The spectral difference in ULF wave amplitude between closely spaced meridional ground stations may be used to measure the eigenfrequency of magnetospheric field lines (Baransky et al., 1985). A more reliable technique based on the crossphase spectrum has been used to identify eigenfrequencies and study the temporal evolution of local field line resonances. Pc3 (22-100 mHz) pulsations recorded with two pairs of low latitude ground stations have been specifically examined

The resonance structure of low latitude Pc3 geomagnetic pulsations

The propagation of MHD waves depends on a local Alfven speed and ambient geometry. The dynamical properties of MHD waves in the plasmasphere and magnetosphere are investigated by assuming a realistic Alfven speed profile in a dipole field. The WKB approximation is used to determine the cutoff boundaries and estimate the wave dispersion over a whole meridional plane. It is found that most wave energy may be transmitted effectively into the inner magnetosphere near the equatorial region, since the reflection of incoming waves at the plasmapause becomes weakest at the equator. It is also examined how the transmission from the outer magnetosphere to the inner magnetosphere depends on wave frequencies and azimuthal wavenumbers. The cutoff boundaries of wave propagation are quantitatively determined for each mode and wavenumber, which show various structures on the meridian. The results suggest that the propagation region may consist of two separable domains of the inner and outer magnetosphere for a relatively low-frequency wave. The inner region of propagation appears to be a distorted torus around the dipole axis. Such spatial separation of the two regions becomes weak and gradually interconnected for the waves with a relatively small azimuthal wavenumber or high frequency. The wave spectra and energy distribution are also investigated for different azimuthal wavenumbers. The numerical results show that the cavity modes may exist in the plasmasphere even at the absence of the outer magnetospheric boundary, which is found to be strongly associated with the characteristics of wave parameters. In particular, it is suggested that the plasmaspheric cavity modes, in the nightside region, may play a crucial role in producing Pi 2 pulsations. In addition, theories of waveguide and cavity modes based on the dipole model are discussed in detail.

Dynamics of MHD wave propagation in the low-latitude magnetosphere

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.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/1999JA900205

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

The diurnal variation in the frequencies of the continuum of ULF field line resonances has been calculated by using the cross-spectral phase of the north-south components of data from latitudinally spaced ground magnetometers in the Canadian Auroral Network for the OPEN Program Unified Study (CANOPUS) array. On most days the continuum is seen only during the local daytime, and only a single harmonic with an inverted U-shaped temporal variation in frequency is seen. At 67° geomagnetic latitude (L = 6.6) the general trend is a resonant frequency around 2 mHz near local dawn, increasing up to ∼5 mHz by 0600-0700 local time, followed by a decrease in frequency to 2 mHz by 1500–1600 local time. Near local noon, the fundamental resonant frequency is ∼3 mHz at 71° (L = 11.3), increasing monotonically to 7 mHz at 65° (L = 6.1). The waves appear to be a part of the resonant Alfven mode continuum as opposed to the single-frequency, driven magnetic field line resonances often seen at high latitudes. The cross-phase spectra show evidence of impulsively driven resonances that energize the continuum over the latitudinal range of the CANOPUS magnetometers. The temporal variation in the resonant frequency is modeled by using the Tsyganenko (1987) magnetic field model and cold plasma MHD theory. With the use of the observed resonant frequencies, the plasma density for June 1, 1990, was 4.2 × 106 H+/m³ at L = 6.6 while the data for June 7, 1990, showed densities up to 100×106 H+/m³. These results suggest that observations of the magnetohydrodynamic continuum in the magnetometer data may give a very effective method for ground-based time-dependent mapping of the equatorial plasma density.

The temporal variation of the frequency of high latitude field line resonances

The Earth's magnetosphere is highly structured, in terms of both magnetic field and plasma characteristics. This structure has a profound influence on the propagation of plasma waves, especially ultra-low-frequency (ULF) waves with mHz frequencies, which have wavelengths comparable with typical magnetospheric dimensions. The basic theory of ULF hydromagnetic wave propagation in an infinite, homogeneous, uniformly magnetized plasma has been extensively modified to cope with the requirements of applying it to the magnetosphere. The authors consider the field-line-guided Alfven wave modes and the isotropic fast hydromagnetic wave modes, and show how the existence of magnetospheric boundaries can affect the structure of both modes. The magnetosphere can also be considered as a cavity in which fast cavity modes may exist, with frequencies quantized by the three-dimensional cavity shape. Azimuthal variation in a system with radial Alfven speed structure leads to the idea of 'field-line resonance'.

https://iopscience.iop.org/article/10.1088/0034-4885/55/5/001/pdf

L.N. Baransky

Papers

High resolution method of direct measurement of the magnetic field lines' eigen frequencies