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Figure 2.21. Distribution of rest frame frequencies, wave numbers, propagation angles, and el-lipticity in the plasma rest frame including error bar estimates. The small plot embedded in the left panel magnifies the frequencies and the wave numbers near the origin. The dotted, straight line in the left panel is the dispersion relation for the extended linear Alfven waves. (From Narita et al., 2004).

of lower frequency, with higher frequency waves only propagating perpendicular to the field.

The right-hand panel in Figure 2.21 shows the distribution of frequencies as a function of wave ellipticity. The average low frequency wave polarisation is left handed, with the higher frequency minor waves being left-handed when propagating upstream and right-handed for downstream propagation.

It is thus concluded that the foreshock in this frequency range is dominated by upstream propagation in agreement with other conclusions (Russell et al., 1971; Hoppe et al., 1981; Hoppe and Russell, 1983; Eastwood et al., 2002, 2003; Narita et al., 2003). In addition, waves at rest frame frequencies ~ 0.1 x Qcp with wave numbers ~ 0.1 x Q.cp/VA (wavelengths ~RE) have been identified. Some wave propagating nearly perpendicular to the magnetic field were also found. Their presence may be important in understanding the physical processes in this region.

2.3.2 Origin of gyrophase bunched ions

Backstreaming ion beams of several keV, collimated along interplanetary field lines, have been observed close to the ion foreshock boundary. Downstream of the field-aligned beam region, distributions characterised by a gyromotion around the magnetic field, i.e., a non-vanishing perpendicular bulk velocity with respect to the background magnetic field, have been reported. These gyrating ion distributions are nongyrotropic or nearly gyrotropic. Numerous studies concerning gy rating ions have been reported in earlier investigations mainly from ISEE 1 and 2 (Gosling et al., 1982; Thomsen et al., 1985; Fuselier et al., 1986; Fuselier et al., 1986a,b), AMPTE (Fazakerley et al., 1995) and WIND (Meziane et al., 1997; Meziane et al., 2001; Mazelle et al., 2000). Gyrating ions are often observed in association with ULF waves having substantial amplitude (Fuselier et al., 1986b). The waves are right-handed and propagate nearly along the ambient magnetic field (Thomsen et al., 1985). It is believed that the ULF waves are excited through a beam plasma instability (Gary et al., 1981) resulting from the propagation of field-aligned ions which precede them closer to the foreshock boundary.

Two mechanisms have been put forward to explain the origin of upstreaming gyrating ions. In one mechanism, a portion of the incoming solar wind is reflected in a specularly manner at the shock (Gosling et al., 1982; Gurgiolo et al., 1983). In the second mechanism, the waves produced through a beam-plasma instability can in turn trap the ions and cause the phase bunching of the distribution in what is called a beam disruption mechanism (Hoshino and Terasawa, 1985). Significant new results have been obtained from Cluster observations on this topic.

2.3.2.1 Bow shock specular reflection mechanism

Solar wind specular reflection at the quasi-parallel bow shock should produce non-gyrotropic ion distributions in the foreshock. When propagating upstream, the bunched ions undergo gyrophase mixing within a few Earth radii from their source on the shock leading to nearly gyrotropic distribution function (Gurgiolo et al., 1983). Gyrotropic distributions have not been observed in 3D measurements; however, 2D measurements suggest their presence within ~ 4 RE from the shock (Fuselier et al., 1986b). This also indicates that shock-produced non-gyrotropic distributions are rarely observed beyond ~ 4 RE . Very few observations of gyrophased bunched ions propagating away from the shock in the upstream region consistent with production by specular reflection have been reported in the literature. Gosling et al. (1982) were the first to report evidence of such specular reflection based on data from the FPE experiment obtained when ISEE was just upstream of the bow shock. Another event consistent with the specular reflection, observed at 4 RE and in association with ULF wave activity, was also reported by Thomsen et al. (1985).

As shown by Gosling et al. (1982), only under quasi-parallel geometries are the guiding centers of the specularly reflected particles oriented upstream, thus allowing them to escape. In fact, because of kinematic considerations, QBn < 39.9° is the limiting shock geometry allowing ions to escape upstream (Schwartz et al., 1983). In presence of large amplitude ULF MHD waves near the shock front, always observed in association with gyrating ions, the angle between the shock normal and the magnetic field can vary substantially. This can cause the shock to switch back and forth from a quasi-parallel to quasi-perpendicular configuration (Greenstadt and Mellott, 1985) and is illustrated in Figure 2.22. As shown theoretically by Fuselier et al. (1986), this effect, which depends on the characteristics of the waves,

Figure 2.22. A sketch showing how 6sn may be modulated by the presence of an upstream wave. (From Meziane et al., 2004a).

Figure 2.22. A sketch showing how 6sn may be modulated by the presence of an upstream wave. (From Meziane et al., 2004a).

z inhibits the escape of specularly reflected ions. When the wave amplitude is high (8|B|/B0 w 1), this effect is relatively strong.

Meziane et al. (2004a) reported clear quantitative evidence for the specular reflection mechanism. They have studied an ion event (Figure 2.23) observed in association with quasi-monochromatic ULF waves which strongly modulate the ion fluxes by nearly two orders of magnitude for some energy ranges, the fluxes coming down close to the instrumental background level for the minima. The analysis of the three-dimensional angular distribution indicates that ions propagating roughly along the magnetic field direction are observed at the onset of the event. Later on, the angular distribution is gyrophase-bunched and the pitch-angle distribution is peaked at ~ 150° in the solar wind frame. Analytic calculations show that the specular reflection of the solar wind proton population with a simple Maxwellian distribution should produced a reflected distribution peaked at a pitch-angle a0 ~ dBn. Since the measurement of particle pitch-angle and the derivation of dBn are independent, they provide a good quantitative test of specular reflection. According to three statistical bow shock position models, the Cluster spacecraft were located at about 0.5 Re from the shock with an averaged bow shock dBn of about 30°. This

Figure 2.23. Ion and magnetic field observations from Cluster 1 between 15:16 - 15:20:30 UT on March 9, 2002. The top two panels show, respectively, energy spectrograms from CIS/HIA (large geometric factor section) integrated over all directions, and over the 145-235° azimuthal look directions; the third and fourth panels display the GSE components and magnitude of the IMF; and the last three panels present solar wind densities and GSE velocities from CIS/HIA (small geometric factor section). The dashed vertical line indicates the magnetic connection time. From Meziane et al. (2004a).

Figure 2.23. Ion and magnetic field observations from Cluster 1 between 15:16 - 15:20:30 UT on March 9, 2002. The top two panels show, respectively, energy spectrograms from CIS/HIA (large geometric factor section) integrated over all directions, and over the 145-235° azimuthal look directions; the third and fourth panels display the GSE components and magnitude of the IMF; and the last three panels present solar wind densities and GSE velocities from CIS/HIA (small geometric factor section). The dashed vertical line indicates the magnetic connection time. From Meziane et al. (2004a).

Count rate versus 6,

Count rate versus 6,

5:00 16:30 17:00 17:30 18:00 18:30 19:00 19:30 20:t Time: 2002 March 09/1516:00 UT

Figure 2.24. The changes of local shock &Bn angle (dashed line-open circles) and the particle count rates during the interval when the ULF waves are present. The dashed horizontal line corresponds to 6gn = 39.9°. For clarity, the particle count rate values have been scaled by a factor 0.5. From Meziane et al. (2004a).

5:00 16:30 17:00 17:30 18:00 18:30 19:00 19:30 20:t Time: 2002 March 09/1516:00 UT

Figure 2.24. The changes of local shock &Bn angle (dashed line-open circles) and the particle count rates during the interval when the ULF waves are present. The dashed horizontal line corresponds to 6gn = 39.9°. For clarity, the particle count rate values have been scaled by a factor 0.5. From Meziane et al. (2004a).

result is therefore fully consistent with the specular reflection production mechanism.

The analysis of the waves has shown that they are left-handed in the spacecraft frame and propagate approximately along the ambient magnetic field. Meziane et al. (2004a) have found that they are in cyclotron resonance with the field-aligned beam observed just upstream of the interval of gyrating ions. Using the measured properties of the waves and particles (Figure 2.23), Meziane et al. have explained the observed particle flux-modulation in term of changes in dBn at the shock due to the low frequency waves. Figure 2.22 shows a sketch of the underlying geometrical model, which illustrates how the instantaneous dBn deviates from the average dBn0, computed from the background field B0, when the the wave field is added. Significant ion fluxes were observed only when the instantaneous dBn was less than 40°, consistent with specular reflection at the shock being the source of the ions.

2.3.2.2 Local production by wave pitch-angle trapping

Fuselier et al. (1986a) made a quantitative analysis of the particles and monochromatic waves from ISEE data, which strongly suggested that there was a coherent wave-particle interaction. They obtained a phase relationship between the gyrove-locity vG and the transverse wave field Bt indicating that energy transfer occurred between the particles and the waves, and that gyrophase trapping by the wave was possible. Since field-aligned distributions propagate deeply into the foreshock, the local production of gyrating ions through this process ought to be able to be observed far from the shock. Meziane et al. (1997) reported the first observations from Wind spacecraft data of several gyrating ion distributions and their association with low frequency waves, at distances larger than 20 RE from the shock. Clear indications of wave-particle interactions were observed. A more detailed study of the three-dimensional ion distributions with a large data set and the highest available time resolution (3 s) has since shown that these observational features can be found up to more than 80 RE from the shock (Meziane et al., 2001). Investigation of the non-linear wave trapping mechanism has shown that it can explain the properties of such gyrating ion distributions registered at large distances from the shock (Mazelle et al., 2000). It has been shown that the particles are not only bunched in gyrophase but also trapped in pitch-angle in velocity space around a value which is directly related to the amplitude of the wave self-consistently generated by the original field-aligned ion beam.

Mazelle et al. (2003) have investigated this local production mechanism to explain the existence of the well-defined gyrating ion distributions observed by the Cluster CIS instrument. The event shown in Figure 2.25 occurred during a long interval of foreshock wave activity. At 23:34:30 UT, energetic ions are revealed in the second energy spectrogram corresponding to measurements by the high-geometrical-factor side of the CIS/HIA instrument (the difference with the first panel showing the solar wind population is quite obvious). High fluxes are then continuously observed until 23:44 UT, followed by two small patches. These ions are mostly propagating sunward, as revealed from the analysis of their guiding center velocity, i.e., they are backstreaming ions. Before 23:34:30 UT, the IMF was nearly quasi-steady. Prominent large amplitude low frequency waves are observed after 23:35:45 UT both on the magnetic field and on the solar wind velocity. Figure 2.26 displays three-dimensional representations of the ion distribution functions registered by CIS/CODIF at 4s cadence. Nine consecutive distributions are shown for one energy channel (^8 keV) for which the observed backstreaming fluxes are maximum for a time interval inside the event displayed on Figure 2.25. Each frame in Figure 2.26 is a projection in gyrophase and pitch-angle with the B-direction located at the center. The three first snapshots indicate an ion beam propagating along the +B direction with a parallel velocity of 1100 kms-1, but the third one also shows a second peak for a large pitch-angle of about 60°. Then after 23:35:45, the spacecraft has entered a gyrating ion region. Gyrating ions are identified by

Figure 2.25. Observations from Cluster CIS and FGM on satellite 1 between 23:33-23:46 UT on April 7, 2001 : energy-time spectrograms of all ions from CIS/HIA for 'solar wind sectors' (sunward looking direction - upper panel) and 'dusk' solid angle (duskward looking direction - second panel), respectively; dc magnetic field components in GSE coordinates and its magnitude; ion density and bulk velocity in GSE coordinates derived from HIA measurements. From Mazelle et al. (2003).

Figure 2.25. Observations from Cluster CIS and FGM on satellite 1 between 23:33-23:46 UT on April 7, 2001 : energy-time spectrograms of all ions from CIS/HIA for 'solar wind sectors' (sunward looking direction - upper panel) and 'dusk' solid angle (duskward looking direction - second panel), respectively; dc magnetic field components in GSE coordinates and its magnitude; ion density and bulk velocity in GSE coordinates derived from HIA measurements. From Mazelle et al. (2003).

Figure 2.26. Sequence of consecutive three-dimensional 4-s display of the proton angular distributions registered by CIS/CODIF on Cluster 3 for an energy of keV (flux maximum) on April 7, 2001. Each frame represents the normalised distribution function on a surface of constant energy in the solar wind frame of reference projected to display 4n-coverage. The Bo vector is located at the center of each plot and the '*'sign indicates the solar wind direction. For each frame, the maximum maximum value of the normalised phase space density is shown in red. From Mazelle et al. (2003).

Figure 2.26. Sequence of consecutive three-dimensional 4-s display of the proton angular distributions registered by CIS/CODIF on Cluster 3 for an energy of keV (flux maximum) on April 7, 2001. Each frame represents the normalised distribution function on a surface of constant energy in the solar wind frame of reference projected to display 4n-coverage. The Bo vector is located at the center of each plot and the '*'sign indicates the solar wind direction. For each frame, the maximum maximum value of the normalised phase space density is shown in red. From Mazelle et al. (2003).

their gyrophase-restricted distribution peaked off the magnetic field direction. The interplanetary magnetic field used to plot the distributions is averaged over the spin interval (4 s) while the local proton cyclotron period is 7 s (i.e., about two ion sampling intervals). The gyrating distributions show a clear rotation of their maximum phase density in the left-handed sense around the magnetic field with alternating values separated by about 180°. Such gyrating ion distributions are observed up to -23:44 UT.

Mazelle et al. (2003) have analysed the associated large amplitude low frequency waves using multi-spacecraft analysis techniques (e.g., Eastwood et al., 2002). The wave are right-hand mode waves ('30-s waves'). They have shown that these wave are in cyclotron resonance with the field-aligned beam observed just before the spacecraft entered the gyrating ion/ULF wave region. This is the first direct quantitative evidence so far of this cyclotron resonance from observations in the ion foreshock. Then, they have studied the possibility of resonantly driving these waves unstable from the electromagnetic ion/ion beam instability by field-aligned beam ions also observed in the same region. The results from the linear theory has led to a very good agreement with the observed wave mode.

The event reported is inconsistent with a specular reflection at the Earth's bow shock since the observed pitch-angle of the gyrating ions are much too large: it should be nearly equal to dBn, which was ~ 30° in this case. It was thus necessary to invoke a local production mechanism for these upstream distributions. The possibility of producing the observed gyrophase-bunched ion distributions from the disruption of the beam by the excited wave has led to a good quantitative agreement from nonlinear trapping theory which predicts that the pitch-angle of the final gyrating ion distribution is related to the wave amplitude (Mazelle et al., 2000). This result is very similar to those obtained from previous studies in the distant foreshock (up to 80 RE) from Wind data with lower backstreaming ion densities and wave amplitude (Meziane et al., 1997; Meziane et al., 2001; Mazelle et al., 2000), which could mean that the present case study corresponds to the same mechanism observed by Cluster closer to the bow shock. Many other events consistent with this trapping mechanism have also been found while only one example of gyrophase-bunched ions produced by specular reflection has been identified by Cluster (Meziane et al., 2004a). However, better statistics are necessary to determine the percentage of gyrating events corresponding to either mechanism. It will be also interesting then to examine the location of such events and compare them with the forward boundary of the foreshock ULF waves.

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