Observations of High Frequency Waves

3.5.1 Electromagnetic waves: Lion roars

Lion roars are intense, short-duration, narrow-band packets of whistler mode waves observed in Earth's magnetosheath, first reported by Smith et al. (1967) using data from OGO 1. The average mean frequency of these waves in the magnetosheath is ~ 100 Hz (0.25-0.5 fee) with typical amplitudes of 0.1 nT and burst durations of 1 -2 s (Smith and Tsurutani, 1976). When Lion roars are excited inside mirror modes, their frequency is much lower because of the strongly depressed magnetic field. A more detailed study of lion roars found that these emissions were most often observed in the inner region of the sunward magnetosheath, and the distribution of their intensity at 200 Hz was highest near the subsolar magnetopause (Rodriguez, 1985). Tsurutani et al. (1982) found that lion roars often coincide with minima of the magnetic field strength and maxima of plasma density, indicative of mirror mode structures. Zhang et al. (1998), using large amounts of data collected by the Geotail spacecraft, argued that only 30% of the lion roars were associated with mirror modes. This was probably due to a selection effect of the magnetometer aboard Geotail as discussed by Baumjohann et al. (1999) who, using the very sensitive magnetometer on Equator-S, found that low frequency lion roars are nicely associated with mirror modes. They consist of very narrow band emissions of a few tens of Hz frequency following the local electron cyclotron frequency and indicating the presence of trapped electrons in mirror modes. Lion roars are most probably gener ated by unstable anisotropic electron distributions, when the perpendicular electron temperature is larger than the parallel temperature. These are the low parallel energy electrons. In the mirror mode structures, the number of resonant electrons is larger for a given anisotropy than outside in the undisturbed magnetosheath (Smith and Tsurutani, 1976).

Early studies of lion roars in the magnetosheath found that they typically propagate with wave vectors at angles less than 30° relative to the magnetic field (Smith and Tsurutani, 1976). Baumjohann et al. (1999) found that the wave vectors were very close to parallel to the magnetic field, taking into account measurements of nearly monochromatic magnetic wave packets detected by the Equator-S spacecraft in the minima of the magnetic field. Some of the lion roars contained in the Geotail study (Zhang et al., 1998) were found to have wave vectors near 90°, suggesting they were downstream propagating whistler waves from the bow shock. Zhang et al. (1998) also found that although the majority of lion roars that were detected by Geotail were propagating in one single direction, one class of lion roars were found to be propagating in two directions simultaneously, suggesting the local plasma as the source.

The multipoint measurements of Cluster are ideally suited for determining the location of the source region and characteristics of the magnetosheath lion roars. Maksimovic et al. (2001), using data obtained in the duskside magnetosheath from the Cluster STAFF Spectrum Analyser (Cornilleau-Wehrlin et al., 1997), found that close to the magnetopause, lion roars in deep magnetic troughs are observed to propagate simultaneously in two directions, both parallel and anti-parallel to the magnetic field, as shown in Figure 3.18. Panels (a) and (b) of this figure show that the lion roars (solid line) are found to be more circular and more right-handed than the other whistler waves (dotted line). Panel (c) shows two peaks for the wave vector of the lion roars. After taking into account Doppler effects and the plasma velocity, these results imply that some lion roars on this date were propagating both upstream and downstream. This suggests that the Cluster spacecraft were in the source region of the lion roars, consistent with the results of Zhang et al. (1998). Far from the magnetopause, the waves were found to propagate in only one direction, roughly anti-parallel to the magnetic field. In addition Maksimovic et al. (2001) found that the lion roars were propagating at angles of 30° to 50° from the local magnetic field direction, which is inconsistent with whistler mode waves which would normally be Landau damped in a bi-Maxwellian plasma. This differs from many of the earlier works which found much smaller angles, and may be due to the sampling and bandwidth characteristics of the STAFF-SA instrument. It is also possible that this angular difference has a physical explanation that will become apparent through future statistical studies of lion roars. One should, however, take into account that the time resolution of the Cluster measurements is conciderably lower than that of the Equator-S measurements, and because of this, the direction finding is less accurate for Cluster measurements than for Equator-

degree of polarization

degree of polarization

Ellipticity

Ellipticity

Figure 3.18. Histograms showing various characteristics of the whistler waves observed on December 10, 2000 near the magnetopause by the STAFF-SA instrument on the Cluster spacecraft: (a) the degree P of polarisation, with a value of 1 indicating the three components are fully coherent and the wave field is fully polarised, (b) the ellipticity (+1 for circular right-hand polarisation), and (c) the angle between the wave vector and Bo, for the lion roars (solid line) and for other whistlers (dotted line). (From Maksimovic et al., 2001).

Figure 3.18. Histograms showing various characteristics of the whistler waves observed on December 10, 2000 near the magnetopause by the STAFF-SA instrument on the Cluster spacecraft: (a) the degree P of polarisation, with a value of 1 indicating the three components are fully coherent and the wave field is fully polarised, (b) the ellipticity (+1 for circular right-hand polarisation), and (c) the angle between the wave vector and Bo, for the lion roars (solid line) and for other whistlers (dotted line). (From Maksimovic et al., 2001).

S, as discussed by Baumjohann et al. (1999) with respect to the measurements of Zhang et al. (1998) for lion roars related to mirror modes. The more sensitive magnetometer aboard Equator-S which allowed for extraordinarily high time resolution clearly identified narrow band low frequency lion roars to propagate very close to parallel or antiparallel to the local magnetic field thus suggesting that the lion roars observed in relation to mirror modes originate from various trapped electron components in different places inside mirror mode bubbles.

The work of Maksimovic et al. (2001) was an introductory study of lion roars using the Cluster fleet. The primary contribution that Cluster can make to the knowledge already gained on the characteristics of lion roars is performing a statistical study of the direction of propagation using the multi-spacecraft measurements of STAFF-SA obtained in various regions of the magnetosheath as well as outside and inside mirror modes. These measurements will be supplemented with information obtained from various Cluster instruments, such as FGM, to determine the fraction of lion roars observed within mirror mode structures, or PEACE to determine whether an electron temperature anisotropy exists for those lion roars observed to be propagating in two directions. In addition, the very high time resolution waveform data of the Wideband (WBD) plasma wave receiver (Gurnett et al., 1997) should help in this regard. Since WBD has a time resolution of 35 ^s and time of measurement accuracies to 10 ^s on all 4 spacecraft, cross-spacecraft correlations of the lion roar waveforms can be performed, yielding information on the propagation of these lion roar wave packets from the source region. A similar correlation analysis has been successfully carried out for the chorus emission region in the inner magnetosphere (Santolik and Gurnett, 2003).

3.5.2 Electrostatic waves: Broadband structures

All of the early plasma wave measurements made by spectrum analyzers showed the prevalence of Broadband Electrostatic Noise (BEN) in many regions of Earth. First discovered by Scarf et al. (1974) and Gurnett et al. (1976) in the distant tail of Earth, BEN was characterized as being bursty and consisting of broadband spectral features usually extending from the lowest frequencies measured up to as high as the plasma frequency. The intensity of BEN was found to decrease with increasing frequency. Rodriguez (1979) provided the first comprehensive survey of BEN in the magnetosheath. He found that the magnetosheath electrostatic turbulence was almost continually present throughout the magnetosheath with broadband (20 Hz to 70 kHz) rms field intensities typically 0.01-1.0 mV m~1. He also found the turbulence to consist of two or three components: a high frequency component (> 30 kHz) peaking at the electron plasma frequency fpe, a low frequency component with a broad intensity maximum below the nominal ion plasma frequency fpi, and a less well defined intermediate component in the range fpi < f < fpe.

Dubouloz et al. (1993) carried out a theoretical investigation that showed that electron acoustic solitons passing by a satellite would generate spectra that could explain the high frequency part of BEN, above the electron plasma frequency, that had been observed in the dayside auroral zone by the Viking satellite. This was followed in 1994 by the findings of Matsumoto et al. (1994) that solitary waves of a few milliseconds in duration were responsible for the high frequency part of BEN observed by the Geotail satellite in the plasma sheet boundary layer. These electrostatic solitary waves appeared in the form of bipolar pulses (one positive electric field peak followed by one negative peak, or vice versa) in the time series data obtained by the Geotail Plasma Wave Instrument. An electron two-stream instability that produced nonlinear Bernstein-Greene-Kruskal (BGK) type isolated potentials was proposed by Matsumoto et al. (1994) as the generation mechanism for the electrostatic solitary waves. The Fourier spectrum of the solitary waves represented by the bipolar pulses was thus the reason for the broad band signature since a single pulse contains all frequencies up to a frequency determined by the time duration of the pulse. Subsequently similar solitary waves were found to be responsible for the BEN observed in several other regions of Earth, c.f. Franz et al. (1998) and Ergun et al. (1998) using Polar and FAST satellite data, respectively. Interferometry data obtained on these satellites allowed for the identification of these solitary waves as coherent potential structures, either electron or ion phase-space holes determined by the direction of propagation of the solitary waves, the hemisphere in which they were detected, and the initial direction (positive or negative electric field) of the pulses. A statistical survey of electron solitary waves observed by the Polar satellite at 2 to 9 Re was carried out by Cattell et al. (2003) with the following findings: 1) the mean solitary wave duration was about 2 ms; 2) the waves have velocities from ~ 1000 km s-1 to > 2500 km s-1; 3) the observed scale sizes (parallel to the magnetic field) are on the order of 1-10 XD, with /kTe from ~ 0.01 to 0(1).

Cluster observations of solitary waves in the magnetosheath were first reported by Pickett et al. (2003). Using Cluster WBD data (Gurnett et al., 1997), the bipolar pulse solitary waves were found to have time durations of ~ 25-100 ^s in the dayside magnetosheath near the bow shock. These solitary waves were found to be consistent with electron phase space holes. They were detected when the magnetic field was contained primarily in the spin plane, indicating that they propagate along the magnetic field. It was not possible for Pickett et al. (2003) to determine the velocity of the structures since the Cluster WBD instrument makes a one axis measurement, that being the average potential between the two electric field spheres. It was also not possible to correlate individual solitary pulses across different Cluster satellites, due to the 1/8 duty cycle of the WBD instrument when using this wideband 77 kHz filter mode and/or the solitary waves evolving (growing/damping) over the distance from one spacecraft to the next. Limited success of correlating solitary waves across satellites has been attained thus far only for the tripolar type solitary wave (discussed below) observed in the auroral region at 4.5 - 6.5 RE, well above the auroral acceleration region (Pickett et al., 2004b).

By using spectrograms of the waveform data obtained from two of the Cluster spacecraft separated by over 750 km in the magnetosheath, Pickett et al. (2003) found that the overall profile of the broad-band noise associated with the solitary waves was remarkably similar in terms of onset, frequency extent, intensity and termination on both spacecraft. This similarity implies that the generation region of the solitary waves observed in the magnetosheath near the bow shock is very large. The generation region may be located at or near the bow shock, or it may be local in the magnetosheath but related to processes occurring at the bow shock. Figure 3.19 shows an example of the broadband structures observed during a Cluster magnetosheath pass at high magnetic latitude on 05 April 2004 when the spacecraft were separated by as little as 150 km (spacecraft 1 and 2) and by as much as 500 km (spacecraft 1 and 4). The top three panels contain data from each of Cluster spacecraft 1,2 and 4 showing the broadband structures spanning the range from the lowest frequency measured, 1 kHz, up to as great as 60 kHz. Intense waves around 2-3 kHz are also observed throughout the interval. Interference from the emission of electron beams from the EDI experiment shows up as horizontal lines in the Cluster 1 data. The waveforms used to create the spectrograms for each of the spacecraft for a small time period around 13:37:00.33 UT are shown in the bottom three panels. Each panel contains 4 ms of data and except for parts of the bottom two panels, the data shown are from slightly different time periods based on the offset time below each panel from the start time shown at the top of the three panels. Solitary waves of a few tenths ofmVm—1 peak-to-peak and time durations of around 90 Ms are seen to dominate the waveform data leading to the broad bands seen in the spectrograms. Evidence of the 2 - 3 kHz sinusoidal type wave is also seen in the Cluster 1 data. Just as for the case with larger separations reported in Pickett et al. (2003), the overall profiles of the broad-band structures associated with the solitary waves are very similar on all spacecraft. Even so, the solitary waves as seen in the bottom two panels of the figure during the parts that overlap in time do not show a correlation.

Because the Cluster WBD plasma wave receiver is particularly suited to making measurements of solitary waves over a large range of time scales (a few tens of microseconds to several milliseconds) and over a wide range of amplitudes due to its automatic gain control feature, data from this instrument were used (Pickett et al., 2004a) in carrying out a survey of solitary waves observed throughout the Cluster orbit, including the magnetosheath. These solitary waves have been referred to as isolated electrostatic structures (IES) because they are isolated pulses in the electric field waveform data and previous studies have found them to be potential structures propagating primarily along magnetic field lines. Pickett et al. (2004a) found that throughout the Cluster orbit, two dominant types of IES are observed, the bipolar pulse type already discussed, and the tripolar pulse, consisting of one positive and

Figure 3.19. Cluster WBD observations of the waves in the magnetosheath. The top three panels contain the data in spectral form produced from high time resolution waveforms obtained on Cluster 1, 2 and 4, respectively, and the bottom three panels show very short time period snapshots of the waveforms from each of these three spacecraft. (From Pickett et al., 2003).

Figure 3.19. Cluster WBD observations of the waves in the magnetosheath. The top three panels contain the data in spectral form produced from high time resolution waveforms obtained on Cluster 1, 2 and 4, respectively, and the bottom three panels show very short time period snapshots of the waveforms from each of these three spacecraft. (From Pickett et al., 2003).

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