studied. In most bins studied, the plasmaspheric hiss diffusion coefficients tend to increase with geomagnetic activity, but our results indicate that new approaches that include natural variability may yield improved parameterizations. We suggest methods like stochastic parameterization of wave‐particle interactions could use variability information to improve modeling of the outer radiation belt

A diagnosis of the plasma waves responsible for the explosive energy release of substorm onset

During geomagnetic substorms, stored magnetic and plasma thermal energies are explosively converted into plasma kinetic energy. This rapid reconfiguration of Earth’s nightside magnetosphere is manifest in the ionosphere as an auroral display that fills the sky. Progress in understanding of how substorms are initiated is hindered by a lack of quantitative analysis of the single consistent feature of onset; the rapid brightening and structuring of the most equatorward arc in the ionosphere. Here, we exploit state-of-the-art auroral measurements to construct an observational dispersion relation of waves during substorm onset. Further, we use kinetic theory of high-beta plasma to demonstrate that the shear Alfven wave dispersion relation bears remarkable similarity to the auroral dispersion relation. In contrast to prevailing theories of substorm initiation, we demonstrate that auroral beads seen during the majority of substorm onsets are likely the signature of kinetic Alfven waves driven unstable in the high-beta magnetotail

A direct examination of the dynamics of dipolarization fronts using MMS

Energy conversion on the dipolarization fronts (DFs) has attracted much research attention through the suggestion that intense current densities associated with DFs can modify the more global magnetotail current system. The current structures associated with a DF are at the scale of one to a few ion gyroradii, and their duration is comparable to a spacecraft's spin period. Hence, it is crucial to understand the physical mechanisms of DFs with measurements at a timescale shorter than a spin period. We present a case study whereby we use measurements from the Magnetospheric Multiscale (MMS) Mission, which provides full 3-D particle distributions with a cadence much shorter than a spin period. We provide a cross validation amongst the current density calculations and examine the assumptions that have been adopted in previous literature using the advantages of MMS mission (i.e., small-scale tetrahedron and high temporal resolution). We also provide a cross validation on the terms in the generalized Ohm's law using these advantageous measurements. Our results clearly show that the majority of the currents on the DF are contributed by both ion and electron diamagnetic drifts. Our analysis also implies that the ion frozen-in condition does not hold on the DF, while electron frozen-in condition likely holds. The new experimental capabilities allow us to accurately calculate Joule heating within the DF, which shows that plasma energy is being converted to magnetic energy in our event

Determining the global scale size of chorus waves in the magnetosphere

Chorus waves outside the plasmapause influence the Earth's radiation belt dynamics by interacting with energetic electrons via cyclotron and Landau resonance. Recent numerical diffusion experiments indicate that the diffusion process is sensitive to the spatial and temporal scale of variability in the wave-particle interaction, which is reported to be more efficient than that based on the traditional average model. Using Van Allen Probes A and B data from November 2012 to July 2019, the spatial and temporal scale size of chorus waves are calculated by the correlation between the wave amplitudes detected by two satellites with varying spatial separation or time lag. We found that, the chorus wave is incoherent when the spatial extent is greater than 433 km or the time lag lasts ∼10 s, which are significantly smaller than that of plasmaspheric hiss. In addition, the spatial correlations of chorus tend to be higher near noon or with lower geomagnetic activity. The temporal correlations of chorus are always statistically near zero, which are not influenced by the location and geomagnetic activity. Our results can help refine the model of the interactions between energetic particles and chorus waves in the radiation belt

Temporal variability of quasi-linear pitch-angle diffusion

This is the final version. Available on open access from Frontiers Media via the DOI in this recordData availability statement; The datasets presented in this study can be found in online repositories. The names of the repository/repositories and accession number(s) can be found below: https://emfisis.physics.uiowa.edu/data/index; https://doi.org/10.17864/1947.212, Ensemble experiment data can be found at https://doi.org/10.25398/rd.northumbria.2126623.Kinetic wave-particle interactions in Earth’s outer radiation belt energize and scatter high-energy electrons, playing an important role in the dynamic variation of the extent and intensity of the outer belt. It is possible to model the effects of wave-particle interactions across long length and time scales using quasi-linear theory, leading to a Fokker-Planck equation to describe the effects of the waves on the high energy electrons. This powerful theory renders the efficacy of the wave-particle interaction in a diffusion coefficient that varies with energy or momentum and pitch angle. In this article we determine how the Fokker-Planck equation responds to the temporal variation of the quasi-linear diffusion coefficient in the case of pitch-angle diffusion due to plasmaspheric hiss. Guided by in-situ observations of how hiss wave activity and local number density change in time, we use stochastic parameterisation to describe the temporal evolution of hiss diffusion coefficients in ensemble numerical experiments. These experiments are informed by observations from three different example locations in near-Earth space, and a comparison of the results indicates that local differences in the distribution of diffusion coefficients can result in material differences to the ensemble solutions. We demonstrate that ensemble solutions of the Fokker-Planck equation depend both upon the timescale of variability (varied between minutes and hours), and the shape of the distribution of diffusion coefficients. Based upon theoretical construction of the diffusion coefficients and the results presented here, we argue that there is a useful maximum averaging timescale that should be used to construct a diffusion coefficient from observations, and that this timescale is likely less than the orbital period of most inner magnetospheric missions. We discuss time and length scales of wave-particle interactions relative to the drift velocity of high-energy electrons and confirm that arithmetic drift-averaging is can be appropriate in some cases. We show that in some locations, rare but large values of the diffusion coefficient occur during periods of relatively low number density. Ensemble solutions are sensitive to the presence of these rare values, supporting the need for accurate cold plasma density models in radiation belt descriptions.Natural Environment Research Council (NERC)Science and Technology Facilities Council (STFC)University of ExeterAlexander von Humboldt Postdoctoral Research Fellowshi