Field Line Resonance Research Articles

Multisatellite observations of the magnetosphere response to changes in the solar wind and interplanetary magnetic field

Abstract. We employ multipoint observations of the Van Allen Probes, THEMIS, GOES and Cluster to present case and statistical studies of the electromagnetic field, plasma and particle response to interplanetary (IP) shocks observed by the Wind satellite. On 27 February 2014 the initial encounter of an IP shock with the magnetopause occurred on the postnoon magnetosphere, consistent with the observed alignment of the shock with the spiral IMF. The dayside equatorial magnetosphere exhibited a dusk–dawn oscillatory electrical field with a period of ∼330 s and peak-to-peak amplitudes of ∼15 mV m−1 for a period of 30 min. The intensity of electrons in the energy range from 31.5 to 342 KeV responded with periods corresponding to the shock-induced ULF (ultralow frequency) electric field waves. We then perform a statistical study of Ey variations of the electric field and associated plasma drift flow velocities for 60 magnetospheric events during the passage of interplanetary shocks. The Ey perturbations are negative (dusk-to-dawn) in the dayside magnetosphere (followed by positive or oscillatory perturbations) and dominantly positive (dawn-to-dusk direction) in the nightside magnetosphere, particularly near the Sun–Earth line within an L-shell range from 2.5 to 5. The typical observed amplitudes range from 0.2 to 6 mV m−1 but can reach 12 mV during strong magnetic storms. We show that electric field perturbations increase with solar wind pressure, and the changes are especially marked in the dayside magnetosphere. The direction of the Vx component of plasma flow is in agreement with the direction of the Ey component and is antisunward at all local times except the nightside magnetosphere, where it is sunward near the Sun–Earth line. The flow velocities Vx range from 0. 2 to 40 km s−1 and are a factor of 5 to 10 times stronger near noon as they correspond to greater variations of the electric field in this region. We demonstrate that the shock-induced electric field signatures can be classified into four different groups according to the initial Ey electric field response and these signatures are dependent on local time. Negative and bipolar pulses predominate on the dayside while positive pulses occur on the nightside. The ULF electric field pulsations of Pc and Pi types produced by IP shocks are observed at all local times and in the range of periods from several tens of seconds to several minutes. We believe that most electric field pulsations of the Pc5 type in the dayside magnetosphere at L<6 are produced by field line resonances. We show that the direction of the shock normal determines the direction of the propagation of the shock-induced magnetic and plasma disturbances. The observed directions of velocity Vy predominately agree with those expected for the given spiral or orthospiral shock normal orientation.

Dayside Magnetospheric and Ionospheric Responses to a Foreshock Transient on 25 June 2008: 1. FLR Observed by Satellite and Ground‐Based Magnetometers

AbstractAs one type of driver of magnetospheric Alfvén waves, foreshock transients have received less attention than, for example, the Kelvin‐Helmholtz instability, discrete and broadband frequency solar wind dynamic pressure oscillations, and interplanetary shocks. Previous works show that foreshock transients can induce both Alfvén mode and compressional mode Pc 3–5 ULF waves inside the magnetosphere. However, to our knowledge, none of these reported Pc 3–5 waves, induced by foreshock transients, are proved to be localized in the magnetosphere. In this paper, using in situ and ground‐based observations, we report the generation of localized magnetospheric compressional waves and field line resonances (FLRs) by a foreshock transient. Both the foreshock transient and Pc 5 ULF waves were found on the duskside; while on the morning side of the magnetosphere, no clear wave signatures were captured. Our results demonstrate that in addition to the global effects of foreshock transients on the magnetosphere reported earlier, foreshock transients can also generate localized magnetospheric responses in the Pc 5 range with clear dawn‐dusk asymmetry. A suite of eight dayside spacecraft plus ground magnetometer measurements make possible the determination of the foreshock transient driver and dawn‐dusk asymmetry of the magnetospheric response not previously reported with such a complete data set.

Modeling the Dawn/Dusk Asymmetry of Field Line Resonances

AbstractField line resonances (FLRs) are observed to occur preferentially and have larger amplitudes at dawn compared to dusk. We present simulations of FLR excitation in a magnetospheric waveguide that can reproduce this behavior. Crucially, our equilibrium is asymmetric about noon. Even when this system is driven in a symmetric fashion about noon, the fast waves that are established in the magnetosphere develop asymmetries—as do the FLRs they excite. Fast mode ray trajectories are employed to show that the asymmetry evolves due to refraction. Preferential FLR excitation at dawn is further reinforced by calculating the Resonance Map. This shows that the Resonant Zone at dawn coincides with a large‐amplitude coherent fast mode driver, which is not the case at dusk. These factors result in FLRs having a larger amplitude at dawn compared to dusk.

Electron Distributions in Kinetic Scale Field Line Resonances: A Comparison of Simulations and Observations

AbstractObservations in kinetic scale field line resonances, or eigenmodes of the geomagnetic field, reveal highly field‐aligned plateaued electron distributions. By combining observations from the Van Allen Probes and Cluster spacecraft with a hybrid kinetic gyrofluid simulation we show how these distributions arise from the nonlocal self‐consistent interaction of electrons with the wavefield. This interaction is manifested as electron trapping in the standing wave potential. The process operates along most of the field line and qualitatively accounts for electron observations near the equatorial plane and at higher latitudes. In conjunction with the highly field‐aligned plateaus, loss cone features are also evident, which result from the action of the upward‐directed wave parallel electric field on the untrapped electron populations.

A Statistical Survey of the 630.0‐nm Optical Signature of Periodic Auroral Arcs Resulting From Magnetospheric Field Line Resonances

AbstractAdvances in networks of ground‐based optical instrumentation have enabled us to identify over 400 examples of auroral arcs with an infrequently observed, temporally periodic auroral morphology. This study focuses on these arcs observed via the 630‐nm (“redline”) auroral emission wavelength and connects them to global magnetospheric wave modes known as field line resonances (FLRs). We show that optical redline FLR auroral arcs occur most frequently near 20 and 4 magnetic local time, in contrast to nonperiodic redline arcs, which occur most frequently near midnight. We find that this periodic type of auroral arc is rare, occurring in approximately 5% of redline aurora observed by the Redline Emission Geospace Observatory all‐sky imagers. We also show Swarm satellite observations of two separate instances of 630‐nm FLR arcs with strong upward field‐aligned currents of the order of 3–6 μA/m2.

On the relevance of source effects in geomagnetic pulsations for induction soundings

Abstract. This study is an attempt to close a gap between recent research on geomagnetic pulsations and their usage as source signals in electromagnetic induction soundings (i.e., magnetotellurics, geomagnetic depth sounding, and magnetovariational sounding). The plane-wave assumption as a precondition for the proper performance of these methods is partly violated by the local nature of field line resonances which cause a considerable portion of pulsations at mid latitudes. It is demonstrated that and explained why in spite of this, the application of remote reference stations in quasi-global distances for the suppression of local correlated-noise effects in induction arrows is possible in the geomagnetic pulsation range. The important role of upstream waves and of the magnetic equatorial region for such applications is emphasized. Furthermore, the principal difference between application of reference stations for local transfer functions (which result in sounding curves and induction arrows) and for inter-station transfer functions is considered. The preconditions for the latter are much stricter than for the former. Hence a failure to estimate an inter-station transfer function to be interpreted in terms of electromagnetic induction, e.g., because of field line resonances, does not necessarily prohibit use of the station pair for a remote reference estimation of the impedance tensor.

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

AbstractDuring 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.

Variations of High‐Latitude Geomagnetic Pulsation Frequencies: A Comparison of Time‐of‐Flight Estimates and IMAGE Magnetometer Observations

AbstractThe fundamental eigenfrequencies of standing Alfvén waves on closed geomagnetic field lines are estimated for the region spanning 5.9≤L < 9.5 over all MLT (Magnetic Local Time). The T96 magnetic field model and a realistic empirical plasma mass density model are employed using the time‐of‐flight approximation, refining previous calculations that assumed a relatively simplistic mass density model. An assessment of the implications of using different mass density models in the time‐of‐flight calculations is presented. The calculated frequencies exhibit dependences on field line footprint magnetic latitude and MLT, which are attributed to both magnetic field configuration and spatial variations in mass density. In order to assess the validity of the time‐of‐flight calculated frequencies, the estimates are compared to observations of FLR (Field Line Resonance) frequencies. Using IMAGE (International Monitor for Auroral Geomagnetic Effects) ground magnetometer observations obtained between 2001 and 2012, an automated FLR identification method is developed, based on the cross‐phase technique. The average FLR frequency is determined, including variations with footprint latitude and MLT, and compared to the time‐of‐flight analysis. The results show agreement in the latitudinal and local time dependences. Furthermore, with the use of the realistic mass density model in the time‐of‐flight calculations, closer agreement with the observed FLR frequencies is obtained. The study is limited by the latitudinal coverage of the IMAGE magnetometer array, and future work will aim to extend the ground magnetometer data used to include additional magnetometer arrays.

Signatures of Alfvenic Field-Line Resonance in the Behavior of Preonset Auroral Arcs

The evolution of preonset auroral arcs before full-scale auroral poleward expansion (the time T0 indicates the expansion onset) is studied based on ground-based optical observations filtered by the gradient method. In one of the three events studied in detail, the preonset arc exhibits periodic poleward excursions ~10 min before T0. The excursions extend over 1° in latitude, being repeated with a period of 2.5 min (frequency 6.7 mHz), and can be explained by the theory of classical (i.e., linear nondispersive) Alfvenic fieldline resonance (FLR), which is proposed to form and evolve at the location of subsequent substorm initiation. In two other events, the preonset arc evolves somewhat differently. Having appeared 15–20 min before T0, the arc brightens and develops a fine structure in the transverse direction, with new arcs detaching and propagating away from it. Such signatures may indicate a nonlinear dispersive FLR that periodically produces soliton-like structures propagating across and away from the resonance layer. The involved nonlinearity has a ponderomotive nature. The dispersive effects become significant if, as a result of fine structuring, perturbations are produced on the scales of order of the electron inertial length or ion gyroradius.

The Broadband Excitation of 3‐D Alfvén Resonances in a MHD Waveguide

AbstractThis paper considers the resonant coupling of fast and Alfvén magnetohydrodynamic (MHD) waves. We perform numerical simulations of the time‐dependent excitation of Alfvén resonances in a dipole magnetic field, with nonuniform density providing a 3‐D equilibrium. Wright and Elsden (2016) showed that in such a system where the poloidal and toroidal Alfvén eigenfrequencies are different, the resonance can have an intermediate polarization, between poloidal and toroidal. We extend this work by driving the system with a broadband rather than monochromatic source. Further, we investigate the effect of azimuthal inhomogeneity on the resonance path. It is found that when exposed to a broadband driver, the dominant frequencies are the fast waveguide eigenfrequencies, which act as the drivers of Alfvén resonances. We demonstrate how resonances can still form efficiently with significant amplitudes, even when forced by the medium to have a far from toroidal polarization. Indeed, larger‐amplitude resonances can be generated with an intermediate polarization, rather than purely toroidal, as a result of larger gradients in the magnetic pressure formed by the azimuthal inhomogeneity. Importantly, the resonance structure is shown to be independent of the different forms of driving, meaning their locations and orientations may be used to infer properties of the equilibrium. However, the amplitude of the FLRs are sensitive to the spatial structure and frequency spectrum of the magnetopause driving. These results have implications for the structure of field line resonances (FLRs) in Earth's magnetosphere, although the focus of this paper is on the underlying physics involved.

Comprehensive Analysis of the Geoeffective Solar Event of 21 June 2015: Effects on the Magnetosphere, Plasmasphere, and Ionosphere Systems

A full-halo coronal mass ejection (CME) left the Sun on 21 June 2015 from active region (AR) NOAA 12371. It encountered Earth on 22 June 2015 and generated a strong geomagnetic storm whose minimum Dst value was −204 nT. The CME was associated with an M2-class flare observed at 01:42 UT, located near disk center (N12 E16). Using satellite data from solar, heliospheric, and magnetospheric missions and ground-based instruments, we performed a comprehensive Sun-to-Earth analysis. In particular, we analyzed the active region evolution using ground-based and satellite instruments (Big Bear Solar Observatory (BBSO), Interface Region Imaging Spectrograph (IRIS), Hinode, Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO), Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI), covering H $\upalpha$ , EUV, UV, and X-ray data); the AR magnetograms, using data from SDO/Helioseismic and Magnetic Imager (HMI); the high-energy particle data, using the Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics (PAMELA) instrument; and the Rome neutron monitor measurements to assess the effects of the interplanetary perturbation on cosmic-ray intensity. We also evaluated the 1 – 8 A soft X-ray data and the ${\sim}\, 1$ MHz type III radio burst time-integrated intensity (or fluence) of the flare in order to predict the associated solar energetic particle (SEP) event using the model developed by Laurenza et al. (Space Weather 7(4), 2009). In addition, using ground-based observations from lower to higher latitudes (International Real-time Magnetic Observatory Network (INTERMAGNET) and European Quasi-Meridional Magnetometer Array (EMMA)), we reconstructed the ionospheric current system associated with the geomagnetic sudden impulse (SI). Furthermore, Super Dual Auroral Radar Network (SuperDARN) measurements were used to image the global ionospheric polar convection during the SI and during the principal phases of the geomagnetic storm. In addition, to investigate the influence of the disturbed electric field on the low-latitude ionosphere induced by geomagnetic storms, we focused on the morphology of the crests of the equatorial ionospheric anomaly by the simultaneous use of the Global Navigation Satellite System (GNSS) receivers, ionosondes, and Langmuir probes onboard the Swarm constellation satellites. Moreover, we investigated the dynamics of the plasmasphere during the different phases of the geomagnetic storm by examining the time evolution of the radial profiles of the equatorial plasma mass density derived from field line resonances detected at the EMMA network ( $1.5 < \mathrm{L} < 6.5$ ). Finally, we present the general features of the geomagnetic response to the CME by applying innovative data analysis tools that allow us to investigate the time variation of ground-based observations of the Earth’s magnetic field during the associated geomagnetic storm.

Synchronization of Human Autonomic Nervous System Rhythms with Geomagnetic Activity in Human Subjects.

A coupling between geomagnetic activity and the human nervous system’s function was identified by virtue of continuous monitoring of heart rate variability (HRV) and the time-varying geomagnetic field over a 31-day period in a group of 10 individuals who went about their normal day-to-day lives. A time series correlation analysis identified a response of the group’s autonomic nervous systems to various dynamic changes in the solar, cosmic ray, and ambient magnetic field. Correlation coefficients and p values were calculated between the HRV variables and environmental measures during three distinct time periods of environmental activity. There were significant correlations between the group’s HRV and solar wind speed, Kp, Ap, solar radio flux, cosmic ray counts, Schumann resonance power, and the total variations in the magnetic field. In addition, the time series data were time synchronized and normalized, after which all circadian rhythms were removed. It was found that the participants’ HRV rhythms synchronized across the 31-day period at a period of approximately 2.5 days, even though all participants were in separate locations. Overall, this suggests that daily autonomic nervous system activity not only responds to changes in solar and geomagnetic activity, but is synchronized with the time-varying magnetic fields associated with geomagnetic field-line resonances and Schumann resonances.

Energy‐banded ions in Saturn's magnetosphere

AbstractUsing data from the Cassini Plasma Spectrometer ion mass spectrometer, we report the first observation of energy‐banded ions at Saturn. Observed near midnight at relatively high magnetic latitudes, the banded ions are dominantly H+, and they occupy the range of energies typically associated with the thermal pickup distribution in the inner magnetosphere (L &lt; 10), but their energies decline monotonically with increasing radial distance (or time or decreasing latitude). Their pitch angle distribution suggests a source at low (or slightly southern) latitudes. The band energies, including their pitch angle dependence, are consistent with a bounce‐resonant interaction between thermal H+ ions and the standing wave structure of a field line resonance. There is additional evidence in the pitch angle dependence of the band energies that the particles in each band may have a common time of flight from their most recent interaction with the wave, which may have been at slightly southern latitudes. Thus, while the particles are basically bounce resonant, their energization may be dominated by their most recent encounter with the standing wave.

Equatorward propagating auroral arcs driven by ULF wave activity: Multipoint ground‐ and space‐based observations in the dusk sector auroral oval

AbstractObservations of multiple equatorward propagating arcs driven by a resonant Alfvén wave on closed field lines are presented. Data sets from the European Incoherent Scatter Svalbard Radar (ESR) and Meridian Scanning Photometer in Longyearbyen, All‐Sky Camera in Ny Ålesund, ground magnetometer data in Svalbard, and Defense Meteorological Satellite Program (DMSP) F16 satellite were utilized to study the arc structures. The arcs had an equatorward phase propagation of ~0.46 km s−1 and were observed in the dusk ionosphere from 1800 to 2030 magnetic local time. Analysis of the optical data indicates that the Alfvén wave had a frequency of 1.63 mHz and an azimuthal wave number, m ~ −20 (the negative sign indicating a westward propagation). Inverted‐V electron populations associated with field‐aligned currents of between 0.5 and 0.8 μA m−2 are observed by DMSP F16 inside the arc structures. In addition to electron density enhancements associated with the arcs, the ESR data show elevated ion temperatures in between the arcs consistent with electric field enhancements and ionospheric heating effects. The combination of ESR and DMSP F16 data indicates that the wave energy was dissipated through ionospheric Joule and/or ion frictional heating and acceleration of particles into the ionosphere, generating the auroral displays. The fine‐scale structuring, in addition to the propagation direction and scale size, would suggest that the auroral features are the signatures of a field line resonance driven by an interaction with a compressional fast mode wave propagating earthward from the magnetotail.

A multispacecraft event study of Pc5 ultralow‐frequency waves in the magnetosphere and their external drivers

AbstractWe investigate a quiet time event of magnetospheric Pc5 ultralow‐frequency (ULF) waves and their likely external drivers using multiple spacecraft observations. Enhancements of electric and magnetic field perturbations in two narrow frequency bands, 1.5–2 mHz and 3.5–4 mHz, were observed over a large radial distance range from r ~ 5 to 11 RE. During the first half of this event, perturbations were mainly observed in the transverse components and only in the 3.5–4 mHz band. In comparison, enhancements were stronger during the second half in both transverse and compressional components and in both frequency bands. No indication of field line resonances was found for these magnetic field perturbations. Perturbations in these two bands were also observed in the magnetosheath, but not in the solar wind dynamic pressure perturbations. For the first interval, good correlations between the flow perturbations in the magnetosphere and magnetosheath and an indirect signature for Kelvin‐Helmholtz (K‐H) vortices suggest K‐H surface waves as the driver. For the second interval, good correlations are found between the magnetosheath dynamic pressure perturbations, magnetopause deformation, and magnetospheric waves, all in good correspondence to interplanetary magnetic field (IMF) discontinuities. The characteristics of these perturbations can be explained by being driven by foreshock perturbations resulting from these IMF discontinuities. This event shows that even during quiet periods, K‐H‐unstable magnetopause and ion foreshock perturbations can combine to create a highly dynamic magnetospheric ULF wave environment.

Global observations of magnetospheric high-m poloidal waves during the 22 June 2015 magnetic storm.

We report global observations of high‐m poloidal waves during the recovery phase of the 22 June 2015 magnetic storm from a constellation of widely spaced satellites of five missions including Magnetospheric Multiscale (MMS), Van Allen Probes, Time History of Events and Macroscale Interactions during Substorm (THEMIS), Cluster, and Geostationary Operational Environmental Satellites (GOES). The combined observations demonstrate the global spatial extent of storm time poloidal waves. MMS observations confirm high azimuthal wave numbers (m ~ 100). Mode identification indicates the waves are associated with the second harmonic of field line resonances. The wave frequencies exhibit a decreasing trend as L increases, distinguishing them from the single‐frequency global poloidal modes normally observed during quiet times. Detailed examination of the instantaneous frequency reveals discrete spatial structures with step‐like frequency changes along L. Each discrete L shell has a steady wave frequency and spans about 1 R E, suggesting that there exist a discrete number of drift‐bounce resonance regions across L shells during storm times.

SC-Triggered 1.6mHz Waves Including an Interval with Latitude-Dependent Phase Shift, Observed by the SuperDARN Hokkaido East Radar in Mid Latitudes: Possible Global Magnetospheric Cavity-Mode Waves and Their Field-Line Resonance with Poloidal Alfven-Mode Waves

In this paper we present a new kind of wave event found in the ground/sea backscattered data of the SuperDARN Hokkaido East radar, located in the mid-latitude area at the AACGM latitude (longitude) of 36.5° (214.7°). The wave event started at the time of an SC at ~09:50 UT on Aug 19, 2009, and continued for about an hour until ~10:50 UT: This relatively short-living wave event, probably triggered by the SC, could be classified as a type different from the typical type seen in the ground/sea backscattered data of SuperDARN radars, i.e., waves which start without a clearly identifiable trigger and continue for a long time (4~5 hours) (e.g., Ponomarenko et al. 2003). Comparisons with ground magnetometer data suggest that the major part of this event consisted of global magnetospheric cavity-mode waves whose typical frequency is in the order of 1mHz (e.g., Kivelson and Southwood 1985, 1986). In addition, in the interval of 10:26~10:42UT which was embedded in the above-stated one-hour interval, we have found the amplitude and phase pattern typically observed when the field-line resonance (FLR) takes place; this pattern is found for the first time in the mid-latitude ground/sea backscattered data, and suggests excitation of poloidal Alfven-mode field-line eigenoscillations during this interval.

Solar wind‐driven Pc5 waves observed at a polar cap station and in the near cusp ionosphere

AbstractWe present the results of a comparative study conducted in Antarctica by using the ULF geomagnetic field measurements at Terra Nova Bay (Altitude Adjusted Corrected Geomagnetic Coordinates latitude 80°S) and simultaneous data from the Super Dual Auroral Radar Network radar at South Pole Station. Pc5 waves observed at Terra Nova Bay around local magnetic noon, when the station is close to the dayside cusp, can be interpreted as spatial integrated signals, produced by ionospheric currents associated to field line resonances at somewhat lower latitudes. The radar, providing the Doppler velocities of ionospheric plasma over a range of geomagnetic latitudes, allows to detect the occurrence of such field line resonances. In the reported case, our analysis shows evidence of resonant signals in the ionosphere at 75°S and 76°S that find correspondence in frequency and time with the geomagnetic signals observed at Terra Nova Bay around local noon. During the period of interest, oscillations of the solar wind dynamic pressure at the same frequency are detected by Geotail, just upstream of the morning flank of the bow shock. All the observations are consistent with the interpretation of the signals at Terra Nova Bay in terms of signatures of field line resonances occurring at lower latitudes, driven by solar wind oscillations transmitted into the magnetosphere. We discuss also the possibility of an additional contribution to the signals at Terra Nova Bay, due to the direct propagation of the solar wind waves along the local open field line.

Energization of outer radiation belt electrons during storm recovery phase

AbstractWe use test particle simulations incorporating an MHD model of ULF wave propagation in the magnetosphere with realistic ionosphere boundary conditions to study electron energization in the dayside outer Van Allen radiation belt, referenced to in situ particle and wave observations. On 7 January 2011 the THEMIS spacecraft detected 3 and 4–5 mHz waves simultaneous with flux enhancement of &gt;10 keV electrons during the early recovery phase of a moderate geomagnetic storm. We find that internal energization of equatorially mirroring electrons via nonresonant ULF wave‐particle interactions can explain these observations. The wave poloidal components cause radial drift of electrons, increasing (decreasing) their kinetic energy as they move inward (outward). Electrons with initial kinetic energies of a few keV can be energized to double these values within an hour by interaction with the 3 mHz waves. The energization rate is somewhat less for the 4–5 mHz waves. An increase in the ionospheric conductance decreases the power of the fast mode wave, reducing radial drift velocities and hence decreasing the rate of energization. The fast mode poloidal field varies with radial distance and longitude, and this also affects energization. Electrons which drift outward encounter a region where the toroidal field due to the field line resonance becomes dominant and produces strong azimuthal drift. These electrons become trapped in an L‐shell range just outward of the resonance region and are not energized.

Latitudinal amplitude-phase structure of MHD waves: STARE radar and image magnetometer observations and modeling

We have developed a numerical model that yields a steady-state distribution of field components of MHD wave in an inhomogeneous plasma box simulating the realistic magnetosphere. The problem of adequate boundary condition at the ionosphere–magnetosphere interface for coupled MHD mode is considered. To justify the model’s assumptions, we have derived the explicit inequality showing when the ionospheric inductive Hall effect can be neglected upon the consideration of Alfven wave reflection from the ionospheric boundaries. The model predicts a feature of the ULF spatial amplitude/phase distribution that has not been noticed by the field line resonance theory: the existence of a region with opposite phase delays on the source side of the resonance. This theoretical prediction is supported by the amplitude-phase latitudinal structures of Pc5 waves observed by STARE radar and IMAGE magnetometers. A gradual decrease in azimuthal wave number m at smaller L-shells was observed at longitudinally separated radar beams.