Field Line Resonance Research Articles

Comprehensive survey of Pc4 and Pc5 band spectral content in Cluster magnetic field data

Abstract. In the first part of this study we present two case studies of pulsations that, with the help of ground-based data, are identified as field line resonances (FLRs). These pulsations occurred at frequencies which belong to a set of frequencies that has been suggested to be preferred in the terrestrial magnetosphere (CMS frequencies). We go on to show that for both events there is a significant signature at the same frequency in the time series of the compressional magnetic field observed by the conjugate Cluster satellites. We interpret these as signatures of the compressional mode driving the FLRs. In the second part we present a statistical study including one year's worth of Cluster magnetic field data. For each orbit between May 2004 and June 2005 we identified a three hour interval during which the satellites were located on closed magnetic field lines. We identified peaks in the spectrum between 1.0 and 15.0 mHz of the compressional, poloidal and toroidal components of the magnetic field. We use this database of spectral peaks observed on closed magnetic field lines to investigate whether peaks occur at a preferred set of frequencies which would be indicative for the Earth's magnetosphere behaving like a cavity/waveguide. We find no consistent preference for all CMS frequencies in our dataset, however we do find a preference for certain higher frequencies suggesting that higher harmonics of the cavity/waveguide are a persistent feature of the inner magnetosphere, and are detected by the Cluster spacecraft. This result could be explained by the polar orbit of the Cluster satellites.

Plasmaspheric dynamics resulting from the Hallowe'en 2003 geomagnetic storms

Cross‐phase‐derived plasma mass density trends during the Hallowe'en 2003 geomagnetic storms are presented for 38° ≲ magnetic latitude ≲ 63° (1.61 ≤ L ≤ 5.10), using data from the SAMNET (Subauroral Magnetometer Network), BGS (British Geological Survey), and SEGMA (South European Geomagnetic Array), ground‐based magnetometer arrays in Europe. At all latitudes monitored, a rapid increase of total mass density is observed immediately following the initial storm sudden commencement at 0611 UT on 29 October, believed to be due to rapid ionospheric O+ outflow. Plasmaspheric density depletion to at least 50° magnetic latitude (L ∼ 2.4) took place over the next 3 days. Poststorm refilling began on 2 November. Following the sudden commencement of another storm on 4 November, a density enhancement was monitored at 2.79 ≤ L ≤ 3.84, with subsequent plasmaspheric depletion occurring by 6 November. Plasma mass density values are compared to empirical plasmapause location model predictions, with reasonable agreement for most days, but density depletion and refilling were monitored 1 day after they are predicted. During poststorm plasmaspheric refilling, some extremely low early morning resonance frequencies are monitored and appear be due to quarter mode standing waves. This study also highlights that care must be taken in the choice of assumed geomagnetic field geometry when deriving plasma mass densities from observed field line resonances during severe geomagnetic storms.

Properties of Hall magnetohydrodynamic waves modified by electron inertia and finite Larmor radius effects

The linear wave equation (sixth order in space and time) and the corresponding dispersion relation is derived for Hall magnetohydrodynamic (MHD) waves including electron inertial and finite Larmor radius effects together with several limiting cases for a homogeneous plasma. We contrast these limits with the solution of the full dispersion relation in terms of wave normal (k⊥,k∥) diagrams to clearly illustrate the range of applicability of the individual approximations. We analyze the solutions in terms of all three MHD wave modes (fast, slow, and Alfvén), with particular attention given to how the Alfvén branch (including the cold ideal field line resonance (FLR) [D. J. Southwood, Planet. Space Sci. 22, 483 (1974)]) is modified by the Hall term and electron inertial and finite Larmor radius effects. The inclusion of these terms breaks the degeneracy of the Alfvén branch in the cold plasma limit and displaces the asymptote position for the FLR to a line defined by the electron thermal speed rather than the Alfvén speed. For a driven system, the break in this degeneracy implies that a resonance would form at one field line for small k⊥ and then shift to another as k⊥→∞. However for very large ωk⊥/VA, Hall term effects lead to a coupling to the whistler mode, which would then transport energy away from the resonant layer. The inclusion of the Hall term also significantly effects the characteristics of the slow mode. This analysis reveals an interesting “swapping” of the perpendicular root behavior between the slow and Alfvén branches.

The structure of low-latitude Pc3 pulsations observed by CHAMP and on the ground

Abstract. The structure of low-latitude continuous pulsations termed Pc3, which are naturally occurring MHD waves in the Earth's magnetosphere, were studied by comparing ground and satellite magnetic field measurements. Data from two induction magnetometers, located at Hermanus and Sutherland in South Africa were used in conjunction with Challenging Minisatellite Payload (CHAMP) satellite observations to study a Pc3 event observed on 15 February 2003, at a time when CHAMP was passing over the ground stations. We observed a number of discrete frequency oscillations for the fast mode wave, one of which drives a field line resonance (FLR) at characteristic latitude as detected by both ground and satellite measurements. Consequently, our observations confirmed the compressional wave as being the driver of the field line resonance. The toroidal mode frequency observed on CHAMP experienced a Doppler frequency shift due to the rapid motion across the resonance region. Polarization hodograms in the resonance region clearly showed the expected 90° rotation of the field line resonant magnetic field components.

Observations and analysis of Alfvén wave phase mixing in the Earth's magnetosphere

Signatures of Alfvén wave phase mixing in the Earth's magnetosphere, observed as polarization rotation of a transverse, Pc5 magnetospheric pulsation, are presented and compared to theory. The polarization rotation occurred during a rare event of a dayside narrowband ULF magnetospheric pulsation that lasted for 5 consecutive days, from 24 to 30 November 1997; details of this event were reported by Sarris et al. (2009) through observations at geosynchronous orbit and on the ground. In this paper we investigate the polarization signatures of the pulsation by performing a detailed analysis of its transverse components as observed through hodogram plots. Density measurements from one of the Los Alamos National Laboratory (LANL) spacecraft which had its L shells closest to GOES‐8 are used to calculate field line resonance frequencies at geosynchronous orbit; these frequency calculations show good agreement with the observed pulsations but also have a local time offset. For an instance of an observed polarization rotation we estimate the observed poloidal lifetime of the pulsation by the time taken for the poloidal and toroidal amplitudes to become equal, which we compare with the theoretical approximation to the poloidal lifetime, as calculated in a box model magnetosphere by Mann and Wright (1995). Density measurements from different LANL spacecraft at geosynchronous orbit and their varying L shells as derived from their varying local times are used to estimate a local gradient in the local Alfvén speed, which is then used in the calculation of the predicted poloidal lifetime. This is the first time that such polarization rotations are directly observed and compared with theoretical predictions.

Characterization of ULF pulsations by THEMIS

The THEMIS five‐probe constellation was launched in 17 February 2007 to study substorms; however its instrumentation and the alignment at distances <1RE among some of the THEMIS probes, particularly in the first period of its mission, provides unique opportunities to study ULF pulsations in the magnetosphere. In the case study presented, electric and magnetic field fluctuations are identified as field line resonances and their modes of oscillation are discussed. Phase‐difference calculations between probes allow estimates of the mode number of the fluctuations. These observations give an excellent source for the verification of model estimates of frequency and polarization of the various modes of field line resonances.

Ground-based Pc5 ULF wave power: Solar wind speed and MLT dependence

Using over 20 years of ground-based magnetometer data from the CANOPUS/CARISMA magnetometer array, we present a statistical characterisation of Pc5 ultra-low frequency (ULF) power in the 2–10 mHz band as a function of magnetic local time (MLT), L-shell, and solar wind speed. We examine the power across L-shells between 4.2 and 7.9, using data from the PINA, ISLL, GILL and FCHU stations, and demonstrate that there is a significant MLT dependence in both the H- and D-component median 2–10 mHz power during both fast (>500 km/s) and slow (<500 km/s) solar wind speeds. The H-component power consistently dominates over D-component power at all MLTs and during both fast and slow solar wind. At the higher- L stations ( L >5.4), there are strong MLT power peaks in the morning and midnight local time sectors; the morning sector dominating midnight during fast solar wind events. At lower L-shells, there is no evidence of the midnight peak and the 2–10 mHz power is more symmetric with respect to MLT except during the fastest solar wind speeds. There is little evidence in the ground-based power of a localised MLT peak in ULF power at dusk, except at the lowest L-shell station, predominantly in the H-component. The median 2–10 mHz power increases with an approximate power law dependence on solar wind speed, at all local times across the L-shell domain studied in both components. The H-component power peaks at the latitude of the GILL station, with significantly lower power at both higher and lower L-shells. Conversely, the D-component power increases monotonically. We believe that this is evidence for 2–10 mHz power accumulating at auroral latitudes in field line resonances. Finally, we discuss how such ULF wave power characterisation might be used to derive empirical radiation belt radial diffusion coefficients based on, and driven by, the solar wind speed dependence of ULF wave power.

Surface waves and field line resonances: A THEMIS case study

Using magnetic field and plasma observations from four of the five Time History of Events and Macroscale Interactions during Substorms (THEMIS) spacecraft, a surface wave at the dawn flank of the magnetopause was identified on 25 April 2007. The wave had an amplitude of about 1 RE and propagated tailward with a velocity of about 190–240 km/s. Its azimuthal wavelength was in the range of 9–11 RE. Magnetosheath velocity values support the hypothesis that this surface wave was generated by the Kelvin‐Helmholtz instability. Simultaneously, an ultralow‐frequency (ULF) pulsation event was detected by the fifth THEMIS spacecraft deeper in the magnetosphere, at a distance of about 5–7 RE from the magnetopause. This ULF event showed all the signatures predicted for waves generated by the classical field line resonance process. Frequency and phases of the detected ULF oscillations were found to be in close agreement with the magnetopause surface periodic disturbances. We conclude that the observed ULF wave event was most likely directly generated by the magnetopause surface wave and thus represents one of the few known manifestations of the classical field line resonance process in space directly observed, a conclusion made possible due to the special configuration of the THEMIS mission and its five spacecraft.

THEMIS observations of consecutive bursts of Pi2 pulsations: The 20 April 2007 event

On 20 April 2007, four Pi2 pulsation bursts occurred successively and simultaneously in the premidnight sector at the E spacecraft and ground‐based observatories for the THEMIS mission, while the AE index was less than 100 nT. Especially for the last three onsets, both ground‐based and GOES 12 magnetometers sensed magnetic perturbations, as expected from the formation of a substorm current wedge (SCW). Moreover, LANL 1994–084 detected an enhancement of energetic particle flux. Spectral analysis shows a matched wave frequency ∼6–8 mHz and another harmonic frequency ∼17 mHz for the fourth burst. The orientation of the major axis of the wave polarization hodogram points toward the SCW location. The first burst has both latitudinal and longitudinal polarization changes from counterclockwise (CCW) to clockwise (CW), in contrast to the other three that have a latitudinal reversal only. The longitudinal CW to CCW change at low latitudes signifies that hydromagnetic waves propagate westward and eastward from the longitude of the impulsive source responsible for SCW. The latitudinal CW to CCW reversal is consistent with induction by a westward moving upward field‐aligned current carried by Alfvén waves leading to field line oscillations. Consequently, they can be explained by the coupling of a fast magnetospheric cavity mode driven by fast compressional waves to field line resonances as expected from braking bursty bulk flows, resulting from magnetotail reconnection, triggered by a preceding northward interplanetary magnetic field turning. This event shows that the source mechanism of consecutive Pi2 onsets at times of weak geomagnetic activity is the same as during substorm times.

Nonlinear field line resonances. Effect of Hall term on plasma compression: 1D Hall-MHD modeling

A model is presented that describes the excitation of small-scale density perturbations and electromagnetic fields by standing shear Alfvén waves in a Cartesian geometry. The model includes the effects of plasma betas and the Hall term effects. The characteristics of magnetospheric density cavities and the formation of the significant peak in density are discussed in the paper.

Monitoring the Dynamics of the Ionosphere–Plasmasphere System by Ground-Based ULF Wave Observations

Cross-spectral analysis of ULF wave measurements recorded at ground magnetometer stations closely spaced in latitude allows accurate determinations of magnetospheric field line resonance (FLR) frequencies. This is a useful tool for remote sensing temporal and spatial variations of the magnetospheric plasma mass density. The spatial configuration of the South European GeoMagnetic Array (SEGMA, 1.56 < L < 1.89) offers the possibility to perform such studies at low latitudes allowing to monitor the dynamical coupling between the ionosphere and the inner plasmasphere. As an example of this capability we present the results of a cross-correlation analysis between FLR frequencies and solar EUV irradiance (as monitored by the 10.7-cm solar radio flux F10.7) suggesting that changes in the inner plasmasphere density follow the short-term (27-day) variations of the solar irradiance with a time delay of 1–2 days. As an additional example we present the results of a comparative analysis of FLR measurements, ionospheric vertical soundings and vertical TEC measurements during the development of a geomagnetic storm.

Characteristics of magnetohydrodynamic waves in Harris-type current sheet with guide magnetic fieldBy

[1] An overview is presented of the characteristics of hydromagnetic waves propagating in Harris-type current sheet with magnetic field of Bx(z) and an embedded guide By component based on the ideal magnetohydrodynamic (MHD) model. The wave equations are expressed in the (k∥, k⊥, z) coordinates, and singularities are identified for general cases of ky ≠ 0 and By ≠ 0, where k∥ and k⊥ are the components of the wave vector parallel and perpendicular to the local magnetic field, respectively, and the inhomogeneity is in the z direction. The presence of By may lead to the rotation of the magnetic field relative to the wave vector so that a singular layer with k⊥ = 0 surrounded by a neighboring region of k⊥ ≠ 0 may exist. This result is in contrast with the case of By = 0 for which Alfven or field-line resonance associated with the mathematical singularity tends to occur for k⊥ ≠ 0 and ω = k∥CA, where CA is the Alfven speed. The possibility for MHD waves with frequency of ω = k∥CA to propagate through the inhomogeneous layer with By ≠ 0 is analyzed, and numerical solutions for discrete eigenmodes with various free parameter values are presented.

Statistical analysis of ground based magnetic field measurements with the field line resonance detector

Abstract. In this paper we introduce the field line resonance detector (FLRD), a wave telescope technique which has been specially adapted to estimate the spectral energy density of field line resonance (FLR) phase structures in a superposed wave field. The field line resonance detector is able to detect and correctly characterize several superposed FLR structures of a wave field and therefore constitutes a new and powerful tool in ULF pulsation studies. In our work we derive the technique from the classical wave telescope beamformer and present a statistical analysis of one year of ground based magnetometer data from the Canadian magnetometer network CANOPUS, now known as CARISMA. The statistical analysis shows that the FLRD is capable of detecting and characterizing superposed or hidden FLR structures in most of the detected ULF pulsation events; the one year statistical database is therefore extraordinarily comprehensive. The results of this analysis confirm the results of previous FLR characterizations and furthermore allow a detailed generalized dispersion analysis of FLRs.

Resonant absorption of ULF waves at Mercury's magnetosphere

Ultra low frequency (ULF) waves, which are assumed to be standing waves on the field, are observed by the Mariner 10 spacecraft at Mercury. These waves are oscillating at 38% of the proton gyrofrequency. It is well known that heavy ions, such as Na+, are abundant in Mercury's magnetosphere. Because the presence of different ion species has an influence on plasma dispersion characteristics near the ion gyrofrequencies, magnetospheric eigenoscillations observed at Mercury with frequency in the gyrofrequency range require a multi‐fluid treatment for the plasma. Thus ULF waves at Mercury may have a distinct difference from typical ULF oscillations at Earth, which are often described in terms of magnetohydrodynamics. By adopting a multi‐fluid numerical wave model, we examine how magnetic eigenoscillations occur in Mercury's magnetosphere. Because protons and sodium ions are the main constituents at Mercury, we assume an electron‐proton‐sodium plasma in our model. Our results show: (1) the observed ULF waves are likely compressional waves rather than standing oscillations such as field line resonances (FLRs), (2) FLRs at Mercury are expected to occur when the ion‐ion hybrid and/or Alfvén resonance conditions are satisfied, (3) the magnetic field of FLRs at Mercury's magnetosphere oscillates linearly in the east‐west (azimuthal) meridian when the frequency is located between two ion gyrofrequencies, and (4) the resonance frequency enables us to estimate the local heavy ion concentration ratio.

Polarization pattern of low and mid-frequency magnetic pulsations in the polar cap: A comprehensive analysis at Terra Nova Bay (Antarctica)

The polarization pattern of ULF pulsations (f≈1–100mHz) at Terra Nova Bay (Antarctica, CGM λ∼80°) has been determined for the entire 2003, soon after the solar maximum. A comparison with the results of previous investigations, conducted at the same station close to the solar minimum (1994–96), allows to focus common elements and major differences among different frequency bands which persist through the entire solar cycle. Basically, between f∼1.5 and 5mHz, the day can be divided into four sectors with alternate polarizations. The local time and latitudinal dependence of the observed pattern can be tentatively interpreted in terms of a latitude of resonant field lines reaching λ∼80° in the noon sector; on the other hand, resonance effects of lower latitude field lines can be clearly identified also far from the noon meridian when the station moves into the deep polar cap. Moreover, in the morning sector the resonance region would extend to lower latitudes than in the evening sector. The proposed profile of the resonant region can interpret also the results obtained at other cusp/auroral stations and appears consistent with that one inferred in the northern hemisphere at smaller latitudes. The resonance region progressively shifts toward lower latitude with increasing frequency; correspondingly, the four-sector pattern progressively disappears at TNB. Above f∼20mHz, the experimental observations might suggest an additional contribution from Sunward propagating waves, possibly via the magnetotail lobes.

THEMIS ESA First Science Results and Performance Issues

Early observations by the THEMIS ESA plasma instrument have revealed new details of the dayside magnetosphere. As an introduction to THEMIS plasma data, this paper presents observations of plasmaspheric plumes, ionospheric ion outflows, field line resonances, structure at the low latitude boundary layer, flux transfer events at the magnetopause, and wave and particle interactions at the bow shock. These observations demonstrate the capabilities of the plasma sensors and the synergy of its measurements with the other THEMIS experiments. In addition, the paper includes discussions of various performance issues with the ESA instrument such as sources of sensor background, measurement limitations, and data formatting problems. These initial results demonstrate successful achievement of all measurement objectives for the plasma instrument.

Phase coherence analysis of a field line resonance and solar wind oscillation

Discrete field line resonances (FLRs) are a common occurrence in the magnetosphere. However, the source of the stable, discrete FLR frequencies is still an unresolved problem. Recent work has proposed that discrete, continuous oscillations in the solar wind directly drive magnetospheric FLRs. However, these studies have only concentrated on common frequency and amplitude comparisons. This paper presents a new technique which utilizes either Fast Fourier Transform or wavelet cross‐phase measurements to demonstrate a high degree of phase coherence between a 1.7 mHz FLR observed with the SuperDARN Kodiak radar and ACE SWE oscillations in solar wind plasma density. A statistical analysis which simulates the solar wind as red noise indicates with 99% confidence that the FLR oscillation is the same as the solar wind plasma density variation.

Multi-spacecraft observations of ULF waves during the recovery phase of magnetic storm on October 30, 2003

Based on observations obtained by Cluster C1, GOES 10, 12, and Polar, the global ULF wave properties are studied during the recovery phase of a very intense magnetic storm-Halloween storm (October 31, 2003, 21:00–23:00 UT). The results indicate that the ULF waves’ properties observed by different satellites, such as amplitude, period, etc. show large variations. This can be interpreted as that Field Line Resonance (FLR) might take place in the region where Cluster C1 passed. The compressional wave of the cavity mode coupled with FLR’s shear Alfven wave and fed energy to the latter, forming a large-amplitude toroidal mode. From the point of period, Cluster C1 observed the shortest period, GOES 10, 12 observed the middle, while Polar observed the longest. The wave period of toroidal mode observed by Cluster C1 kept almost unchanging when Cluster C1 passed L range from 11.7 to 5.3. Using the Squared Wavelet Coherence analysis method, we estimated that the FLR region in the dayside magnetosphere could expand to at least 4 local time widths. The toroidal mode observed by Polar was a standing wave, while the poloidal mode was a propagating wave, the observation results could be well explained by the waveguide mode theory. Since the solarwind speed Vx was −800 km/s and the dynamic pressure varied little, we speculated that the source of the ULF wave was the Kelvin-Helmholtz instability at the magnetopause triggered by high speed solarwind.

Numerical study on ULF waves in a dipole field excited by sudden impulse

A three-dimensional numerical model is employed to investigate ULF waves excited by the sudden impulse (SI) of the solar wind dynamic pressure interacting with a dipole magnetosphere. We focus on the solar wind-magnetosphere energy coupling through ULF waves, and the influences of the SI spectrum on the cavity mode structure and the energy deposition due to field line resonances (FLRs) in the magnetosphere. The numerical results show that for a given SI lasting for 1 min with amplitude of 50 mV/m impinging on the subsolar magnetopause, the total ULF energy transported from the solar wind to the magnetosphere is about the magnitude of 1014 J. The efficiency of the solar wind energy input is around 1%, which depends little on the location of the magnetopause in the model. It is also found that the energy of the cavity mode is confined in the region near the magnetopause, whereas, the energy of the toroidal mode may be distributed among a few specific L-shells. With a given size of the model magnetosphere and plasma density distribution, it is shown that the fundamental eigenfrequency of the cavity mode and the central locations of the FLRs do not vary noticeably with the power spectrum of the SI. It is worth noting that the spectrum of the SI affects the excitation of higher harmonics of the global cavity mode. The broader the bandwidth of the SI is, the higher harmonics of cavity mode could be excited. Meanwhile, the corresponding FLRs regions are broadened at the same time, which implies that the global cavity modes and toroidal modes can resonate on more magnetic L-shells when more harmonics of the global cavity modes appear.

Coupling of Pi2 wave energy in the inner magnetosphere as inferred from low-latitude ground observations

Taking advantage of high time-resolution (1 s) geomagnetic field measurements obtained at low-latitude stations, we investigated frequency differences of Pi2 pulsations between the dayside and the nightside. Firstly, we examined two Pi2 cases globally observed by multiple ground stations and found that the dominant frequency peaks at the dayside showed latitudinal dependence, i.e., the higher (lower) frequency peak was predominant at lower (higher) latitude. We also noticed that the dominant Pi2 frequency on the nightside was apparently higher than that on the dayside. We argue that the multiple frequency peaks observed on the ground are harmonics of a plasmaspheric cavity resonance mode (CRM) and that the latitudinal dependence of the dominant frequency peaks may result from the energy coupling between the CRM and field line resonance (FLR) occurred in the near Earth space. We also argue that the frequency difference between the dayside and the nightside could be caused by the reason that a higher harmonic was observed in the nightside plasmasphere but was not effectively observed in the dayside. In addition, we statistically examined 829 Pi2 events that were simultaneously recorded at Kakioka (KAK, Maglat=27.2°) and Jicamarca (JIC, Maglat=0.0°), the two stations separated by ∼10 h in local time (LT) and one of them (JIC) is located at the dip equator. We found that the Pi2 frequency observed at KAK on the nightside was higher than that observed at JIC on the dayside on average. After investigating the occurrence histogram of the frequency difference (Δf=fJIC?fKAK) for the events simultaneously observed at KAK and JIC, we found that close to half of the events had the identical frequency (|Δf|<1.0 mHz). The statistical results are consistent with the facts reflected by case studies.