Field Line Resonance Frequencies Research Articles

Field line resonant frequencies and ionospheric conductance: Results from a 2‐D MHD model

The magnetised plasma of the near‐Earth space environment supports ultra‐low frequency (ULF; 1–100 mHz), magnetohydrodynamic (MHD) oscillations. For sufficiently large ionospheric conductances, field line resonances (FLRs) form between the northern and southern ionospheres. These conditions are usually met for daytime ionosphere conductance values. The FLRs are normal modes of the system and may be used to remote sense plasma mass densities in the magnetosphere. The oscillations lose energy in the ionosphere whose properties determine the boundary conditions, particularly resonance damping effects. Using a two dimensional (2D) MHD model of the magnetosphere and realistic ionosphere boundary conditions, the variation in resonant frequency with ionosphere conductivity is reported. For typical mid to low latitude summer and winter ionosphere parameters, the FLRs change by less than 5%. This translates to an uncertainty of 7% in plasma mass density.

Ground magnetometer observation of a cross‐phase reversal at a steep plasmapause

The cross‐phase technique employs ground‐based magnetometer data in order to determine the resonance frequency of a geomagnetic field line. Typically, a positive cross‐phase maximum identifies the field line resonance frequency, but occasionally, a negative cross‐phase maximum is observed and is believed to be a feature of the steep density gradient at the plasmapause. For a few hours during the local morning of 14 May 2001 the cross‐phase maximum, observed using two pairs of ground‐based magnetometer stations from the European sector, with midpoints at L = 3.16 and L = 3.34, reversed polarity from positive to negative. All other British Geological Survey, Sub‐Auroral Magnetometer Network, and International Monitor for Auroral Geomagnetic Effects (IMAGE) magnetometer array station pairs examined between L = 2.39 and L = 6.54 showed a positive cross‐phase maximum throughout the day. The Imager for Magnetopause‐to‐Aurora Global Exploration (IMAGE) satellite made an excellent close magnetic conjunction with these ground‐based magnetometer arrays on this day, and data from the IMAGE Radio Plasma Imager instrument show a very steep plasmapause in this region during this UT interval. IMAGE Extreme Ultraviolet Imager global plasmasphere images show that the plasmapause moved outward through the day, passing through the region of the observed negative cross‐phase maxima. This rare observation of a negative cross‐phase maximum occurs at the location of a plasmapause with a gradient steeper than r−8 and thus is in agreement with theory. The two cross‐phase peak polarity reversals are explained by the evolution of the local density profile.

Comparison of Fourier and wavelet techniques in the determination of geomagnetic field line resonances

Fourier transforms have traditionally been used in the past for time‐frequency analysis of numerous physical problems. Recently, a new time‐frequency analysis technique using temporally confined base functions, called wavelets, has been applied to many problems. The advantage of the wavelets over the conventional sinusoidal functions is their time localization property, providing information not only about the frequency or scale size of the features present but also about their location in the time series. Here we compare the performance of the two techniques on the time‐frequency analysis of ground magnetometer data and especially their ability to pick up the field line resonance (FLR) frequency of a resonating magnetic field line using automated FLR determination techniques. We find that the automated techniques work better with the Fourier transforms giving less variable FLR frequency. The high temporal resolution of the wavelet transforms can be useful for detailed analyses of short time periods, but it becomes a disadvantage when it comes to automated techniques for the entire dayside magnetosphere, yielding a highly variable FLR frequency.

Solar activity dependence of geomagnetic field line resonance frequencies at low latitudes

ULF field line resonance frequencies (fR) of three different magnetic shells (L = 1.61, 1.71, and 1.83) have been monitored during a 4‐year period (2001–2004) using a cross‐phase analysis of magnetic measurements recorded at the South European Geomagnetic Array (SEGMA). We find that the variations of the daily averages of fR, which reflect changes in plasmaspheric mass density, follow the variations of the daily values of the 10.7‐cm solar radio flux F10.7 with an estimated time delay of 1–2 days. The analysis of selected events indicates that the sensitivity of fR to short‐term (27‐day) variations in the solar flux is the same as that for long‐term (solar cycle related) variations. On the other hand, the results of the overall statistical analysis seem to indicate a lower sensitivity (by a factor of ∼2) of fR to short‐term solar flux variations with respect to long‐term variations. Geomagnetic activity effects and/or different solar variabilities of EUV and 10.7‐cm flux for different timescales are suggested as a possible cause for such a difference. Experimental results are also compared with those provided by a physical‐numerical model of the ionosphere‐plasmasphere system. Last, we find some evidence for a slight annual variation in fR with an estimated summer/winter ratio of ∼1.1–1.2. The inferred corresponding annual variation in the equatorial mass density is in line with previous estimates for the European longitudinal sector as obtained from whistler measurements.

Multiple field line resonances: Optical, magnetic and absorption signatures

We present multi-instrument observations of ultra low frequency (ULF) wave activity from the dawn flank magnetosphere during the period 12:00–13:30 UT on the 16 December 2003. Optical, magnetic and riometer measurements from the Churchill line meridian in the Canadian sector are presented which demonstrate the presence of multiple discrete auroral arc structures accompanied by periodic magnetic and riometer absorption perturbations in the Pc5 (150–600 s) ULF band. Clear polewards propagation is demonstrated in all the instrument data sets, the magnetic signals showing most clearly the amplitude and phase characteristics consistent with discrete frequency field line resonances (FLRs) on closed field lines. Two discrete frequency field line resonant signals are apparent, at 1.8 and 3.0 mHz which resonate at approximately the same latitude. We explain this via the calculation of the Alfvén continuum, and show that both frequencies may be resonant in the same latitudinal region within instrumental resolution. The meridian scanning photometer (MSP) observations from polewards of the magnetometer determined resonant latitudes show evidence of low intensity (∼200 R) poleward moving discrete arcs related to the ULF waves. Interestingly the MSP observations demonstrate poleward phase propagation with variable rates across the field of view; faster apparent polewards phase propagation being seen at higher latitudes. We demonstrate that the complicated “braided” phase of the arcs can be explained via the precipitation resulting from the superposition of two discrete FLRs. Furthermore, we characterise the ≳25 keV energetic electron precipitation in the region of the FLRs and the arc structures via periodic D-region absorption. In this way, we link the magnetic and both soft and energetic particle precipitation signatures of FLRs together for the first time. Our results demonstrate that riometer absorption can be used to characterise FLRs, however, this is only generally possible at lower L-shells where energetic electrons in the ring current overlap with the FLR fields in the equatorial plane.

ULF fluctuations of the geomagnetic field and ionospheric sounding measurements at low latitudes during the first CAWSES campaign

Abstract. We present an analysis of ULF geomagnetic field fluctuations at low latitudes during the first CAWSES campaign (29 March-3 April 2004). During the whole campaign, mainly in the prenoon sector, a moderate Pc3-4 pulsation activity is observed, clearly related to interplanetary upstream waves. On 3 April, in correspondence to the Earth's arrival of a coronal mass ejection, two SIs are observed whose waveforms are indicative of a contribution of the high-latitude ionospheric currents to the low-latitude ground field. During the following geomagnetic storm, low frequency (Pc5) waves are observed at discrete frequencies. Their correspondence with the same frequencies detected in the radial components of the interplanetary magnetic field and solar wind speed suggests that Alfvénic solar wind fluctuations may act as direct drivers of magnetospheric fluctuations. A cross-phase analysis, using different pairs of stations, is also presented for identifying field line resonant frequencies and monitoring changes in plasmaspheric mass density. Lastly, an analysis of ionospheric vertical soundings, measured at the Rome ionosonde station (41.8° N, 12.5° E), and vertical TEC measurements deduced from GPS signals within an European network shows the relation between the ULF resonances in the inner magnetosphere and thermal plasma density variations during geomagnetically quiet conditions, in contrast to various storm phases at the end of the CAWSES campaign.

Realistic magnetospheric density model for 29 August 2000

Using a two dimensional image of the Earth's plasmasphere taken by the Extreme Ultraviolet Imager (EUV) on the Imager for Magnetopause-to-Aurora Global Exploration (IMAGE) spacecraft, in-situ electron density measurements from the IMAGE Radio Plasma Imager (RPI) instrument, measurements of magnetospheric mass density inferred from field line resonant frequencies measured by magnetometers on the Earth's surface, and a model for the density field aligned variation, we construct a computer model for the magnetospheric density on 29 August 2000 at 1519 UT. The purposes of this study are to demonstrate how a density model can be constructed using multiple data sources, to document this particular model, which is being used in studies of ultra low frequency Pi-2 oscillations and plasmaspheric cavity modes, to describe some of the problems involved with EUV density inversion, and to demonstrate some features of the plasmaspheric density, particularly in the region of the dusk plasmatrough and plume.

The computation of field-line resonance frequencies in general geometries: a tool for improving the understanding of magnetospheric configurations

Until recently, the calculation of field-line resonance (FLR) frequencies from magnetic field data, generated by magnetospheric models such as BATSRUS and Tsyganenko (T01), was restricted to orthogonal coordinate systems. With this restriction, only dipolar and axisymmetric configurations are admissible. The matter of addressing more general configurations such as non-axisymmetric stretched and twisted magnetic field topologies requires the use of a non-orthogonal coordinate system. This coordinate system can be constrained by defining the magnetic field as the product of Euler potentials, B = ∇α i × ∇α j , and imposing the condition, V B = 0, everywhere. As a consequence, the coordinates, α i , must satisfy the partial differential equation, B·∇α i = 0. In other words, α i must be constant along magnetic field lines. Upon solving this differential equation implicitly using known magnetic field intensities, the metric tensor for the resulting basis can be computed. The elements of this tensor can be substituted directly into the eigenvalue problem for general coordinate systems written in covariant notation. The equation for FLR modes has been developed for arbitrary incompressible magnetospheric conditions and has been specialized to the case where spatial variations are constrained along the magnetic field. The result is a fourth-order system of ordinary differential equations, which can be evaluated numerically, provided that the variation of the metric coefficients as a function of the distance along field lines is sufficiently smooth. The eigenvalue problem is solved at several latitudes for a broad range of magnetospheric conditions.

An automated method for the detection of field line resonance frequencies using ground magnetometer techniques

This report describes an automated method developed to quickly and precisely determine field line eigenfrequencies from ground magnetometer data using the statistical properties of cross‐phase and power ratio spectra. This new automated method allows for routine monitoring of field line resonant frequencies, and hence plasma mass density of the inner magnetosphere, with better temporal coverage and over longer intervals than previous studies, which were limited simply due to the time‐consuming nature of making selections “by hand.” To demonstrate the usefulness of the automated procedure, 2 years of data from a pair of magnetometers in the MEASURE array at L = 1.74 were analyzed, and the annual variation in plasmaspheric density was observed. The equatorial mass density reaches a maximum in the Northern Hemisphere winter, and a minimum in summer, with winter values two to three times higher than in summer. This result confirms previous whistler observational studies and theoretical modeling studies.

Coordinated ground-based and Cluster observations of large amplitude global magnetospheric oscillations during a fast solar wind speed interval

Abstract. We present magnetospheric observations of very large amplitude global scale ULF waves, from 9 and 10 December 2000 when the upstream solar wind speed exceeded 600 km/s. We characterise these ULF waves using ground-based magnetometer, radar and optical instrumentation on both the dawn and dusk flanks; we find evidence to support the hypothesis that discrete frequency field line resonances (FLRs) were being driven by magnetospheric waveguide modes. During the early part of this interval, Cluster was on an outbound pass from the northern dusk side magnetospheric lobe into the magnetosheath, local-time conjugate to the Canadian sector. In situ magnetic fluctuations, observed by Cluster FGM, show evidence of quasi-periodic motion of the magnetosheath boundary layer with the same period as the ULF waves seen on the ground. Our observations represent the first simultaneous magnetometer, radar and optical observations of the characteristics of FLRs, and confirm the potential importance of ULF waves for magnetosphere-ionosphere coupling, particularly via the generation and modulation of electron precipitation into the ionosphere. The in situ Cluster measurements support the hypothesis that, during intervals of fast solar wind speed, the Kelvin-Helmholtz instability (KHI) can excite magnetospheric waveguide modes which bathe the flank magnetosphere with discrete frequency ULF wave power and drive large amplitude FLRs. Paper submitted to the special issue devoted to "Cluster: First scientific results", Ann. Geophysicae, 19, 10/11/12, 2001.Key words. Magnetospheric physics (magnetopause, cusp and boundary layers; MHD waves and instabilities; solar wind-magnetosphere interactions)

Resonance frequency of stretched magnetic field lines based on a self‐consistent equilibrium magnetosphere model

Field line resonance (FLR) has the potential to account for magnetic and electric oscillations observed near the equatorial region of the magnetosphere and on the ground associated with auroral arcs. Previous theoretical works based on dipolar field lines give frequencies too high to match with the observed frequencies when typical mass density is used. Inclusion of magnetic field stretching from empirical magnetic field models brings good agreement, but these models have no assurance of specifying an equilibrium magnetosphere. In this paper we present, for the first time, quantitative results of the resonance frequencies for the shear Alfvén and slow mode branches of FLR threading the auroral zone for field lines stretched to various distances in the nightside based on a self‐consistent equilibrium magnetosphere. The calculation is done in two steps. For a given degree of field line stretching we first obtain an MHD equilibrium magnetosphere with a finite temperature through a self‐consistent solution of the Grad‐Shafranov equation. We then solve for FLR frequencies of stretched magnetic field lines in the equilibrium magnetosphere according to the MHD theory of FLR. The results show that field line stretching can lead to low frequencies of FLR as observed without invoking unrealistically high mass density. Dependent on the wave mode and the amount of field line stretching, the FLR frequencies found in this calculation differ from those for a simple magnetic dipole of the Earth by varying degrees, from agreement within a factor of 2 to a disparity of greater than a factor of 10.

Observations of Pc 3-4 and Pi 2 geomagnetic pulsations in the low-latitude ionosphere

Abstract. Day-time Pc 3–4 (~5–60 mHz) and night-time Pi 2 (~5–20 mHz) ULF waves propagating down through the ionosphere can cause oscillations in the Doppler shift of HF radio transmissions that are correlated with the magnetic pulsations recorded on the ground. In order to examine properties of these correlated signals, we conducted a joint HF Doppler/magnetometer experiment for two six-month intervals at a location near L = 1.8. The magnetic pulsations were best correlated with ionospheric oscillations from near the F region peak. The Doppler oscillations were in phase at two different altitudes, and their amplitude increased in proportion to the radio sounding frequency. The same results were obtained for the O- and X-mode radio signals. A surprising finding was a constant phase difference between the pulsations in the ionosphere and on the ground for all frequencies below the local field line resonance frequency, independent of season or local time. These observations have been compared with theoretical predictions of the amplitude and phase of ionospheric Doppler oscillations driven by downgoing Alfvén mode waves. Our results agree with these predictions at or very near the field line resonance frequency but not at other frequencies. We conclude that the majority of the observations, which are for pulsations below the resonant frequency, are associated with downgoing fast mode waves, and models of the wave-ionosphere interaction need to be modified accordingly.Key words. Ionosphere (ionosphere irregularities) · Magnetospheric physics (magnetosphere-ionosphere interactions) · Radio science (ionospheric physics)

Monitoring spatial and temporal variations in the dayside plasmasphere using geomagnetic field line resonances

It is well known that the resonant frequency of geomagnetic field lines is determined by the magnetic field and plasma density. We used cross‐phase and related methods to determine the field line resonance frequency across 2.4≤<L≤4.5 in the Northern Hemisphere at 78°–106° magnetic longitude and centered on L=2.8 in the Southern Hemisphere at 226° magnetic longitude, for several days in October and November 1990. The temporal and spatial variation in plasma mass density was thus determined and compared with VLF whistler measurements of electron densities at similar times and locations. The plasma mass loading was estimated and found to be low, corresponding to 5–10% He+ on the days examined. The plasma mass density is described by a law of the form (R/Req)−p, where p is in the range 3–6 but shows considerable temporal variation, for example, in response to changes in magnetic activity. Other features that were observed include diurnal trends such as the sunrise enhancement in plasma density at low latitudes, latitude‐dependent substorm refilling effects, shelves in the plasma density versus L profile, and a longitudinal asymmetry in plasma density. We can also monitor motion of the plasmapause across the station array. Properties of the resonance were examined, including the resonance size, Q, and damping. Finally, we note the appearance of fine structure in power spectra at these latitudes, suggesting that magnetospheric waveguide or cavity modes may be important in selecting wave frequencies.

Discrete Field Line Resonances and the Alfvén Continuum in the Outer Magnetosphere

Using Pc5 pulsation events observed with the IMAGE magnetometer array, we demonstrate that mHz frequency field line resonances (FLRs) represent local enhancements in the background Alfvén continuum of field line eigenfrequencies. By comparing resonance profiles for a typical event with the continuum frequency profile determined using cross‐phase techniques, we show that pulsation frequencies as low as 1–2 mHz can couple to FLRs on high latitude closed field lines. We also suggest that the transition to open field lines on days of higher geomagnetic activity may lead to a breakdown in pulsation characteristics at the highest latitudes of the IMAGE array. In addition, we show evidence of the U‐shaped diurnal variation in field line eigenfrequency and suggest that this is primarily due to field line stretching, especially on the magnetosphere flanks.

An interpretation of the cross‐phase spectrum of geomagnetic pulsations by the field line resonance theory

The cross‐phase spectrum of the magnetic fields at two closely spaced stations located on the same meridian can be used to determine the field line resonance frequencies in the magnetosphere. The model of two harmonic oscillators previously proposed in the literature to interpret this technique, however, deviates from the traditional field line resonance model and it fails to interpret the cross‐phase spectrum for the Z component. We show that the cross‐phase spectrum can be interpreted by traditional field line resonance theory with consideration of ionospheric effects even in the presense of a continuum of non‐interacting resonating field lines.

Pc5 field line resonance frequencies and structure observed by SuperDARN and CANOPUS

We have analyzed a number of low‐m Pc5 field line resonance events observed simultaneously by one or more of the Super Dual Auroral Radar Network (SuperDARN) radars and the Canadian Auroral Network for the OPEN Unified Study (CANOPUS) magnetometer array. At times there was excellent agreement in the Pc5 signal frequencies observed by radar and magnetometers. For events with good agreement in the measured signal frequencies, there was also reasonable agreement in the observed resonance positions and m numbers. Sometimes, however, the ordering of frequencies by their spectral power did not coincide between the radar and magnetometer data and even the frequencies of the spectral peaks did not always coincide. In these cases, there was also some apparent discrepancy in the observed resonance positions and m numbers. The resonance half power widths observed by the magnetometers were found to be a factor of 2 – 6 wider than those measured with the radar, owing to the spatial integration by ground‐based magnetometers of ionospheric current structures having scale size less than ionospheric height. Although there was general agreement in the direction of the longitudinal propagation, the m numbers obtained from the magnetometer data were found to be somewhat smaller that those calculated from the radar data. We consider and discuss possible reasons for the observed discrepancies.

Variation of plasmatrough density derived from magnetospheric field line resonances

The diurnal variation of ULF field line resonant frequencies has been calculated using the cross phase of data from the north‐south components recorded at seven latitudinally spaced ground magnetometers in the Canadian Auroral Network for the OPEN Program Unified Study (CANOPUS) array. CANOPUS magnetometers range in latitude from Rankin Inlet (L = 12.4) south to Pinawa (L =4.3). Using cold plasma MHD theory, an R−4 plasma density function, and the T87 magnetic field model, the variation of plasma density in the equatorial region has been calculated from the experimentally determined resonant frequencies. Consecutive, adjacent magnetometer pairs provide six local daytime spatial estimates of the variation in plasma mass density between 4 and 11 RE. Typical values are 1–20 H+cm−3 for the plasmatrough and 50–200 H+cm−3 for the plasmasphere. The data recorded on June 7, 1990, shows an afternoon increase in density near geosynchronous orbit in agreement with convection models of the magnetosphere. The ground‐based measurements of plasma mass density have been compared with data from the Los Alamos Magnetospheric Plasma Analyser on board the 1989‐046 geosynchronous spacecraft. These comparisons show that the ground‐based technique should allow a robust procedure for calculating dayside, time‐dependent mappings of the equatorial plasma mass density from the plasmapause to the magnetopause in near real time.

Statistical survey of auroral latitude Pc 5 spectral and polarization characteristics

Recent magnetometer and HF radar observations have indicated the existence of multiple, discrete field line resonances with remarkably stable frequencies of 1.3, 1.9, 2.6, and 3.4 mHz, apparently driven by MHD waveguide/cavity modes in the magnetosphere. Given the dynamic nature of the magnetosphere, the apparent stability of these frequencies is difficult to understand, and it is therefore important to examine this question on the grounds of a larger database. In this paper we present a statistical survey of the occurrence of Pc 5 field line resonance frequencies based on 1 year of data from several stations of the CANOPUS magnetometer array. Pure state filtering techniques were used to investigate various statistical aspects of auroral latitude Pc 5 characteristics, with emphasis on the occurrence of preferential, discrete spectral peaks. A number of case studies exploiting the full spatial extent of the CANOPUS array were carried out to complement the statistics. Although the results provide further support for the existence of discrete (spatially monochromatic) field line resonances, we find that the apparently stable frequencies do not seem to be particularly distinguished from other Pc 5 frequencies, except perhaps the 1.9‐mHz peak. Discrete field line resonance characteristics were also observed for other sets of frequencies, and we therefore conclude that the apparently stable waveguide/cavity mode frequencies do not necessarily represent a unique set. The implications of these results with respect to various possible Pc 5 wave generation mechanisms are discussed.

Ponderomotive saturation of magnetospheric field line resonances

Compressional Alfvén waves in the terrestrial magnetospheric cavity constitute a discrete spectrum of global modes which can resonate with specific components of the continuum spectrum of shear Alfvén wave (SAW) field line resonant frequencies. We investigate the effect of the ponderomotive force (PF) of excited standing SAWs on the nonlinear saturation of field line resonances (FLRs). In low β plasmas FLR saturation occurs due to a nonlinear phase slip between the fast mode driver and SAW field. Ponderomotive forces also lead to density depletions at the ionospheres, nonlinear narrowing of the FLR and meridional scales comparable to those embedded within temporally modulated discrete auroral arcs. Observational features relating to these effects are discussed.

On the existence of purely transverse field‐line oscillations

We have shown that transverse toroidal (or poloidal) oscillations are possible in a dipole field, provided they are sufficiently localized in radial (azimuthal) direction for the Hall current‐generated electric fields to be relevant. Explicit solutions are obtained for azimuthal oscillations and it is shown that these are localized in the radial direction with an exponential decay length in the equatorial plane; where L0 is the equatorial distance of the field line; ω and ωci are field line resonance and ion cyclotron frequencies, and k is the zonal wave number of the mode. It is also shown that a superposition of a continuum of such structures centered over a range of L values can generate the fluctuations that are observed.