On July 3, 2007 from 1,645 to 1720 UT, the Cluster spacecraft approached the high-latitude dawn side magnetopause at the border between the magnetosheath and closed magnetospheric field lines (the coordinates in Geocentric Solar Ecliptic (GSE) system were X ≈ −10 R_E, Y ≈ −15 R_E, Z ≈ −9.4 R_E). Observed plasma signatures of this event are shown in Figure 1. These measurements, which were obtained through the Cluster Science Archive [27], came from the Cluster Ion Spectrometry (CIS) experiment’s [28] COmposition and DIstribution Function (CODIF) sensor and the Hot Ion Analyser (HIA). The magnetic field components were measured by Cluster’s onboard fluxgate magnetometer (FGM) [29]. Further documentation regarding the Cluster mission can be found through Escoubet et al. [30].

The ion density and velocity profiles measured by the CIS/HIA instrument, in conjunction with the proton energy spectrograms measured by the CIS/CODIF instrument, showed the oscillation of plasma populations (see Figure 1). Velocity fluctuations from the strongly anti-sunward to the weakly anti-sunward or sunward direction were experienced by both Cluster spacecraft (SC) 1 and 3 starting after 1645 UT (HIA data were unavailable for SC 2 and 4 during the event). The proton energy spectrograms for SC 4 displayed similar alternations between high-energy (∼ 5–10 keV) plasma typical for the magnetospheric environment and lower energy (∼ 0.3 eV–1 keV) plasma typical for the magnetosheath. Those alternations corresponded with fluctuations in the SC 1 and 3 ion densities, n, from tenuous (<1 cm ⁻³) to dense (3–10 cm⁻³), respectively. These fluctuations indicate that the spacecraft were observing alternating regimes between the magnetosheath and closed magnetospheric magnetic field lines ¹ as expected within KHWs. The vertical, B _Z , magnetic field component is strongly northward in the magnetosheath region at SC 1, 3 and 4 from 1640 to ∼1700 UT, see Figure 1. Also at these SC, the total magnetic field oscillates at the boundary between the two regimes, see discussion in Section 2.2. SC 2, which has the innermost location within the magnetosphere compared to the other SC, mainly shows higher values for the total magnetic field.

The OMNI-calculated solar wind parameters during this event can be found in Figure 2. There was a solar wind speed of ∼375 km s⁻¹, nearly constant IMF of ∼10.5 nT and the B_Z component of the IMF was southward. The wavelet analysis for wave power of the corresponding 3 s WIND data does not show any prominent spikes in the Pc4-Pc5 range (not shown). The horizontal component of the IMF was in Parker spiral orientation (B_X ≈ 5 nT, B_Y ≈ -6 nT). There were pressure fluctuations up until about 1635 UT which then ceased and remained rather stable throughout the event time frame. The Dst index (not shown) revealed that there wasn’t a geomagnetic storm during the time of the event; however, the AE index indicated that a geomagnetic substorm had occurred.

The profiles of velocity; magnetic field, ion density and total pressure, including its magnetic and plasma components, using Cluster SC 1 data for the time interval from 1640 to 1705 UT are shown in Figure 3. The total pressure was calculated as the sum of the magnetic (p _mag ) and plasma (p ), calculated using observations from the CIS/HIA instrument) pressures.

The magnetic field and velocity data for this time interval were transformed to the (L, M, N) components which describe local boundary normal coordinate system. For this we used the Siscoe method [31]. The coordinate vectors L and M are mutually orthogonal and tangential to the boundary. N is the coordinate vector in the boundary normal direction. It is orthogonal to L and M, forming a right-handed coordinate system. The averaged values of (L, M, N) are as follows. L = [−0.62, −0.69, 0.37] and is directed mostly dawnward and tailward. M = [−0.67, 0.22, −0.71] and is directed mostly anti-sunward and southward. N = [−0.41, 0.69, 0.60] and is directed mostly duskward and northward. The eigenvalues of the system are [λ ₁, λ ₂, λ ₃] = [149, 46, 8]. The ratio λ ₂/λ ₃ = 5.6, indicates that the normal direction is well-defined [32]. Also, L and M are reasonably defined because λ ₁/λ ₂ = 3.2. A well-defined Siscoe normal direction was also found for SC 4 during the event (not shown).

The three dimensionality of the boundary normal relative to the GSE coordinate system, produced by complex processes at the boundary, can lead to twisting of the magnetic field in the magnetosheath in the northward direction. This can also result in a discrepancy between the southward direction as seen in the OMNI data and that observed by THEMIS-C and D at the subsolar point (not shown), see discussion in Section 5.2.

The vortex formations are indicated when the M and N coordinates are mainly in anti-phase for both the velocity and magnetic field, according to Yan et al. [33], see Figure 3. However, observations of B _M and B _N in anti-phase can also be associated with reconnection. As an indicator of KHI vortices, it is expected to observe anti-phase V _M and V _N oscillations.

In the vortex rest frame, centrifugal force moves plasma outwards from the central part of the rolled-up KHI vortices. This leads to the formation of a local minimum in total pressure at the center and a maximum at the hyperbolic point between vortices [17,34]. The hyperbolic point is also associated with the local absolute maxima of the normal magnetic field component and jumps in the density [17]. Bipolar fluctuations in the normal component of the magnetic field and flow reversals in the normal component of the velocity occurred throughout the entirety of the event, from 1645 to 1705 UT (see Figure 3). The ion density, total pressure, and other magnetic and velocity component profiles were also highly oscillatory. The vertical dashed lines mark the local total pressure maxima that are mostly aligned with the local absolute maxima of B_N and with jumps in the density. This indicates the formation of the rolled-up KHI vortices (see also Discussion 5.1, (1) below).

We calculated the individual (L, M, N) coordinates for subsequent 1 min windows centered on each point in the time series, between 1640 and 1705 UT. The first panel in Figure 4 shows the values of the λ ₂/λ ₃ ratios, which are mostly well-defined throughout the event. The variation of the X, Y, and Z components of the boundary normals are also shown in Figure 4. One can see from the plot that the boundary normal is very dynamic. The angle between the averaged and individual boundary normals changes quasi-periodically in opposite directions indicating the oscillation of the boundary direction, as is typical for rolled-up KHWs.

We transformed the velocity into the deHoffmann-Teller (HT) frame, which is co-moving with the discontinuity [35]. The HT velocity, V H T ⃗ , is determined by minimizing | ( V ⃗ H T − V ⃗ ) × B ⃗ | 2 to obtain the constant transformational velocity V H T ⃗ for a given dataset. Here V ⃗ and B ⃗ are the observed time series of the ion velocities and of the magnetic field. We calculated the HT velocity for every minute and plotted its vectors and the normal vectors, as determined above, along the Cluster trajectory for this event, see Figure 5. It shows that, after a solar wind period when HT velocity vectors were in the negative X_GSE direction, Cluster entered a region with rotating deHoffmann-Teller velocity vectors and normal vectors associated with the boundary direction oscillations.

The existence of fast-moving, low-density plasma is typical for the KHI associated with mixing of two plasma environments [36,37]. We demonstrate this existence by plotting V _M versus ion density in Figure 6. The color of each point indicates the ion specific entropy, S, calculated as S = T / n 2 / 3 . (1)

The black line in the figure shows the fast-moving plasma population, with speeds in the range of −400 to −200 km s⁻¹, low ion density of < 5.5 cm⁻³, and specific entropy values in the intermediate range between that of magnetospheric and magnetosheath ions [38] .

The spectral wavelet analysis of the magnetic field normal fluctuations as observed by Cluster is shown in Figure 7. The periods of KHWs were defined manually using pressure maxima criteria and are marked in Figure 3 as the time between dashed lines. These periods were 173, 143, 64, 167, 113, 81, 79, 98, 142 and 62 s at ∼ 16:46:00, 16:48:53, 16:51:16, 16:52:20, 16:55:07, 16:57:00, 16:58:21, 16:59:40, 17:01:18, 17:03:40 and 17:04:42 UT, respectively. We see that the KHW-associated periods mainly coincide with power spectra increases of the magnetic field (excluding the period at 98 s, which is approximate minimum of the Fourier power spectra, and the period at 113 s, which is at the boundary between the local maximum and minimum). Within the range of marked periods we observe two power peaks in the global wavelet spectrum for the magnetic fluctuations: at periods of about 133 s and 70 s, see panel (c). These are fluctuations within the Pc4 range [39] . It seems that we observe a primary wave mode with a period ∼ 133 s and its submode at ∼ 70 s.

We also tested if reconnection was observed during this event. The Walén relation calculated in the HT frame shows the relation between the plasma velocity in the HT frame and the Alfvén velocity, V A ⃗ = B ⃗ / μ 0 ρ [35]. We found a 1 min deHoffmann-Teller interval from 16:45:58-16:47:01 UT (HT slope is one and correlation coefficient (CC) is 0.99) where the Walén relation is very well met (Walén slope = −0.99 and Walén CC = −0.87), see the Supplementary Material S1. The Walén slope was negative, which means the spacecraft crossed the rotational discontinuity (RD) tailward of the X-line [40]. The interval is marked by a gray shadowed bar in Figure 3. There were several other frames that met the “strict” HT (HT Slope = 0.9–1.1 and CC > 0.95) and RD (HT Slope = 0.7–1.1 and CC > 0.95) qualifications according to Nykyri et al. [41]. These were from 16:42:30–16:43:00 UT, 16:45:30–16:46:00 UT and 16:51:30–16:52:00UT. If the correlation requirements and slope requirements for the Walén relation are both relaxed (CC > 0.85, Walén slope > 0.5), then two RD intervals can be extended: 16:43:00–16:43:30 UT and 16:51:00–16:51:30 UT. Also an additional interval can be gained: 16:44:30–16:45:00 UT. All these RD intervals are marked by gray shadowed bars in Figure 3. In this figure we can see that the hyperbolic points of the rolled-up KHWs indicated by the dashed lines are in two cases accompanied by the RD likely associated with reconnection.

Field-aligned ion beams were observed at three instances during these marked intervals: 16:45:58.748 (V _par = 2,300 kms⁻¹, V _perp = 900 kms ⁻¹), 16:56:06.596 (V _par = 1,400 kms⁻¹, V _perp = − 700 kms ⁻¹) and 16:59:12.674 UT (V _par = 1,700 kms⁻¹, V _perp = − 500 kms ⁻¹), see Figure 8. The field-aligned beams may be an indication of ions moving along a separatrix and further imply that reconnection may have occurred. In the distribution function 1) at 1645 UT one can also simultaneously observe a perpendicular beam. This can happen if Cluster was crossing different magnetic field lines during the same data accumulation interval. The perpendicular beam can indicate that there are demagnetized ions in the reconnection exhaust region. Additionally during this interval the crescent distribution is seen, see Figure 8. This is a sign that the ions are demagnetized and the satellite was crossing the diffusion region [42]. There are multiple observations of the crescent distributions from 1640 to 1650 UT (not shown).

Based on the Cluster observations, the Pc4 event shown here can be interpreted as the KHI because:

1) The magnetic field magnitude and normal component maxima were aligned with the pressure maxima, indicating that the spacecraft were traversing the rolled-up KHWs [5,17]. This differs from instances of observing either FTEs or persistent surface waves. In the case of FTE observation, the pressure maxima is expected at its core (the center of the bipolar B_N) and the bipolar B_N fluctuations are separated by repetitious quiet periods with periods longer than 4 min [6]. In the case of persistent surface waves, the pressure maxima would be associated with the bipolar B_N = 0 crossings. These KHW magnetic field and total pressure signatures occurred in conjunction with periodical observations of magnetospheric and magnetosheath plasma populations (jumps in the density at the hyperbolic points), indicating that the KHI had developed into the vortices necessary for energy transport across the magnetopause [61];

The interpretation of the observations is also supported by the global modeling. The rolled-up vortices were clearly seen in LFM simulation results for the event, confirming that the solar wind conditions were favorable for KHW development. The favorable solar wind conditions are also supported by the analysis of the magnetopause shear angle. It has been shown that when the IMF has a strong Parker spiral component, the KHI can develop with tilted k-vectors with respect to the shear flow plane to maximize the onset condition [8,41,62], which could explain why KHWs were observed by Cluster at high latitudes.

Several of the KHI vortices observed in this event were likely accompanied by reconnection events as indicated by the Walén relation, the presence of deHoffmann-Teller frames, field-aligned ion beams observed together with bipolar fluctuations in the normal magnetic field component, and crescent distributions. The relation between the KHI and reconnection is highly dependent upon the magnetic field direction with respect to the sheared flow.

For northward IMF conditions, Otto and Fairfield [3] demonstrated that as long as there is a KH wave vector component along the magnetic field, the nonlinear KH mode can twist the magnetic field line and consequently generate a strong anti-parallel component. This then triggers magnetic reconnection (even without an anti-parallel magnetic component in the initial condition). Later, Nakamura et al. [63] showed that if there is an anti-parallel magnetic component across the sheared flow, the spin region (trailing edge) of the KH wave can thin the current sheet, which also triggers magnetic reconnection. The above two KH driven reconnection mechanisms are described in a two-dimensional perspective. In three-dimensions, the KHI can strongly twist magnetic field lines in its active region, which triggers a pair of middle-latitude component reconnections (e.g., [64–66]).

For the southward IMF condition, as is namely the case in this paper according to the OMNI data and THEMIS observations at the subsolar point, there are pre-existing anti-parallel magnetic field components (mainly along the north-south direction) that are mostly perpendicular to the sheared flow (mainly along the Sun-Earth direction). This configuration is unstable for both magnetic reconnection and KHI. Thus, both KHI (mostly in XY_GSE plane) and reconnection (mostly in XZ_GSE plane) can operate simultaneously [23], One process can be initialized earlier or grow faster than the other. But it does not have to be that one triggers another. The onset of KHI can locally thin the current sheet which triggers reconnection, especially in the spine region (trailing edge) (see illustration of such coupling in Figures 4, 6, 11 (at t = 124 s) in Ma et al. [24]). Note that the majority of open flux are connected through the spine region. In the vicinity of vortices, plasma flow strongly twists magnetic field lines which generates patchy reconnection and complex flux rope structures. Both strongly anti-parallel magnetic field and reconnection jets (i.e., along the Z-direction), may not be easily observed (see also [67]). In our study we observe field-aligned beams together with bipolar B _N magnetic field fluctuations as an indication of reconnection. The onset of magnetic reconnection can change the width of the sheared flow, and consequently changes the KH wavelength [25]. This event demonstrates the complexity of the instabilities generated at the magnetopause.

Source regions for longer wavelengths and lower frequencies are expected farther down the magnetotail. For the present KHI associated with reconnection event, there are three possible source regions. The first is close to the subsolar point where magnetosheath flow first starts to diverge and where KHI growth may be enhanced by both dayside reconnection [25] and by solar wind velocity and pressure fluctuations [60]. The latter enhancement was also demonstrated by the LFM simulation of this event. The second source region is at the dawn sector of the southern cusp [68], and the third region is farther down the tail where flow from tail reconnection is moving Earthward and forms a shear layer. This velocity shear layer is observable in the LFM simulation, see, e.g., Figure 12. Most relevant for the present event are the first two source regions, and future work will need to address the possible KHI associated with reconnection interference from multiple sources.

ULF waves in the magnetosphere have been correlated with solar wind conditions. For example, dynamic pressure variations are known to generate pulsations [69]. However, the solar wind speed, IMF magnitude, Alfvénic Mach number (not shown), and flow dynamic pressure from the OMNI data all remained nearly constant during the event, ruling out the likelihood of the ULF waves observed by Cluster being driven directly by pressure perturbations.

There were solar wind ion pressure pulsations preceding the event which may have acted as seed perturbations at the subsolar point, providing for the propagation and development of the event KHWs seen farther down the flank [70]. In fact, three of the THEMIS spacecraft situated in the magnetosheath at the subsolar point during this event recorded signatures of significant boundary motion, including pressure perturbations, which further supports this hypothesis. Figure 14 shows the pressure tensor for the xx −, yy −, and zz − components (red, blue, green, respectively) recorded by the Electrostatic Analyzer (ESA) onboard THEMIS-E (P4). The ion pressure moment data were obtained from reduced-mode data, which has a degraded angular resolution, but high time resolution (∼ 3 s). Similar plots for THEMIS-C and THEMIS-D can be found in the Supplementary Materials, see Supplementary Figures S4, S5.

We did the wavelet analysis of the magnetic field B _Z,GSE fluctuations observed by THEMIS-E, see Figure 15. We do observe spikes of the wave power at the periods of 140 and 70 s which is in agreement with the spikes observed by Cluster. Therefore, these fluctuations (via reconnection) may have further modulated the KHWs.

THEMIS-E also observes magnetosheath jets (see the plasma ram pressure pulsations in Supplementary Figure S6 in the Supplementary Materials) with a periodicity of about 5 min, which would result in dayside magnetopause oscillations and/or magnetopause reconnection [71,72], and possibly also modulate the KHWs and associated reconnection. The origin and dynamics of these jets is beyond the scope of this paper and is left for a future study.