Robert Lysak

The theory of the acceleration of auroral particles is reviewed, focusing on developments in the last 15 years. We discuss elementary plasma physics processes leading to acceleration of electrons to energies compatible with emission observed for quiet, discrete auroral arcs, defined as arcs that have time scales of minutes or more and spatial scales ranging from less than 1 km to tens of kilometers. For context, earlier observations are first described briefly. The theoretical fundamentals of auroral particle acceleration are based on the kinetic theory of plasmas, in particular the development of parallel electric fields. These parallel electric fields can either be distributed along the magnetic field lines, often associated with the mirror geometry of the geomagnetic field, or concentrated into narrow regions of charge separation known as double layers. Observations have indicated that the acceleration process depends on whether the field-aligned currents are directed away from the Earth, toward the Earth, or in mixed regions of currents often associated with the propagation of Alfvén waves. Recent observations from the NASA Fast Auroral SnapshoT (FAST) satellite, the ESA satellite constellation Cluster, and the Japanese Reimei satellite have provided new insights into the auroral acceleration process and have led to further refinements to the theory of auroral particle acceleration.

The theory of the acceleration of auroral particles is reviewed, focusing on developments in the last 15 years. We discuss elementary plasma physics processes leading to acceleration of electrons to energies compatible with emission observed for quiet, discrete auroral arcs, defined as arcs that have time scales of minutes or more and spatial scales ranging from less than 1 km to tens of kilometers. For context, earlier observations are first described briefly. The theoretical fundamentals of auroral particle acceleration are based on the kinetic theory of plasmas, in particular the development of parallel electric fields. These parallel electric fields can either be distributed along the magnetic field lines, often associated with the mirror geometry of the geomagnetic field, or concentrated into narrow regions of charge separation known as double layers. Observations have indicated that the acceleration process depends on whether the field-aligned currents are directed away from the Earth, toward the Earth, or in mixed regions of currents often associated with the propagation of Alfvén waves. Recent observations from the NASA Fast Auroral SnapshoT (FAST) satellite, the ESA satellite constellation Cluster, and the Japanese Reimei satellite have provided new insights into the auroral acceleration process and have led to further refinements to the theory of auroral particle acceleration.

Field‐aligned currents (FACs) are a primary signature of magnetosphere‐ionosphere coupling (MIC). However, establishing FACs requires the propagation of Alfvén waves. Large‐scale quasi‐static FACs are well‐organized into large‐scale Region 1 (R1) and Region 2 (R2) systems during intervals of southward interplanetary magnetic field (IMF); however, the scale‐dependent spatiotemporal variability and related electrodynamics are less well understood. Using the electric and magnetic field data from Swarms A and C, we examine the role of Alfvén waves in MIC at a range of scales during two auroral crossings during southward IMF on May 16, 2016. Interspacecraft techniques reveal large amplitude small‐scale (10s km) non‐stationary magnetic fields inconsistent with a quasi‐static formulation. Cross‐phase techniques reveal a frequency‐dependent E/B ratio and E‐B phase difference consistent with an Alfvén wave interpretation, validated using the Lysak (1991, doi: 10.1029/90JA02154) ionospheric Alfvén resonator model constrained by inferred local Swarm plasma mass density. Local large amplitude E and B fields indicate the importance of Alfvénic energy transport at small scales. Evidence for Poynting flux concentration at the boundary between large‐scale upward and downward FACs is also presented. Our results suggest that cross‐scale FAC characteristics can be explained by a single Alfvén wave paradigm: quasi‐static large‐scale FACs representing the ω → 0 limit of a broader continuum of spatial scales associated with MIC. Future work should assess in more detail the energetic significance of small scales and the potential localization of large amplitude small‐scale disturbances at large scale FAC boundaries and assess related scale‐dependent MIC including Alfvénic ionospheric feedback.

The study demonstrates the importance of electromagnetic wave phenomena in global magnetosphere‐ionosphere coupling dynamics during conditions associated with southward interplanetary magnetic fields. Such conditions are associated with strong energy input into geospace and with driving large flows in the ionosphere. The importance of wave phenomena for transporting energy from the magnetosphere to the ionosphere is not well understood, and this study assesses the potential role of waves during conditions of strong flows, which are typically encountered in near‐Earth geospace at these times. The study demonstrates the importance of wave phenomena during these conditions and, in particular, evaluates the energetic significance of small‐scale electromagnetic perturbations.

Pi2 oscillations (40–150 s) in the nightside upper ionosphere are studied using magnetic field data acquired by multiple Swarm spacecraft in low‐Earth orbit and at the low‐latitude Bohyun (BOH, L = 1.3) station on 22 October 2014. Four Pi2 events were identified from the BOH data near midnight (magnetic local time = 1.5 hr), while Swarm‐A, Swarm‐B, and Swarm‐C spacecraft were orbiting in the premidnight (magnetic local time = 21–22 hr) meridian from 70° to −60° in magnetic latitude at ∼450‐ to 500‐km altitudes. Unlike previous low‐Earth orbit studies, which used a single point observation, the latitudinal structure of the amplitude and phase of ionospheric magnetic field perturbations can be determined by simultaneous multipoint observations along the latitude at a constant radial distance. We observed that the horizontal H component of BOH data is well correlated with the compressional (B_z) component of ionospheric magnetic fields when Swarm spacecraft were at |magnetic latitude|  < 30° with or without an accompanying ionospheric field perturbation in the radial (B_x) component, depending on the latitude of the spacecraft. It is found that the phase and amplitude relationship between B_x and B_z along the latitude is consistent with the model ionospheric field perturbations at 500‐km altitude, which are associated with a plasmaspheric resonance excited in a dipole numerical simulation. This indicates that the latitudinal variation of the ionospheric Pi2 pulsations in both B_x and B_z components is the consequence of the spatial mode structure in the north‐south direction of trapped fast mode waves inside the plasmasphere.

In one model, Pi2 pulsations are driven pulse by pulse by fast mode pulses that are launched as periodic bursty bulk flows brake when they approach the Earth. We have examined this model by analyzing data from multiple spacecraft and ground magnetometers for a Pi2 pulsation event. During the event, which started at ∼2226 UT on 8 November 2014, Time History of Events and Macroscale Interactions during Substorms (THEMIS)‐D detected an ∼2‐min‐period plasma bulk flow oscillation in the near‐Earth magnetotail, while THEMIS‐E and Van Allen Probes‐B, both located on the nightside just earthward of the electron plasmapause, detected a Pi2 pulsation consisting of a 10‐mHz oscillation in the azimuthal component of the electric field and a 19‐mHz oscillation in the compressional component of the magnetic field. On the ground, magnetic field oscillations containing both frequencies were observed both on the nightside and on the dayside. The nightside observations indicated that the pulsation had a radially standing structure, which is consistent with plasmaspheric virtual resonances (PVRs) excited in a magnetohydrodynamic simulation assuming an impulsive energy source. Cross‐spectral analysis of the magnetotail flow oscillation and the Pi2 pulsation indicated low coherence between them. These results suggest that the flow oscillation contributed to the Pi2 pulsation as a broadband energy source and that only the spectral components matching the PVR frequencies were detected with well‐defined frequencies. Ionospheric currents connected to the PVRs may be responsible for the appearance of the pulsation on the dayside.

Cavity mode oscillations (CMOs) are basic magnetohydrodynamic eigenmodes in the magnetosphere predicted by theory and are expected to occur following the arrival of an interplanetary shock. However, observational studies of shock‐induced CMOs have been sparse. We present a case study of a dayside ultralow‐frequency wave event that exhibited CMO properties. The event occurred immediately following the arrival of an interplanetary shock at 0829 UT on 15 August 2015. The shock was observed in the solar wind by the Time History of Events and Macroscale Interactions during Substorms‐B and ‐C spacecraft, and magnetospheric ultralow‐frequency waves were observed by multiple spacecraft including the Van Allen Probe‐A and Van Allen Probe‐B spacecraft, which were located in the dayside plasmasphere at L ∼1.4 and L ∼ 2.4, respectively. Both Van Allen Probes spacecraft detected compressional poloidal mode oscillations at ∼13 mHz (fundamental) and ∼26 mHz (second harmonic). At both frequencies, the azimuthal component of the electric field (E_ϕ) lagged behind the compressional component of the magnetic field (B_μ) by ∼90°. The frequencies and the E_ϕ‐B_μ relative phase are in good agreement with the CMOs generated in a dipole magnetohydrodynamic simulation that incorporates a realistic plasma mass density distribution and ionospheric boundary condition. The oscillations were also detected on the ground by the European quasi‐Meridional Magnetometer Array, which was located near the magnetic field footprints of the Van Allen Probes spacecraft.

The electrodynamics associated with dual discrete arc aurora with antiparallel flow along the arcs were observed nearly simultaneously by the enhanced Polar Outflow Probe (e‐POP) and the Swarm A and C spacecraft. Auroral imaging from e‐POP reveals 1–10 km structuring of the arcs, which move and evolve on second timescales and confound the traditional single‐spacecraft field‐aligned current algorithms. High‐cadence magnetic data from e‐POP show 1–10 Hz, inferred Alfvénic, perturbations coincident with and at the same scale size as the observed dynamic auroral fine structures. High‐cadence electric and magnetic field data from Swarm A reveal nonstationary electrodynamics involving reflected and interfering Alfvén waves and modulation consistent with trapping in the ionospheric Alfvén resonator (IAR). These observations suggest a role for Alfvén waves, perhaps also the IAR, in discrete arc dynamics on 0.2–10 s timescales and ~1–10 km spatial scales and reinforce the importance of considering Alfvén waves in magnetosphere‐ionosphere coupling.

An ongoing question in space physics is whether the energy that powers the vibrant and dynamic aurora is the result of static electric fields or magnetic waves. We address this question using data from three observational satellites, e‐POP, Swarm A, and Swarm C. We compare electric and magnetic field measurements at the locations of the spacecraft to high‐speed images of the aurora below as the satellites traveled over northern Canada. We show that as the satellites traveled over the aurora they detected magnetic waves known as Alfvén waves. We argue that these waves play an important and underappreciated role in transporting energy from near‐Earth space to the atmosphere in order to power the aurora.

High‐resolution multispacecraft Swarm data are used to examine magnetosphere‐ionosphere coupling during a period of northward interplanetary magnetic field (IMF) on 31 May 2014. The observations reveal a prevalence of unexpectedly large amplitude (>100 nT) and time‐varying magnetic perturbations during the polar passes, with especially large amplitude magnetic perturbations being associated with large‐scale downward field‐aligned currents. Differences between the magnetic field measurements sampled at 50 Hz from Swarm A and C, approximately 10 s apart along track, and the correspondence between the observed electric and magnetic fields at 16 samples per second, provide significant evidence for an important role for Alfvén waves in magnetosphere‐ionosphere coupling even during northward IMF conditions. Spectral comparison between the wave E‐ and B‐fields reveals a frequency‐dependent phase difference and amplitude ratio consistent with interference between incident and reflected Alfvén waves. At low frequencies, the E/B ratio is in phase with an amplitude determined by the Pedersen conductance. At higher frequencies, the amplitude and phase change as a function of frequency in good agreement with an ionospheric Alfvén resonator model including Pedersen conductance effects. Indeed, within this Alfvén wave incidence, reflection, and interference paradigm, even quasi‐static field‐aligned currents might be reasonably interpreted as very low frequency (ω → 0) Alfvén waves. Overall, our results not only indicate the importance of Alfvén waves for magnetosphere‐ionosphere coupling but also demonstrate a method for using Swarm data for the innovative experimental diagnosis of Pedersen conductance from low‐Earth orbit satellite measurements.

The study shows evidence that electromagnetic waves in the ionosphere and currents flowing into the ionosphere can be described by the same physical model. This is important for estimating the total energy going into the ionosphere and potentially allows deriving important high‐resolution information about the ionosphere by studying data recorded when spacecraft fly over the auroral region.

Quarter‐wave modes are standing shear Alfvén waves supported along geomagnetic field lines in space. They are predicted to be generated when the ionosphere has very different conductance between the north compared with the south ionosphere. Our previous observation reported that the resonant frequency is sometimes very low around the dawn terminator and suggested these were due to quarter‐wave modes. In this paper, we examine the resonance structure that provides further evidence of the presence of quarter‐wave modes. Data from three magnetometers in New Zealand were analyzed. Four events are discussed which show extraordinarily low eigenfrequencies, wide resonance widths, and strong damping when the ionosphere above New Zealand was in darkness while the conjugate northern hemisphere ionosphere was sunlit. Later in the morning, the eigenfrequencies and resonance widths changed to normal daytime values. The wide resonance width and the strong damping of the quarter‐wave modes arise from strong energy dissipation in the dark side ionosphere. One event exhibited field line resonance structure continuously through a transition from very low frequency to the normal daytime values. The frequency change began when the dawn terminator passed over New Zealand and finished 1 h later when the ratio of the interhemispheric ionospheric conductances decreased and reached ~5. These observations are strong evidence of the presence of quarter‐wave modes and mode conversion from quarter‐ to half‐wave resonances. These experimental results were compared with the ULF wave fields obtained from a 2.5‐dimensional simulation model.

Localized fast flows that impinge on the inner magnetosphere from the plasma sheet are observed to oscillate on time scales of minutes. The compression ahead of these flows will launch fast mode waves, while the velocity shears at the edges of these flows directly excite shear Alfvén waves. These waves, which are coupled by gradients in the Alfvén speed, have been suggested as a source for the Pi1 and Pi2 waves that are observed at both high and low latitudes in the ionosphere. A new three‐dimensional simulation of the propagation of ULF waves in the dipolar region of the magnetosphere has been developed to study these coupled wave modes. This model includes a height‐resolved ionospheric conductivity so that ionospheric fields can be more realistically determined, as well as a direct calculation of ground magnetic fields to compare with ground magnetometers using an inductive ionosphere model. Results from this model show that a plasmaspheric resonance can be set up by waves with periods about 1 min and that field line resonances can be excited both inside and outside the plasmasphere. The use of the inductive ionosphere model leads to the conclusion that even a uniform Hall conductivity can break the dawn‐dusk symmetry of the convection pattern. Waves from a source at 10 Earth radii reach the ionosphere with time delays between high and low latitudes of tens of seconds, with implications for the timing of substorm phenomena observed by spacecraft and by ground magnetometers and radars.

There are two low frequency, magnetised, cold plasma wave modes that propagate through the Earth’s magnetosphere. These are the compressional (fast) and the shear Alfvén modes. The fast mode distributes energy throughout the magnetosphere with the ability to propagate across the magnetic field. Previous studies of coupling between these two modes have often focussed on conditions necessary for mode coupling to occur in the magnetosphere. However, Kato and Tamao (1956) predicted mode coupling would occur for non-zero Hall currents. Recently, the importance of the Hall conductance in the ionosphere for low frequency wave propagation has been studied using one dimensional (1-D) models. In this paper we describe effects of the ionosphere Hall conductance on field line resonance and higher frequency, 0.1–5 Hz waves associated with the Ionospheric Alfvén Resonator (IAR). The Hall conductance reduces the damping time of field line resonances and Joule dissipation into the ionosphere. The Hall conductance also couples shear Alfvén waves trapped in the IAR to fast mode waves that propagate across the ambient magnetic field in an ionospheric waveguide. This coupling leads to the production of low frequency magnetic fields on the ground that can be observed by magnetometers.

A new model for the propagation of ultralow‐frequency (ULF) waves in dipolar geometry has been developed. This model features a full height‐resolved ionosphere including finite Pedersen, Hall, and parallel conductivities. By using a nonorthogonal coordinate system, this model is capable of calculating the ground magnetic field produced by ULF waves and comparing these fields to those measured in the ionosphere and magnetosphere. This model has been used to investigate the properties of the ionospheric Alfvén resonator (IAR) in a dipolar magnetosphere. Although the IAR mode frequencies are not strongly affected by the finite magnetic zenith angle, the damping of these waves is enhanced by the presence of the height‐resolved ionosphere. Pedersen conductivity shields higher frequency ULF waves such as Pc1 from penetrating through the ionosphere, limiting the magnitude of the ground magnetic field, whereas Hall conductivity and finite azimuthal wave number enhance the coupling to the ground. Results for runs in which a wave packet is introduced into the model show that the ground magnetic field is enhanced when the central frequency of the wave packet matches a resonant frequency of the IAR. Including a more realistic height‐resolved ionosphere yields a more direct calculation of ionospheric fields, allowing a comparison between ground and ionospheric fields.

Many measurements of auroral particles, in particular recent measurements from the FAST satellite, indicate that the auroral electron distribution is often broad in energy and field‐aligned in pitch angle. Such electrons are seen in conjunction with strong kinetic Alfvén waves with small perpendicular wavelength, and so the aurora produced by these electrons has been termed the “Alfvénic aurora.” The Alfvénic aurora is predominant at the polar cap boundary of the aurora as well as in the auroral arc that brightens during substorm onset. The process of forming parallel electric fields in Alfvén waves has been investigated by means of three‐dimensional two‐fluid simulations. Waves with small perpendicular wavelengths can be produced by phase mixing when perpendicular gradients are present in the plasma. At lower altitudes, Alfvén waves can interact with the ionospheric Alfvén resonator and phase mix to scales of a few kilometers. At higher altitudes, the electron thermal speed becomes comparable or larger than the Alfvén speed, and parallel electric fields due to the Landau resonance can develop. This has been modeled in the fluid code by an approximation to the plasma dispersion function used in kinetic theory. Phase mixing is most effective when there are strong gradients, such as at the plasma sheet boundary layer. Simulations indicate that these processes can produce parallel electric fields on scales of a few kilometers (in the cold plasma case) to a few tens of kilometers (in the warm plasma case), comparable to the scale sizes of auroral arcs.

In cold magnetospheric plasmas, ultra‐low frequency (ULF) waves occur in either the Alfvén or magnetosonic mode. Owing to the strong inhomogeneity of the near‐Earth plasma, these waves can produce cavity‐like or waveguide‐like eigenmodes which are mutually coupled by wave‐driven ionospheric currents and perpendicular plasma inhomogeneity. Here we present results from a numerical study of the ionospheric Alfvén resonator (IAR) and the ULF waves generated by wave‐driven field‐aligned currents (FACs) in the ionosphere. We demonstrate the excitation of cavity and waveguide eigenmodes of the IAR by a localized field‐aligned current, and examine the polarization patterns of the resultant ground magnetic fields. We find that the distribution of ellipticity reflects the configuration of the magnetospheric source while the distribution of polarization angles depends primarily on the localization of the signal. The pattern of magnetosonic waves generated by ionospheric Hall currents is generally isotropic, but its configuration is representative of the structure of the incident FAC. Apparent preferences for wave propagation eastward and to lower latitudes are identified, and implications for the interpretation of ground magnetic signatures are discussed.

Observations of timing sequences of substorms expected in various onset mechanisms are examined by using a space‐time diagram, which correlates observed space signatures and auroral signatures on the ground during substorm onset. Results from a statistical study of 11 substorms show that signatures in the midtail (x ∼ 15–25 R_E) typically occur before the ground signatures and those in the near‐Earth tail (x ∼ 10 R_E) and that signatures in the midtail region observed prior to the substorm onset often occur at a time which was shorter than that expected from MHD wave propagation between the different regions. This suggests that the disturbance onsets in different active regions do not seem to have a simple causal relationship between them as described by the reconnection or current disruption models of substorms. The activation of perturbed fields and plasma flows in space including the signatures of reconnection and current disruption may occur in multiple localized regions throughout the stressed tail current sheet. The activation seems to be continuously observed well after the substorm onset. These results to some extent are consistent with suggested global Alfvénic interaction considerations, in which the substorm onset is the result of Alfvénic interaction in the global current systems.

Recent observations from the THEMIS mission have focused attention on the timing of events in the magnetotail during magnetospheric substorms and other periods of geomagnetic activity. Standard models of substorms have generally emphasized convective flows as the major source of energy and momentum transport; however, Alfvén wave propagation can also be an important transport mechanism. The propagation of Alfvén waves and the related field-aligned currents are studied by means of ideal MHD simulation of the tail. Perturbations of the cross-tail current can lead to the generation of such waves, and the resulting propagation both through the tail and along the plasma sheet boundary layer can lead to enhanced transport. Implications of this wave propagation on the interpretation of results from the THEMIS mission will be discussed.

Recent observations of particle distributions that are narrow in pitch angle and broad in energy have suggested that kinetic Alfvén waves are a significant contributor to auroral particle acceleration. Oscillations at frequencies near 1 Hz are a natural consequence of the propagation of Alfvén waves in the strongly varying Alfvén speed profile above the auroral ionosphere, the so‐called ionospheric Alfvén resonator. These waves often propagate in the presence of perpendicular density gradients at various spatial scales. Simulations have been performed to study the evolution of these fields including both parallel and perpendicular inhomogeneity. Phase mixing at the boundaries of the density cavity leads to small‐scale Alfvén waves, which can develop the parallel electric fields needed to accelerate the Alfvénic aurora. These simulations verify the kinetic Alfvén wave dispersion relation in the electron inertial limit, which predicts that the perpendicular phase and group velocity of these waves are in the opposite direction. In addition, the results show that narrow spatial scales are favored by high ionospheric conductance.

The kinetic Alfvén wave has been recognized as an important wave mode in magnetospheric plasmas and laboratory plasmas, and has potential application in many areas of cosmic plasma physics. The kinetic dispersion relation of this mode has been described including finite frequency and finite ion gyroradius corrections. Laboratory plasmas as well as plasmas in space often contain strong gradients perpendicular to the background magnetic field. In this case, the dispersion relation must be generalized to include changes in the plasma parameters on each side of the gradient. In the presence of such gradients, localized modes can be found in the plasma. Depending on the relative values of the Alfvén speed and the plasma beta across these gradients, these modes can be trapped within the cavity or enhancement or propagate across the gradient.

The strong inhomogeneities in plasma parameters in the ionosphere and adjacent regions can trap waves in the upper end of the ULF range (Pc1/Pi1). The topside ionosphere is characterized by a rapidly increasing Alfvén speed with a scale height the order of 1000 km. Shear mode Alfvén waves in this region can be partially trapped at frequencies in the 0.1-1.0 Hz range. The same structure can trap fast mode compressional waves in this frequency band. Since these waves can propagate across magnetic field lines, this structure constitutes a waveguide in which energy can propagate at speeds comparable to the Alfvén speed, typically the order of 1000 km/s. Hall effects in the ionosphere couple these two wave modes, so that the introduction of a field-aligned current by means of a shear mode Alfvén wave can excite compressional waves that can propagate in the waveguide. In the limit of infinite ionospheric conductivity, these waves are isolated from the atmospheric fields; however, for finite conductivity, ionospheric and atmospheric waves are coupled. TM modes in the atmosphere can propagate at ULF frequencies, and form global Schumann resonances, with the fundamental at 8 Hz. It has been suggested that signals that propagate at the speed of light through this atmospheric waveguide can rapidly transmit signals from the polar region to lower latitudes during storm sudden commencements.

Many numerical models of magnetospheric dynamics treat the ionosphere as an inner boundary condition. These models have traditionally used the current continuity condition, treating the ionosphere as a sheet current in which the electric field is electrostatic. A more general boundary condition is suggested that not only is more complete, but also straightforward to implement. Results from a model using this boundary condition applied to the excitation of field line resonances in the magnetosphere are presented.

A linear, one‐dimensional gyrofluid code has been used to determine the characteristics of propagating Alfvén waves and the ionospheric Alfvén resonator on a Jupiter‐Io flux tube. This model includes electron inertia, electron pressure gradient, and finite ion gyroradius effects, as well as the displacement current correction to prevent the Alfvén velocity from exceeding the speed of light. A quasi‐steady Vlasov code provides realistic density profiles along the flux tube as input parameters for the gyrofluid model. In this paper, we demonstrate that the majority of the wave energy from an initial pulse with a long wavelength (∼0.1 R_J) is unable to reach Jupiter’s ionosphere without wave breaking, phase mixing, and/or other nonlinear processes; however, a significant energy flux may be transferred via high‐frequency, small‐wavelength waves to the ionosphere. The waves that reach the ionosphere stimulate an ionospheric Alfvén resonator which is generated between the ionospheric boundary and the first velocity peak of the Alfvén phase speed. The ionospheric density and scale height play important roles to determine the resonant frequency. The eigenfrequency decreases with increasing scale height and with increasing ionospheric density. The fundamental frequency and higher harmonics of the Alfvén resonator are comparable to the observed reoccurring frequency of S bursts between a few and hundreds of Hz. On the basis of this information, we suggest the Alfvén resonator as the likely driver explaining multiple occurrences of S bursts.

This article explores a possible relationship between S bursts and trapped Alfvén waves in Jupiter’s upper ionosphere. Eigenmodes of inertial Alfvén waves in Jupiter’s ionosphere are predicted to have frequencies (∼20 Hz) that match the repetition frequency of S bursts and the two phenomena are colocated, suggesting such an association is possible. Electron acceleration or modulation may provide the physical mechanism that transfers energy from the Alfvén wave to the S burst. Inertial Alfvén waves are known to accelerate electrons with fluxes that are modulated at Alfvén wave eigenmode frequencies. The modulated electron fluxes, in turn, may generate or modulate the generation of the S burst emissions. The exact growth mechanism has not been identified, but we put forth and discuss two possibilities, an anti‐Jovian electron beam or a ring distribution created from impulsive acceleration and mirroring. Since the Alfvén wave eigenmode phenomena and electron acceleration are seen on Earth, we rely heavily on analogy with Earth‐based observations.

We show for the first time the dynamical relationship between the generation of magnetic field-aligned electric field (E||) and the temporal changes and spatial gradients of magnetic and velocity shears, and the plasma density in Earth’s magnetosphere. We predict that the signatures of reconnection and auroral particle acceleration should have a correlation with low plasma density, and a localized voltage drop (V||) should often be associated with a localized magnetic stress concentration. Previous interpretations of the E|| generation are mostly based on the generalized Ohm’s law, causing serious confusion in understanding the nature of reconnection and auroral acceleration.

The interaction of auroral electrons with kinetic Alfvén waves is complicated by the fact that the Alfvén speed above the ionosphere is strongly inhomogeneous, leading to a region often referred to as the ionospheric Alfvén resonator (IAR). For these waves, the wave‐particle interaction must be treated with a nonlocal kinetic approach. Linear damping of these waves due to the wave‐particle interaction has been calculated based on a quasi‐dipolar field line model; however, particle orbits in the wave field are not well described by perturbation theory due to the development of new turning points in the particle trajectories, especially for low‐energy particles. Full orbit calculations of such particles have been performed in order to assess the validity of the linear theory and to determine how much wave energy is converted into electron energy flux that is precipitated into the ionosphere. In addition, the precipitating electrons show a phase shift with respect to the field‐aligned current in the waves, leading to a modification of theories of ionospheric feedback in the ionospheric Alfvén resonator.

Numerical modeling of magnetosphere‐ionosphere coupling by Alfvén waves has proven to be a valuable tool in describing the propagation and evolution of field‐aligned currents and the magnetic fields produced by these waves as observed on the ground. Although many models of this type have assumed that magnetic field lines penetrate the ionosphere vertically, this assumption is not valid at lower latitudes, where the dipole tilt is significant. This paper presents a new model of this interaction that takes the dipole geometry into account, while including an ionosphere that is radially stratified. Since the orthogonal dipole coordinates that have been used in previous studies do not come to a constant radial distance at the ionosphere, a nonorthogonal system is developed that reduces to the orthogonal system at high altitudes. This model is useful for many different problems of wave coupling and is applied here to the propagation of ducted Pc1 oscillations that can propagate thousands of kilometers across magnetic field lines.

Recent observations have indicated that in addition to the quasi‐static acceleration of electrons in inverted V structures, auroral electrons frequently have a spectrum that is broad in energy and confined to parallel pitch angles, indicative of acceleration in low‐frequency waves. Test particle models have indicated that these electrons may be accelerated by the parallel electric fields in kinetic Alfvén waves. However, such models are not self‐consistent, in that the wave structure is not influenced by the accelerated particles. A nonlocal kinetic theory of electrons along auroral field lines is necessary to provide this self‐consistency. Results from such a model based on electron motions on dipole field lines are presented. For a typical Alfvén speed profile, kinetic effects lead to significant energy dissipation when the electron temperature exceeds ∼100 eV. The dissipation generally occurs near the peak of the Alfvén speed profile. This dissipation generally increases with increasing temperature and decreasing perpendicular wavelength up to ∼1 keV and 10 km, respectively. At larger temperatures and smaller perpendicular wavelengths the dissipation begins to decrease and the ionospheric Joule dissipation goes to zero, indicating that the wave is reflected from the dissipation region. Dissipation in the 0.1–1.0 Hz band is structured by the modes of the ionospheric Alfvén resonator.

Recent observations have indicated that in addition to the classical “inverted‐V” type electron acceleration, auroral electrons often have a field‐aligned distribution that is broad in energy and sometimes shows time dispersion indicating acceleration at various altitudes up the field line. Such acceleration is not consistent with a purely electrostatic potential drop and suggests a wave heating of auroral electrons. Alfvén waves have been observed on auroral field lines carrying sufficient Poynting flux to provide energy for such acceleration. Calculations based on the linear kinetic theory of Alfvén waves indicate that Landau damping of these waves can efficiently convert this Poynting flux into field‐aligned acceleration of electrons. At high altitudes along auroral field lines that map into the plasma sheet boundary layer (PSBL), the plasma gradients are relatively weak and the local kinetic theory can describe this wave–particle interaction. At lower altitudes, the gradient in the Alfvén speed becomes significant, and a nonlocal description must be used. A nonlocal theory based on a simplified model of the ionospheric Alfvén resonator (IAR) is presented. For a given field‐aligned current (FAC), the efficiency of the wave–particle interaction increases with the ratio of the thermal velocity of the electrons to the Alfvén speed at high altitudes. These calculations indicate that wave acceleration of electrons should occur at and above the altitude where the quasi‐static potential drops form.

The ionospheric feedback instability has been invoked as a possible mechanism for the formation of narrow auroral arcs. This instability can excite eigenmodes of both field line resonances and the ionospheric Alfvén resonator, producing narrow‐scale structures. Although the basic dispersion relation of this instability has been discussed for both of these cases, the energetics of this instability has not been discussed quantitatively and questions remain as to the nonlinear evolution of this instability. The free energy for this instability comes from the reduction of Joule heating due to the preexisting convection caused by the self‐consistent changes in ionization and conductivity due to Alfvénic perturbations on the ionosphere. In an active ionosphere, narrow‐scale Alfvén waves can be overreflected; i.e., the reflected wave can have a larger amplitude than the incident wave, with the extra energy coming from a local reduction of Joule heating. Recombination produces a damping of this instability, particularly for high background conductivity, indicating that this instability operates best in a dark background ionosphere. This feedback interaction produces narrow‐scale currents when strong gradients in the conductivity are produced, and effects from parallel resistivity or possibly kinetic effects will become important in its evolution. Theoretical constraints on low‐spatial resolution observations of the energy dissipated by precipitation as opposed to Joule heating will be discussed.

The propagation of Alfvén waves in the auroral ionosphere is important in the determination of ground signatures of time-varying currents, in the formation of Pc1 compressional waves that can be ducted in the ionospheric waveguide, and in the development of field-aligned currents and parallel electric fields during auroral acceleration processes. This report presents the first results from a three-dimensional model of the linear propagation of these waves. In this model, the ionosphere is treated as a thin slab carrying Pedersen and Hall currents. The jump conditions across this boundary lead to the coupling of shear and compressional MHD modes at the ionosphere and also allow the ground signatures of these waves to be calculated within the context of the model. This model has been used to study this coupling and to illustrate the excitation and propagation of compressional MHD waves within the ionospheric waveguide. A new numerical scheme for the modeling of parallel electric fields is introduced and the excitation of resonance cone structures by narrow impulses is demonstrated.