Hodograph method to estimate the latitudinal profile of the field-line resonance frequency using the data from two ground magnetometers

Abstract

The hodograph method enables estimating the latitudinal profile of the field-line resonance (FLR) frequency ( f R ) using the data from two ground magnetometers. This paper provides the full details of this method for the first time, and uses a latitudinal chain of ground magnetometers to examine its validity and usefulness. The hodograph method merges the widely-used amplitude-ratio and cross-phase methods in a sense that the hodograph method uses both the amplitude ratio and the phase difference in a unified manner; further than that, the hodograph method provides f R at any latitude near those of the two ground magnetometers. It is accomplished by (1) making a complex number by using the amplitude ratio (phase difference) as its real (imaginary) part; (2) drawing thus obtained complex numbers (one number for one frequency) in the complex plane to make a hodograph; and (3) fitting to thus obtained hodograph a model satisfying the FLR condition, which is a circle with the assumption that the resonance width is independent of the latitude. To examine the validity and usefulness of the hodograph method, we apply it to a Pc 4 event observed by the Scandinavian BEAR array. We also apply the amplitude-phase gradient method (Pilipenko and Fedorov, 1994;Kawano et al., 2002) to the same event, and compare the results; this is the first article applying the both methods to the same dataset.

An investigation into the spectral parameters of ultra-low-frequency (ULF) waves in the polar caps and magnetotail

“…It has been shown by Pilipenko et al (2013) that the characteristics of the magnetotail are highly sensitive to the polarisation parameters of the pulsations (in comparison to a simple amplitude-based investigation). The wave polarisation characteristics were changing during the interval analysed, as seen from the variations in the spectral power ratio (R) and phase difference ( ϕ) for the b || b ρ and the b || b ϕ component pairs (Fig.…”

“…The above-mentioned authors showed that at least some of the frequencies of global pulsations in the millihertz range can originate from the mesoscale SW structures. Thus, if the ULF variations in the SW are negligible, pulsations might result from exciting Kelvin-Helmholtz instability in the magnetosphere (Mann et al, 2002;Rae et al, 2005;Keiling, 2009).…”

“…While ULF fluctuations almost die out in the SW and IMF, ULF activity starts to grow and become more coherent in the magnetosphere, as shown by both the Cluster and ground magnetometer data in both polar caps. To minimise the possible influence of both extra-magnetospheric fluctuations and residual activity related to the recovery phase of a geomagnetic storm (Posch et al, 2003) or recent substorm activations, an interval with quiet conditions in both interplane- tary space and the magnetosphere have been chosen using the same set of parameters as in Yagova et al (2017).…”

A case study of the spectral parameters of ULF fluctuations before substorms with no evident trigger in the interplanetary space

“…The characteristics of the magnetotail are more sensitive to the polarization parameters of the pulsations (in comparison to a simple amplitude based investigation) (Pilipenko et al, 2013). Let us consider how spectral shape and polarisation of the magnetotail pulsations change during the day.…”

On the Estimation of Resonance Widths of Field Line Resonances Using Ground Magnetometer Data

“…The mathematical forms of the APM and ADM are given in Section 2. A hodograph method to measure the spatial resonance width was discussed by Kurchashov and Pilipenko (1996), Vellante et al (2002) and Pilipenko et al (2013). The hodograph method requires the complex ratio R(f) = H P (f)/H E (f) over a range of frequencies near a resonant frequency, f R , where H P and H E are the spectral amplitudes detected at a poleward and equatorward station respectively.…”