Cm Pi

Figure 10.15. Left: Structure of the diffusion region from a numerical Hall fluid simulation by Rogers et al. (2003). The magnetic field lines are shown in white, the out-of-plane magnetic field is colour coded (white duskward, black dawnward). Also shown: projection of Cluster configuration with colour coded spacecraft, and approximate location relative to the diffusion region. Right: Cluster observations, simulation results are in grey lines. a: Reconnecting magnetic field component. b: Out-of-plane magnetic field component. c: Normal magnetic field component. d: Electric field normal to the magnetopause, directly observed (solid lines), j x B/ne (dotted lines). e: Tangential electric field with average value about -1 mVm—1. f: plasma density from satellite potential. At the bottom the spatial scale obtained from the four-spacecraft magnetopause velocity estimate is given. The observations are consistent with fast collisionless reconnection. (From Vaivads et al., 2004).

rent layer (bottom of figure). The current sheet thickness is about 300 km, ~ 4Ai-. All 4 spacecraft observe a similar current structure (panel a), with the largest deviation seen by Cluster-3. Thus, the current sheet is planar on the scale of spacecraft separation Xj) and is stable on the time scale of one second (approximately the ion gyroperiod). In addition, all 4 spacecraft observe that the current sheet is bifurcated, with strongest current (gradient in BL) along the outer edges.

The Hall magnetic field BM (panel b) exhibits a bipolar variation. There is no significant constant offset in BM, indicating the absence of an extra (external) guide field in this case. The fact that all 4 spacecraft, crossing the magnetopause consecutively, observe Hall fields indicates that this is a stable spatial feature of the diffusion region rather than some brief temporal variation. This is an important conclusion that was not possible to confirm with the measurements from earlier single spacecraft missions. The negative sign of the normal component of the magnetic field Bn w-3 nT in combination with a negative BM followed by a positive BM is consistent with the Cluster spacecraft crossing the diffusion region south of the X-line.

For the local magnetopause being a rotational discontinuity, the BN ~10% of BL yields a reconnection rate of ~0.1, a value that is obtained in numerical simulations of fast collisionless reconnection (e.g., Hesse et al., 2001; Shay et al., 2001). It corresponds to an inflow velocity of ^25 kms-1, or a tangential electric field in the magnetopause reference frame of Etang ~ 1 mV m . The observed tangential electric field component fluctuates, but is on average of this value (panel e).

Panel f shows that in the center of the current sheet (plasma outflow region) the density increases significantly (by ~50%), and there is a similarly large density dip when entering the current sheet. The density dips had been seen in simulations (e.g., Shay et al., 2001) along the separatrices as a result of enhancements of the magnetic field strength associated with the Hall current loops. The absence of a significant density gradient across the magnetopause shows that reconnection is almost symmetric at this position where the magnetospheric mantle and magne-tosheath fields reconnect.

In addition to the Hall magnetic field, Cluster also observed the Hall electric field (panel d). The electric field component normal to the magnetopause, En changes sign from positive to negative in the center of the current sheet. The dotted lines show the corresponding j x B/ne terms of the generalised Ohm's law, Eq. 10.2. En and j x B/ne are of same order and exhibit very similar variations thus indicating that most of the electric field En is balanced by the j x B/ne-Hall term in the generalised Ohm's law. This good agreement is best seen within the narrow region of strong En at ~ 13:22:04 UT. Thus the Cluster measurements confirm the dominant role of the Hall term on the scale of the ion diffusion region. In addition, the presence of a cross-magnetic field electric field on a spatial scale comparable to, or smaller than, the ion gyroradius implies that ions will be accelerated by this field as they move from the outside of current sheet to the center of current sheet. The cross-field potential drop across the region of the strongest electric field amounts to ^300 V. A proton accelerating through 300 V increases its speed by ^250 km s^1. This is approximately the Alfven velocity in the inflow region and comparable to the predicted outflow velocity of ions from the reconnection region.

Figure 10.16 shows the location of the parallel currents in the ion diffusion region of the reconnection site. The out-of-plane magnetic field component BM in panel a exhibits a bipolar signature which is attributed to the Hall currents in the reconnection region. Panel b shows the parallel current obtained by using the four Cluster spacecraft to define the appropriate coordinate system and then using the single spacecraft magnetic field perturbations to calculate the current. As predicted by simulations, strong parallel currents in the direction away from the X-line occur all along the outer edge of the bipolar BM structure. (Since V • J = 0, there must also be return currents toward the X-line further inward from the separatrix.)

10.3.3 High-frequency waves

High frequency plasma waves at the magnetopause can be taken as indicators of electron beams which have been accelerated at the magnetopause. In the absence of very high temporal resolution (<4s) of the electron distribution measurements this is the best and in most cases the only way of inferring such beams. Since the main reasons for particle acceleration along the magnetic field can be sought in the process of reconnection, such beams provide information on the processes inside the diffusion region. Here we report on two such observations, one of which is the event described in the previous section. The key finding is that localised high frequency waves along the separatrices are directly related to field-aligned currents.

Figure 10.16 shows the relation between the passage of an ion diffusion region tailward of the cusp during reconnection as was discussed above. In this figure, panel c shows the electric field power integrated over a broad frequency range from 2-80 kHz which includes the plasma frequency fpe. All four spacecraft show that the highest amplitudes of the waves are along the external edges of the bipolar disturbance in BM. These regions coincide with the separatrix of the reconnection site which is located north of the Cluster quartet. As shown above, the regions of strong emissions coincide with narrow regions of strong parallel currents. For the first time the high-frequency waves in the vicinity of a reconnection site are directly related to the parallel currents flowing along the separatrices. While single spacecraft measurements have indicated a relation between high frequency waves and separatrices already earlier (Farrell et al., 2002), the multi-point measurements were crucial to establish the existence of a direct relation between the two.

The wave spectrum is broad-band, exhibiting a spectral peak near the plasma frequency, panel d. This suggests that these waves are a combination of Langmuir (or upper hybrid) waves and solitary structures or electron acoustic emissions. The presence of these waves indicates the presence of electron beams along the separa-trix and thus serve as a diagnostic tool for the reconnection site. The waves could also play a role in electron thermalization. Neither the beam nor this thermalization is, however, observable due to the narrowness of the transition.

Figure 10.17 shows another example of high-frequency wave observations associated with reconnection, but obtained at some distance from the X-line and in

Figure 10.16. Observations of field-aligned currents and Langmuir/upper hybrid waves at the separatrix. For Cluster 2,3 and 4 the time series have been shifted -0.09 s, -0.3 s, and +0.55 s into the magnetopause frame. a: Out-of-plane magnetic field component; b: Field-aligned current with direction away from the X-line; c: Total spectral density in the frequency range 2-80 kHz; d: Wave spectrum exhibiting intense emissions at the plasma frequency, fpe ~ 28 kHz, marked by the red dot in panel c. (From Vaivads et al., 2004).

Frequency [kHz]

Figure 10.16. Observations of field-aligned currents and Langmuir/upper hybrid waves at the separatrix. For Cluster 2,3 and 4 the time series have been shifted -0.09 s, -0.3 s, and +0.55 s into the magnetopause frame. a: Out-of-plane magnetic field component; b: Field-aligned current with direction away from the X-line; c: Total spectral density in the frequency range 2-80 kHz; d: Wave spectrum exhibiting intense emissions at the plasma frequency, fpe ~ 28 kHz, marked by the red dot in panel c. (From Vaivads et al., 2004).

a high plasma-ß region. The figure shows a sequence of Cluster 3 measurements on March4,2002 (Khotyaintsev et al., 2004). The spacecraft was in the high-ß regime at this time outside the magnetopause with the exception of the short time interval around 09:38:30 UT, when it crossed the center of an FTE (as indicated by the maximum in the total magnetic field and the fast tailward flow with negative vy-component, and with low ß).

Figure 10.17. Cluster-3 measurements on March 4,2002. a: total magnetic field magnitude, b: magnetic field components, c: plasma flow velocity, d: plasma ¡5, e: electric field spectrogram between 2-40 kHz, f: magnetic field spectrogram, between 8 Hz and 4kHz. (From Khotyaintsev et al., 2004).

The interesting times are at -09:39:20 UT and —09:40:15 UT when the electric spectrum exhibited intense high frequency emissions. The first of these events is a broadband event, while the second shows a spectral peak around the local plasma frequency at fpe -40 kHz. Both events are close to narrow strong current sheets, with currents up to 0.5 ^A m-2 (determined by using the multi-spacecraft curlome-ter technique, but not shown here) of which the first coincides with the end of the passage across the FTE. The second is much closer to the magnetopause crossing at -0940:30 UT.

Figure 10.18 shows the integrated electric wave power in the frequency interval 2-80 kHz (top panel) and the magnetic component BX-GSE (maximum variance)

x 10"1

ß| l "T " I I '-T—" ~ I I I 1 — --'T— ----'J'

x 10"1

ß| l "T " I I '-T—" ~ I I I 1 — --'T— ----'J'

09:40:15 09:40 20

Ol Mar 2002

09:40:15 09:40 20

Ol Mar 2002

Figure 10.18. Integrated wave power. Top: Integrated electric wave power integrated in the frequency range 2-80 kHz. Bottom: The Bx-GSE component. (From Vaivads et al., 2004).

for the second high frequency event for all 4 spacecraft (the spacecraft at this time are at their closest separation, ^100 km). All spacecraft see the highest electric wave power at the edges of the current sheet (indicated by the change in Bx) but at different intensities. Since the whole crossing of the layer took not more than 2 s, it was not possible for the PEACE instrument to provide a sufficiently fast measurement of the electron distribution. The observation of high frequency waves is the only and strongest indication for the presence of electron beams flowing along the magnetic field. Presumably these beams are emanating from the reconnection site at the cusp magnetopause along the magnetic separatrices.

10.3.4 Lower-hybrid waves

In this section we describe Cluster observations of intense lower-hybrid wave activity along the separatrix at the inner edge of the magnetopause boundary layer. Electron beams are the probable energy source for these waves.

Satellite measurements show that the magnetopause is almost always subject to enhanced wave activity, often of broad-band character, at frequencies close to the local lower hybrid frequency (Gurnett et al., 1979; Anderson et al., 1982; Tsuru-tani and Thorne, 1982; LaBelle and Treumann, 1988; Andre et al., 2004). Since the magnetopause is characterised by density gradients and by electron motion relative to the ions that is directed transverse to the magnetic field, some of the instabilities that may occur are drift instabilities, in particular the lower-hybrid drift instability (Davidson, 1978), electron beam instabilities and/or the electron-shear flow instability (Drake et al., 1994). These waves may be involved in particle acceleration, in diffusive plasma entry across the magnetopause from the magnetosheath into the magnetospheric boundary layer, and in reconnection.

The current understanding of the role of lower hybrid waves in reconnection remains controversial. Particle-in-cell (PIC) full particle simulations in 2-D and 3-D demonstrate that lower hybrid waves evolve in the current sheet and contribute to the onset of reconnection (Shinohara et al., 2001; Scholer et al., 2003). It seems that once reconnection has developed, it is no longer sensitive to the presence of lower hybrid waves. The reason for this insensitivity is that the reconnection rates obtained in different simulations either allowing or inhibiting lower hybrid waves are similar. From a crossing of the Polar spacecraft close to the reconnection site at the magnetopause, Bale et al. (2002) showed that lower-hybrid wave amplitudes were too small to support reconnection. Similar results have been obtained in laboratory experiments (Carter et al., 2002). More elaborate observations of such waves are therefore very helpful and can improve our understanding of their role in reconnection.

Andre et al. (2004) and Vaivads et al. (2004) have recently used Cluster wave-field measurements at frequencies near fLH, taken some distance from the reconnection site at the magnetopause to infer the nature and intensity of the waves. Vaivads et al. (2004) studied a high latitude, northern hemisphere, dayside magnetopause crossing at MLT ^14 on February 6, 2002 at 08:11:57 UT (see Figure 10.19). Cluster was at minimum spacecraft separation of ^100 km, The magnetopause normal nMP was obtained from times when the spacecraft detected the magnetopause density gradient. Cluster 1 and 4 were closest to being on the same flux tube, with only ^20 km separation transverse to B. Cluster 3 was the last to cross the magnetopause while Cluster 1, 2, and 4 crossed it in rapid sequence.

The overall structure of this dayside magnetopause region equatorward of the cusp has been described by Andre et al. (2004). These authors, using high time resolved PEACE electron data from Cluster sampled at a time resolution below the spacecraft spin period, showed that the largest amplitude electric fields were found on scales between c/a>pe and c/mpi in the region marked in yellow in Figure 8.24 of De Keyser et al. (2005). These coincide with a narrow density depletion layer inside the magnetopause with steep density gradients and strong currents. Field-aligned currents flowing in this region are associated with field-aligned electron beams (Andre et al., 2004). This layer might be associated with the separatrix emanating from a distant reconnection site. It also coincides with the inner boundary of the magnetopause separating regions with and without high energy plasma sheet electrons.

The lower hybrid waves are expected to have wavelengths much shorter than the spacecraft separation and thus they are not expected to be correlated between different spacecraft. We therefore show data from only Cluster- 4, which had the

Figure. 10.19. Lower hybrid drift wave observations near the magnetopause on February 6,2002. a: plasma density iiyps derived from satellite potential, b: electric field between pi and p3. p2 and p3 band-pass filtered 15-35 Hz (inset showing geometry of probes), c: E-spectrogram. d: B-spectrogram. e: field-aligned Poynting flux spectrogram. /: band-pass filtered density fluctuations dnvps at 15-35 Hz. g: electron flux across magnetopause: vertical axis on the right gives an estimate of diffusion coefficient D for a density gradient of 25 m 4. (From Vaivads et al., 2004).

highest time resolution as the EFW instrument was in the internal burst mode. The importance of having multiple spacecraft will be discussed later.

Figure 10.19a shows the density as seen by Cluster-4. Figure 10.19b shows the band-pass filtered (15-35 Hz) electric wave field measured between the probes p13 and p23 (see inset). The lower-hybrid frequency is — 30 Hz. This frequency range shows a strong wave packet in coincidence with the density gradient. The plasma-5 during the event was in the range of 0.3 to 0.5. The wave amplitude is mainly perpendicular to the local magnetic field indicating that these are lower-hybrid drift waves, excited by the density gradient. Panels c and d of the same figure show the respective electric and magnetic wavelet spectra of the measured signals between 0-180 Hz. Panel e gives the corresponding Poynting flux, panel f the band-pass filtered density fluctuations, and panel g the band-pass filtered 'diffusive' flux of electrons across the magnetopause. The last two panels will be discussed later when we consider anomalous diffusion.

The wavelet spectra show the broadband character of the localised emissions. Furthermore, the peaks near the lower-hybrid frequency are well expressed in the electric spectrum, and at 08:11:57.5 UT one also observes a peak at — 100 Hz in the whistler band in both electric and magnetic fluctuations. It is interesting to consider the colour-coded field-aligned Poynting flux (green antiparallel, red parallel). The energy flux is largest in the low frequency range and lowest for the whistlers, where it is about 2 orders of magnitude less. The whistlers move antiparallel to the ambient magnetic field which is also anti-parallel to the electron beam at the density gradient. On the other hand, the field aligned velocity of the lower hybrid-frequency waves is positive (parallel to the electrons). Both these observations and the fact that electron beams carry much more energy than the waves suggest that the electrons are involved in the interaction, possibly generating the lower hybrid and whistler waves. Moreover, the lower hybrid waves propagate obliquely possessing a magnetic component, i.e., they are not purely electrostatic. In this frequency range the presence of the magnetic component suggests that the lower hybrid waves are partially in the whistler mode and probably propagate near the resonance cone.

Estimates of the phase velocity across the magnetic field, applying interferomet-ric methods (Vaivads et al., 2004), yield large though strongly fluctuating lower hybrid phase velocities (m/k)LH > 100 km s-1. Typical wave lengths lie between 3-10 km, substantially shorter than the spacecraft separation, which in retrospect explains the de-correlation of the waves between the spacecraft even for these short spacecraft separations. These observations do not resolve the importance of lower-hybrid waves in reconnection. They do, however, show that in certain regions (e.g., along the separatrices), the lower-hybrid wave activity can be intense.

The example above demonstrates that Cluster can provide very detailed information on the dispersive properties of the lower-hybrid waves at the magnetopause. However, more events will be needed to understand the role of these waves in the reconnection process. Particularly useful would be cases where Cluster is located closer to the X-line.

10.3.5 Low-frequency waves

This section describes Cluster observations of low-frequency waves at, and in the vicinity of, the magnetopause. The main points are:

■ Determination of the dispersion relation and the identification of low-frequency wave modes in the magnetopause and magnetosheath region.

■ Observations of turbulence in the magnetopause over a wide range of frequencies.

■ Conclusion that electromagnetic broadband waves might be the result of weak turbulence processes

Identification of low frequency wave modes in the magnetopause current and boundary layers, respectively, during reconnection and in the absence of reconnection, is of importance for the understanding of the internal dynamics of the magnetopause, plasma transport across the magnetopause, and the onset, maintenance and spatio-temporal evolution of reconnection. Theoretically, the magnetopause and boundary layer can be subject to different instabilities, fluid and kinetic, driven by the inhomogeneities and currents present in the plasma and fields encountered in the transition region or convected into the magnetopause enabling wave transformation. In all cases the magnetopause current layer is subject to enhanced wave activity at low and high frequencies.

In this section we focus on low frequency waves in the frequency range well below fce. Near the magnetopause the plasma is usually overdense, i.e., the electron cyclotron frequency is much less than the plasma frequency, fce ^ fpe.

10.3.5.1 Spectral properties

It is well known (Gurnett et al., 1979; Perraut et al., 1979; Anderson et al., 1982) that low-frequency waves observed at the magnetopause appear in both the electromagnetic and electrostatic polarisations. They are most intense at the magnetopause boundary itself. For illustration we show in Figure 10.20 an example of such waves measured by Cluster 2 during a particular crossing of the magnetopause. These spectra have been obtained by combining FGM data and STAFF data for the magnetic field measurements, EFW for the electric field. The low frequency spectra are obtained with the waveform unit, the high frequency parts from the onboard Spectrum Analyser (STAFF-SA). The spectra of the electric and magnetic fluctuations in the frequency range from ^0 Hz to near the lower hybrid frequency fLH — \/fcefc are quite different.

For frequencies below the proton gyrofrequency (fci) the slopes of the electric and magnetic spectra are similar, with the magnetic intensity exceeding the elec-

Figure 10.20. Low-frequency electric and magnetic wave power spectra measured by the various wave instrumentation on Cluster 2 at a crossing of the dayside magnetopause. Red: electric wave spectrum (right ordinate). Black: magnetic power spectrum (left ordinate). The curve labeled 'STAFF sensitivity' is the magnetic instrumental noise level. (Figure provided by D. Attie).

Figure 10.20. Low-frequency electric and magnetic wave power spectra measured by the various wave instrumentation on Cluster 2 at a crossing of the dayside magnetopause. Red: electric wave spectrum (right ordinate). Black: magnetic power spectrum (left ordinate). The curve labeled 'STAFF sensitivity' is the magnetic instrumental noise level. (Figure provided by D. Attie).

tric by two orders of magnitude as is expected for magnetohydrodynamic waves. Stepping up in frequency, the magnetic spectrum retains its slope of ~ f-2 5 up to frequencies above the lower hybrid frequency fLH in the whistler range. In contrast, the electric spectrum flattens out with increasing frequency into the ion cyclotron harmonic range, exhibiting a significant hump around the lower hybrid frequency. This hump ends at ^50 Hz, in coincidence with the decay in the magnetic wave power. At higher frequencies the electric wave power starts exceeding the magnetic power. It decreases roughly like ~ f-1, while close to the electron gyrofrequency the magnetic power drops to the instrumental noise level. These spectra are interpreted as broadband magnetic noise with its electric counterpart, ion-cyclotron waves and superposition of electrostatic waves around the lower hybrid frequency (lower hybrid waves). Waves of the latter kind were discussed in Section 10.3.4.

The low-frequency, broadband magnetic wave spectra resemble the neighboring magnetosheath ULF waves. Their intensity is very low on the magnetospheric side where they decay with frequency as ~ f-2 7. In the magnetosheath the waves are much more intense having a spectral slope of ~ -2.3. In the magnetopause they

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