88 6.6 The pulsation signals that travel simultaneously on the ground and along CHAMP. a) H and D components of the Pc3 pulsation activity observed on the ground on 13 February 2002. 90 6.8 The pulsation signals observed simultaneously on the ground and next to the CHAMP. a) H and D components of the Pc3 pulsation activity observed on the ground on 18 February 2003.
Introduction
The Sun and the solar wind
The corona is the outermost layer of the Sun and expands into interplanetary space and becomes the solar wind. In the equatorial regions of the Sun, the magnetic field begins and ends at the surface of the Sun.
The Magnetosphere
The closed magnetosphere model
These studies reviewed by Mead (1967) postulate that the boundary shape of the magnetosphere is determined by a pressure balance between the solar wind and the geomagnetic field. The effect of the bow shock is to reduce the speed of the solar wind from supersonic to subsonic as it flows around the magnetosphere.
The open magnetosphere model
As shown in Figure 2.3, the bow shock has a nearly parabolic shape, which is symmetrical about the Sun-Earth line, and the conditions that create the bow shock occur at ∼14 RE (Burgess, 1995). On the day (upstream) side at the magnetopause boundary location, it is understood that the dynamic pressure from the solar wind balances the static pressure in the geomagnetic field.
Magnetohydrodynamic waves
Therefore, the dispersion relation of the transverse Alfv´en mode is deduced from equation 2.21 and can be expressed as. The velocity perturbation is in the direction perpendicular to the plane containing the wave vector and the magnetic field (Southwood, 1985).
Standing waves
Because of the standing structure, the wavefield shows some symmetry around the center at z = 1/2d, where d is the conduction plane separation. If the ionosphere is treated as a fully conducting boundary, the standing oscillation of the magnetospheric dipole field line has a similar structure and should have some symmetry with respect to the field line equator.
The effect of ionospheric currents on MHD wave propagation
When propagating from the magnetosphere to the earth, these wave modes are affected by the ionosphere and atmosphere. The magnetic signal on the ground is rotated by 900 with respect to the transverse Alfv'en mode magnetic field in the magnetosphere because the signal below the ionosphere is proportional to the Hall current (Kivelson and Southwood, 1988).
Geomagnetic pulsations
These currents cause modifications in the wave modes as they are transmitted through the ionosphere and atmosphere (Hughes and Southwood, 1976). Thus, if the ionosphere were not inductive, the magnetic field in the earth would line up in the same way as the transverse poloidal component of the magnetospheric wave field.
Pulsation classification
Examples of simultaneous magnetic oscillations at conjugate points are available in the literature (Wilson and Sugiura, 1961; Nagata et al., 1963). The resonance mechanism follows three steps: the source wave is excited at or near the dayside magnetopause/bow shock, it propagates in the magnetosphere as a fast mode magnetosonic wave, and the latter couples to the local Alfv´en standing wave (Southwood, 1974).
Solar wind as a source and control of ULF waves
Upstream wave path
ULF waves generated in the region upstream of the bow shock are convected downstream by the solar wind into the magnetosheath. The magnetopause responds to these pressure fluctuations and transfers wave energy to the daytime magnetosphere, where they can excite field line resonances.
The observable relationship between the upstream wave and Pc3-4 pul-
The relationship between IMF strength and wave frequency is explained by linear theory (Fairfield, 1969), as the majority of waves are believed to be generated by resonant interactions originating from the bow shock (Barnes, 1970; Gary et al., 1981) . . It was shown that the dominant frequency of Pc3-4 pulsations observed on the ground was controlled by the strength of the IMF (Green et al., 1983).
Field line resonances (FLR)
L-dependence of FLR frequency
From equation 2.29 and 2.30, the wave vector can be expressed as a function of field line length kz = π. Therefore, the field line resonance frequency depends on the background magnetic field strength, the field line length and the plasma density along the geomagnetic field line.
Field line resonance at high latitudes
The structure of field line resonance at low latitudes
A comparison of calculated and observed natural periods at low latitudes led to the conclusion that the inclusion of the F O+ region in the plasma distribution noticeably affects the calculated natural periods of the ULF (Hattingh and Sutcliffe, 1987). The observed periods in Figure 2.13 show the importance of including O+ in the plasma model if realistic periods are to be calculated at a low value.
Field line resonances and wave guide mode at low latitudes
The observed periods in Figure 2.13 demonstrate the importance of including O+ in the plasma model if realistic periods are to be calculated at low. b) The Alfv´en velocity (solid line) and FLR frequency variation with x (dotted line) used in the 1-D model (Waters et al., 2000). Using the work by Waters et al. 2000) who solved a 1-D cavity model of the magnetosphere, McPherron (2005) illustrated the nature of cavity resonances.
Summary
The model assumed that cavity modes couple energy to field line resonances, and that field line resonances are damped by the conductivity of the ionosphere (e.g. Waters et al., 2000). This study uses the background magnetic field and a low-pass filter to calculate the angles required to rotate data in field-aligned coordinates.
The CHAMP mission
CHAMP orbit characteristics
The satellite was launched in a nearly circular orbit, as this has the advantage of providing homogeneous and complete global coverage of the globe. The line plotted across the map indicates a 96-minute satellite ground trajectory as the satellite orbits the Earth.
Magnetometer instrumentation and data
The CHAMP data used in this study are preprocessed (level 2) Fluxgate vector magnetometer data (product identifier CH-ME-2-FGM-FGM). In this work, satellite data are used in conjunction with data recorded on the ground by equipment typically operated by magnetic observatories.
A field-aligned coordinate system
Using vector plots in Figures 3.4 and 3.5, the background field is used to calculate the angles required for rotation to field-aligned coordinates. Shown in Figure 3.4a is the geometry used to calculate the resultant magnetic field BH of BX.
The effect of field-aligned currents (FAC) on pulsation measurements
Successful completion of the experiment required knowledge about the magnetic activity in the magnetosphere. The events were then grouped in terms of magnetosphere status or conditions, represented by Kp index values.
Summary
The two analysis techniques are used to calculate spectral estimates of the generated test signals. This chapter ends with the brief discussion of the cross-phase technique used in this work to facilitate the detection of field line resonance.
Fourier Transform and Fourier Integral
Essentially, the Fourier transform of a waveform breaks down or separates the waveform into a sum of sinusoids of different frequencies. This interpretation is used in the current study, since pulsation signals must be decomposed into sinusoids that approximate the actual observed signal.
The Discrete Fourier Transform (DFT) and Fast Fourier Transform (FFT)
Fast Fourier transform
IDL implementation of the FFT is based on the Cooley-Tukey algorithm which breaks transform of a length N into a transform of length N/2. The standard development of the Cooley-Tukey algorithm is presented in Oppenheim and Schafer (1975) and Brigham (1988) shows how the DFT of a length N series can be simply calculated from the two length N/2 DFTs of the even index terms and the odd index terms.
Maximum Entropy Spectral Analysis
Derivation of the MESA Spectral Estimator
For a stationary complex discrete time series x(t) with sampling interval dt and Nyquist frequency fN = 2dt1, the use of MESA would be to select the spectrum that maximizes the entropy of the process (ie, the spectrum corresponding to the most unpredictable time series). The LS estimator approach minimizes the error prediction power over all autoregression (AR) coefficients at a given order of AR.
The application of the FFT and MESA
Length of Prediction Error Filter
The spectra are all labeled according to the PEF length value used to determine each spectrum. The spectra are all relabeled according to the PEF length values used to determine the spectra.
Detection of FLR’s
They showed that the original theory of field line resonance and ionospheric effects in pulse signals can explain the cross-spectral properties of pulses. The phase difference of the measured signals from the two stations, S2 and S1 can be read from the left-hand scale and is shown in Figure 4.16(b).
Summary
Structure of Pc3 pulsations observed at low latitudes on land and by CHAMP. This was achieved by comparing the frequency structure in the spectra of the field-aligned and transverse components in the ionosphere and the H- and D- components on the ground and investigating the ionospheric rotation.
First CHAMP Pc3 observation
Measurements made by a satellite moving along x with velocity Vsat would be affected by the Doppler effect, which determines the observed frequency (Vellante et al. also studied the effect of the ionosphere on pulsation polarization. A direct comparison of SEGMA and CHAMP pulsations showed a 900-degree rotation polarization ellipse of ULF waves through the ionosphere.
Event selection and Data Analysis
By comparing the satellite velocity, Vsat, and the apparent phase velocity, Vphase, one can get an idea of the importance of this effect.
Observations
The dynamic spectrum of the compressive component, Bcom, has some similarities to the spectrum of the ground D component. The intense oscillation in the H- component at 45 mHz is attributed to a field line resonance and manifests below 45 mHz in the Btor of the satellite dynamic spectrum.
Discussion
The observation of an apparent Doppler shift in Btor frequency for the first part of the dynamic spectrum, where the intensities are high, agrees with Vellante et al. In the case of the example given by Vellante et al. 2004) was the Doppler shift to higher frequencies due to CHAMP moving equatorward.
Summary and Conclusions
In the first part of this chapter a brief overview of L-dependent oscillations observed in the outer magnetosphere for L > 3 is given. L-dependent observations of the inner magnetosphere for L < 3 are studied in the second part of this chapter.
L-dependent pulsations in the outer magnetosphere for L > 3
In order to correct the lack of observations of Pc3 magnetic pulsations in the outer magnetosphere, Takahashi et al. 1990) begins with an analysis of magnetic field data between L = 2 and 6 obtained by the AMPTE CCE spacecraft. As shown in Figure 6.1, their dynamic spectra were characterized by traces of pulsational activity with a frequency falling with L between L = 3 and 6. 1987) observed toroidal oscillations with frequencies that decreased as a function of increasing L- shell from L = 4.5 to 9.1 and it increased again as the satellite moved to lower L shells for a single full orbit as shown in Figure 6.2.
Inner magnetosphere Pc3 observation
- Current Observations
- Event 1
- Event 2
- Event 3
After the satellite crosses L ~ 1.6, the toroidal resonant frequency decreases with increasing L value to about 27 mHz at 13:31 UT and L ~ 2.1. Shown in Figure 6.10 are Pc3 events observed simultaneously on the ground at HER and along CHAMP trajectory.
Discussion
The frequency shift to higher frequencies is attributed to the equatorward motion of the satellite. Doppler shift signals are stable and depend on the direction of the satellite's motion.
Summary
The reason for the size differences is not clear; however, the larger offset for Event 2 may be due to the significant longitude difference between the satellite orbit and the Hermanus ground station.
Introduction
Data selection
Therefore, the second step in the establishment of the database of events was the determination of the presence of FLR using the cross-phase technique. In this technique, a peak in the H-component phase difference spectrum identifies the natural frequency of the geomagnetic field line that has its footing between the two stations.
Upstream wave conditions
For this data set for February 7, 2002, the total IMF strength, solar wind speed, and cone angle are shown from top to bottom, respectively. The cone angle is the only variable of the three that varies over a 10 minute period.
Criteria for quantifying the FLR
ULF upstream waves are driven by a wave-particle interaction in the terrestrial foreshock and as a result their frequency is proportional to the size of the IMF. It is expected that polarization hodograms in the resonance region will clearly show a 900 rotation of the field line resonant magnetic field components.
Data base
The observations in Chapter 5 clearly demonstrated the 900 rotation of the transverse resonant magnetic field components. Therefore, we also attribute the result of the experiment to the strength of the observed resonance.
Summary
T., 1998, An interpretation of the cross-phase spectrum of geomagnetic pulsations using the field line resonance theory., Geophys. F., 1983, The relationship between the strength of the IMF and the frequency of magnetic pulsations on the Earth and in the solar wind., Planet.
