Figure 2 displays MMS-1 burst mode observations at 1028:29–1030:34 UT when the MMS satellites were located at (x,y,z)_GSM = (5.0, 7.5, −4.6) R_E. These data cover two complete KH wave periods consisting of three short intervals in a cold magnetosheath plasma and two longer intervals in a KH vortex region, where MMS typically measured a more isotropic ion temperature (Figure 2F). The magnetosheath plasma is characterized by a very low energy flux of electrons in the 250–500 eV energy range (Figures 2A,B) that corresponds to anti-parallel strahl electrons from the Sun (Feldman et al., 1975; Vernisse et al., 2016). The higher-density (Figure 2E) magnetosheath periods are also characterized by a high ion energy flux below 2 keV with a core ion distribution at 90–110^o pitch-angle (Figures 2C,D) and Ti_perp > Ti_|| (Figure 2F) in agreement with a tailward magnetosheath flow deflected along the dusk flank magnetopause, Vx < 0 and Vy > 0 (Figure 2G), with the ions gyrating about a pre-dominantly northward (Bz > 0) magnetic field with weaker in-plane components generally displaying Bx > 0 and By > 0 (Figure 2H). The trailing edges of the two KH vortex regions are associated with more intense CSs, characterized by significant rotations of the By component. Figure 2I displays the magnitude of the GSM current density vector J = Ne(Vi-Ve), measured by the FPI ion and electron instruments. Here, N is the plasma number density, Vi the ion velocity and Ve the electron velocity. The trailing KH regions support some of the strongest CSs of this ∼2-min interval with J∼1 μA/m². In fact, one such CS encountered just before 1029:30 UT also supports a local, vortex-induced “type-I” reconnection exhaust (Nakamura et al., 2013) with a measured Vy∼100 km/s flow enhancement in the positive Y_GSM direction relative the Vy∼200 km/s external flow (Eriksson et al., 2016a; Li et al., 2016; Vernisse et al., 2016). The adjacent magnetosheath does not support many intense CSs, where MMS typically measured J < 0.4 μA/m². The two KH vortex regions support localized CSs with typical magnitudes 0.5 < J < 1 μA/m².

Figure 3 displays three ion VDFs in a plane that consists of a vertical axis along one of the two ion velocity components perpendicular to the magnetic field (V_BxV) and a horizontal axis that shows the ion velocity along the magnetic field (V_B). MMS-1 sampled the 150-ms ion VDF of Figure 3A in the magnetosheath-proper at 1029:39.084–1029:39.234 UT, which is marked as a red, vertical dotted line between the two KH vortex intervals of Figure 2. The core magnetosheath population shows up as a slow, mostly negative 50–200 km/s drift in a direction opposite the magnetic field direction. The ion VDF thus reflects the fast tailward (Vx < 0) ion flow with a southward (Vz < 0) flow deflection (Figure 2G) in a magnetic field with a positive Bx > 0 component and a stronger Bz > 0 component (Figure 2H) that MMS measured in a southern hemisphere location at Z_GSM = −4.6 R_E. Figure 3 compares this ion VDF of the magnetosheath proper with two ion VDFs measured by MMS-1 in two LLBL regions, which are marked as the black vertical dotted lines in Figure 2. MMS-1 measured the two ion VDFs just Earthward of the two intense trailing edge CSs of the two tailward-propagating KH vortices with Figure 3B showing the 150-ms ion VDF at 1029:26.599 UT, and Figure 3C showing the ion VDF at 1030:09.450 UT. This side-by-side comparison shows how the LLBL ion velocity distributions are hot and more isotropic as compared with a cold anisotropic magnetosheath ion VDF, which is also reflected in the corresponding 1-D cuts taken along the magnetic field V_B direction at V_BxV = 0 km/s and shown in Figures 3D–F.

The left-side column of Figure 4 presents the 2-D plane ion VDFs as observed by all four MMS satellites at approximately the same time with MMS-1 recording the ion VDF at 1029:55.284–1029:55.434 UT. This time is embedded within a 4.1-s long interval as displayed in Figure 2 between the two, pink vertical lines at 1029:51.849 UT and 1029:55.900 UT. The corresponding 1-D field-aligned cuts at V_BxV = 0 km/s are shown in the right-side column of Figure 4. There are two very distinct ion beams that propagate both parallel and anti-parallel to the local magnetic field at this time. The MMS-1 satellite (Figures 4A,E) measured a parallel D-shaped ion beam with a PSD peak around V_B = 550 km/s and a roughly D-shaped anti-parallel ion beam with a PSD peak near V_B = −525 km/s. The kinetic energy W_K = m_pV_B ²/2 corresponding to protons traveling southward at this fast field-aligned V_B speed is W_K∼1.4 keV for the anti-parallel ions, and W_K∼1.6 keV for the parallel ions traveling northward. The PSD of the two parallel beams is similar, and roughly two orders of magnitude lower than the PSD of the slowly drifting ion core distribution. The MMS-2 satellite (Figures 4B,F) observed two very similar counter-propagating ion beams as MMS-1 along this local magnetic field with a similar PSD and V_B magnitude, but obtained in a more southward location with a separation (ΔX,ΔY,ΔZ)_GSM=(−43,−85,−119) km from the MMS-1 satellite. The MMS-4 satellite (Figures 4D,H) also observed the two counter-propagating ion beams of similar PSD as MMS-1 and MMS-2, despite a more tailward separation (ΔX,ΔY,ΔZ)_GSM = (−178,−24,−42) km from MMS-1. However, MMS-4 measured a positive ion beam with a faster V_B = 600 km/s speed (W_K∼1.9 keV) and a negative ion beam that peaked at a slower V_B = −500 km/s speed (W_K∼1.3 keV) as compared with the MMS-1 ion observation. Finally, the MMS-3 satellite (Figures 4C,G) observed a strikingly different ion VDF as compared with the other MMS satellites with a much diminished PSD in velocity phase space, where the other satellites had recorded a distinct anti-parallel ion beam. Moreover, the parallel ion beam displayed the lowest PSD and the fastest V_B = 700 km/s (W_K∼2.6 keV) at MMS-3 as compared with the other locations in the MMS tetrahedron at this same time. Interestingly, this MMS-3 observation was obtained in a much more northward location (ΔX,ΔY,ΔZ)_GSM = (−17,−78,164) km relative MMS-2, and in a more earthward location (ΔX,ΔY,ΔZ)_GSM = (−60,−162,45) km from MMS-1.

The 4.1-s long interval marked in Figure 2 consists of 27 separate MMS-1 ion VDFs that displayed structurally very similar ion distributions as the ones illustrated in Figure 4A with two ion beams streaming up and down the local magnetic field, and superposed on a third, slowly drifting core population typically opposite the magnetic field. Figure 2 shows that the ion VDFs of Figure 4 were sampled well inside the leading edge of one KH vortex as MMS moved from the cold magnetosheath proper into a warmer section of the KH vortex, but before the satellites entered the hot, isotropic ion temperature region of the KH vortex that we associate with the LLBL-proper (Figures 3C,F). A closer examination of the ion VDF observations across the entire MMS tetrahedron through this particular KH vortex shows how MMS-2 measured two counter-propagating ion beams during a continuous ∼4.4 s period at 1029:51.299–1029:55.650 UT, while the MMS-4 satellite observed the two ion beams in two separate intervals; first as a short 0.70 s “burst” (1029:51.900–1029:52.599 UT) and then again as a longer ∼3.6 s period (1029:52.950–1029:56.500 UT). In contrast to the other satellites, the most earthward MMS-3 satellite recorded the two clearly resolved ion beams in three separate “bursts” with durations 0.30 s (1029:51.099–1029:51.400 UT), 0.95 s (1029:52.150–1029:53.099 UT), and 0.80 s (1029:54.099–1029:54.900 UT).

Figure 5 shows all four MMS satellite observations of parallel ion temperature and ion velocity through this KH-vortex encounter with Figure 5A showing the MMS-1 omni-directional ion energy-time spectrogram for reference. A cold Ti_||<100 eV ion temperature (Figure 5B) clearly displays a faster tailward Vix<0 (Figure 5C) and a fast southward Viz<0 (Figure 5E) magnetosheath flow before and after the KH vortex encounter, while a Ti_||>400 eV plasma corresponds with an LLBL domain characterized by slower Viz > −20 km/s. The two vertical, dotted lines again mark the 4.1 s interval when MMS-1 recorded the two ion beams. Interestingly, the MMS satellites remained within a Viz < −40 km/s magnetosheath-like flow regime at this time of interest with an intermediate Ti_|| between that of a cold magnetosheath proper and the subsequent hotter LLBL plasma.

We can display the time intervals of the two ion beams by converting the temporal information of Figure 5 into four MMS trajectories along a M _GSM = [0.717852, −0.696196, 0.0] in-plane direction that we define as M _GSM = −Vi_GSM/|Vi_GSM|. Here, Vi_GSM = [−155.37, 150.68, 0.0] is the average in-plane ion velocity that MMS-1 measured during the entire 1029:37–1030:21 UT KH-vortex time interval of Figure 5 with a magnitude V_KH = |Vi_GSM| = 216.4 km/s. The two components of the average in-plane speed (Vx = −155.4 km/s, Vy = 150.7 km/s) are shown as the dotted, horizontal lines of Figures 5C,D, respectively. The estimated propagation velocity of this KH vortex (V _KH = Vi_GSM) is corroborated using a timing boundary normal analysis (Schwartz, 1998), since there are measurable time delays of a sudden increase of Ti_|| at the 1029:43.5 UT beginning of this KH vortex encounter at the three MMS satellites (Δt₂ = −0.01 s, Δt₃ = 0.29 s, Δt₄ = −0.53 s) relative the MMS-1 satellite. These time delays and the other MMS satellite positions relative MMS-1 at this time, with MMS-2 at R ₂ = [−43.05, −84.85, −118.73] km, MMS-3 at R ₃ = [−59.55, −162.51, 45.28] km, and MMS-4 at R ₄ = [−177.65, −24.35, −42.05] km, resulted in a V = 219 km/s boundary normal speed along a boundary normal direction U _GSM = [−0.654991, 0.748380, −0.104472]. This local U _GSM direction is only separated 7.6^o from −M _GSM with a comparable speed. This means that −M _GSM and V_KH∼216 km/s represent a realistic, single KH vortex propagation direction and speed for the data displayed in Figure 5. The local V_KH∼216 km/s KH vortex speed is only somewhat slower than the mean V_KH∼258 km/s KH propagation speed of the many vortices that MMS traversed during the entire KH event (Eriksson et al., 2016a).

Figure 6 illustrates the four MMS satellite observations of the XY_GSM-plane ion velocity as shown in Figure 5 in the KH vortex co-moving frame of reference. Each MMS trajectory is aligned with the sunward-directed M _GSM satellite propagation direction through this tailward-moving KH vortex with the horizontal M _GSM-projections of the ion velocity vectors showing ΔV_M = V_M+216 km/s. The vertical axis displays the projection of the measured ion velocity along N _GSM = L _GSM × M _GSM = [0.696196, 0.717852, 0.0], where L _GSM≡[0,0,1]. The horizontal axis of Figure 6 also shows the distance, M = V_KH·t, that each satellite travelled along the M _GSM direction in time (t) from their start positions relative MMS-1, R ₁ = [0,0], at 1029:37 UT (t = 0) using V_KH∼216 km/s. At time t = 0, MMS-2 started at [M,N] = [28.13, −90.86] km, MMS-3 started at [M,N] = [70.40, −158.12] km and MMS-4 started at [M,N] = [-110.57, −141.19] km. The MN-plane ion velocity vectors are also color-coded using the individually measured Ti_|| (see Figure 5B) with a deep red color corresponding to a maximum Ti_||∼800 eV and a deep blue color corresponding to a minimum Ti_||∼52 eV. Figure 6 shows that all satellites recorded an earthward V_N<0 flow in the cold magnetosheath (M < 1250 km) prior to entering the warmer mixing region of the KH vortex. Figure 6 also confirms that all satellites measured an accelerated, counter-clockwise ion flow around the downstream KH vortex after M > 8250 km and until 1030:21 UT.

Figure 6 marks the individual times of two counter-streaming ion beams that we listed above as colored dots along each separate MMS trajectory. MMS-1 (black dots) observed the two ion beams at 3214 < M < 4091 km and MMS-2 (red dots) observed the same beams at 3095 < M < 4037 km. MMS-4 (blue dots) encountered the first instance of two ion beams at 3225 < M < 3376 km, and then again at 3452 < M < 4221 km. The most earthward MMS-3 satellite (pink dots) first came across the two ion beams at M = 3052 km, and it exited a more “filamentary” region of two ion beams at M = 3874 km. Note that MMS-2 was located at a distance Rz = −119 km from MMS-1 at 1029:37 UT, with MMS-3 at Rz = 45 km and MMS-4 at Rz = −42 km from MMS-1. However, despite the individual Z _GSM separations from MMS-1, it appears that all four satellites came across a region of similar dimension and location when two ion beams were present. Moreover, although the KH-vortex region mostly reflected an outward V_N>0 flow deflection from M∼2500 km to M∼7500 km, as typically expected in a KH co-moving frame of reference, it appears that the region of the two opposite ion beams displayed a more V_M-aligned ion flow direction with occasional earthward deflections (V_N<0).

Figure 2 marks another, 0.9-s period of similar counter-streaming ion beams at the very leading ion edge of the preceding KH vortex, which is marked between the two, pink vertical lines at 1028:42.950 UT and 1028:43.849 UT. An ion VDF example of the counter-streaming ion beam nature in this shorter time period is shown in Figures 7A,D with a clear D-shaped ion beam streaming in a parallel direction, while the anti-parallel beam appears as a shoulder in a 1-D cut of the 2-D ion VDF at a similar PSD and peak |V_B|∼500 km/s velocity as the parallel beam.

The two intervals of sustained, counter-streaming ion beams that we highlighted in the MMS-1 observations of Figure 2 also coincide with bi-directional electrons in the 250–500 eV energy range as shown in Figure 2B. However, it is clear from this electron measurement that such bi-directional electrons are prevalent in most of the two KH-vortex regions. In order to appreciate these ion DIS and electron DES measurements, for both intervals of distinctly counter-streaming ion beams inside the leading edges of the two KH vortices, we now compare the field-aligned energy fluxes of electrons in the 250–500 eV energy range at pitch-angles 0–10^o and 170–180^o with the pitch-angle observations of 2–3 keV ion energy fluxes in the immediate surroundings of the two intervals of distinctly counter-streaming ion beams.

Figure 8 displays the 16-s interval of observations in a region surrounding the first interval of counter-streaming ion beams at the very leading ion edge of the first KH vortex. We note how MMS-1 observed a sudden increase of the electron energy fluxes in both directions along the magnetic field at ∼1028:43 UT (see Figure 8E), near the onset time of the two ion beams. The DES instrument then recorded a second energy flux enhancement of electrons at the end of the period of the two ion beams at ∼1028:44 UT. The electron energy fluxes were essentially balanced in both directions along the magnetic field. In contrast, MMS-1 recorded a starkly different electron signature after the counter-streaming ion period between ∼1028:46.0 UT and ∼1028:47.5 UT when the anti-parallel electron energy flux suddenly decreased, while the parallel streaming electrons essentially maintained a similar energy flux level until decreasing as well toward the end of this ∼1.5-s period. In comparison, Figure 8D shows how the pitch-angle of the 2–3 keV ion energy flux displayed a dominant parallel component at ∼1028:44.5–1028:47.5 UT that overlaps with the 1.5-s period of unbalanced electron energy flux. Figure 7B shows an ion VDF example from this overlapping period at 1028:47.000 UT, which is characterized by a single D-shaped parallel ion beam with a peak V_B = 600 km/s velocity (W_K∼1.9 keV) along the magnetic field, superposed on a slowly drifting ion core population and a much reduced PSD of ions propagating opposite the magnetic field at speeds V_B < −350 km/s.

Figure 8D indicates another period of apparently counter-streaming ion beams in the pitch-angle distribution of the 2–3 keV ion energy flux at ∼1028:52–1028:53 UT deep inside this first KH vortex. This period coincides with a presence of weak energy fluxes of high-energy 3–10 keV electrons as shown in Figure 8A, indicating that MMS-1 sampled magnetic fields deeper in the magnetosphere at this time. The 2-D ion VDFs and the 1-D cuts along V_BxV = 0 km/s at this time do not display a distinct counter-streaming ion beam distribution of the nature displayed in Figure 4. The ion VDFs (not shown) rather suggest a heated magnetosphere-like ion population in a direction opposite the magnetic field, similar to that displayed along the magnetic field in Figure 3C, and a potentially diffuse ion beam propagating along the magnetic field.

Figure 9 displays a 19-s period of observations in a region surrounding the second interval of counter-streaming ion beams well inside the warm leading edge (Figure 9G) of the subsequent KH vortex. Figure 9E shows how the energy flux (E_f) of 250–500 eV electrons gradually increased by 85% in both directions along the magnetic field across the period of counter-streaming ion beams from <E_f>∼2.0·10⁸ keV/(cm²·s·sr·keV) at 1029:47–1029:49 UT to <E_f>∼3.7·10⁸ keV/(cm²·s·sr·keV) at 1029:55–1029:56 UT. The MMS-1 DES instrument also recorded three periods of localized E_f depletions in the immediate vicinity of the ion beam interval. The first period, centered near 1029:50 UT, is associated with substantial E_f depletions in both directions along the magnetic field. The second E_f depletion, centered near 1029:52.5 UT, is embedded with the counter-streaming ion beams. A third E_f depletion is observed again at ∼1029:56–1029:58 UT. In the first and second E_f depletions, Figure 9F shows how the electron plasma density (Ne) also decreased substantially at these times and relative the average Ne = 13.5 cm⁻³ of this 19-s period, with localized minima of Ne = 6.2 cm⁻³ (54% reduction) and Ne = 8.2 cm⁻³ (39% reduction), respectively. In fact, Ne correlates very well with the energy flux of bi-directional 250–500 eV electrons across most of the 19-s period. Figure 9A indicates a presence of 3–10 keV high-energy electrons centered at both E_f depletions. These observations suggest how the first two depletions of the bi-directional electron energy flux may be associated with a temporary region of embedded closed magnetic fields that connect much deeper into a low-density magnetosphere, where the 250–500 eV electron population is less prominent (Figure 1B). The third depletion of the 250–500 eV electron energy flux at ∼1029:57 UT is different in several aspects with a parallel electron energy flux that dropped to <E_f>=2.6·10⁸ keV/(cm²·s·sr·keV) and an anti-parallel electron energy flux that dropped to <E_f>=2.3·10⁸ keV/(cm²·s·sr·keV) relative the preceding 1029:54.849–1029:55.929 UT period of a balanced <E_f>=3.6·10⁸ keV/(cm²·s·sr·keV). First, there are no high-energy electrons in the 3–10 keV energy range. Second, the plasma density Ne∼12 cm⁻³ remained close to the mean value with no significant density reduction as compared with the first two E_f depletions. Finally, the 2–3 keV ion energy flux displayed a significant drop in the anti-parallel direction, with a dominant ion component streaming parallel to the magnetic field at 1029:56–1029:58 UT (Figure 9D). Figures 7C,F demonstrate how the anti-parallel ion beam that MMS-1 measured with a speed V_B < −350 km/s at 1029:55.349 UT (Figures 4A,E) had essentially disappeared by this time, as shown in an example ion VDF at 1029:57.299 UT, which rather consists of a single D-shaped parallel ion beam with a PSD peak at V_B = 550 km/s (W_K∼1.6 keV) and a slowly drifting ion core population.

Figure 8H shows the parallel electric field measurement by the ADP electric field instrument, but interpolated from 8192 Hz to the 30-ms cadence of the DES electron observations during the 16-s interval associated with a leading edge region of the KH vortex at 1028:40–1028:56 UT. MMS-1 observed a large E_|| = −6 mV/m at this 30-ms cadence near the onset-time of the counter-streaming ion beams at 1028:43 UT. It should accelerate electrons northward along the Bz > 0 magnetic field, and it could accelerate some ions in a southward direction. This E_||<0 is nearly 50% the surprisingly large E_|| = −14 mV/m that MMS-3 recorded inside a confirmed electron diffusion region (Eriksson et al., 2016b) associated with an intense J_|| = −2 μA/m² trailing-edge CS in this same KH event. However, whereas the DES instrument measured a large energy flux increase of the parallel 0–10^o electrons in the 250–500 eV energy range at this time (Figure 8E), it also recorded an immediate and equal energy flux response in the 170–180^o anti-parallel direction at the same time. Figure 8D shows how the ion energy flux first increased in a southward, anti-parallel direction at the time of the E_||<0 as might be expected from a local E_|| acceleration. However, the subsequent increase of the parallel ion energy flux toward the end of this 0.9-s interval of counter-streaming ion beams is not associated with a positive E_|| of any significant magnitude.

Figure 9H displays a variable E_|| with a magnitude below 2 mV/m throughout the 1029:51.8–1029:55.9 UT period of counter-streaming ion beams inside the warm leading edge of a subsequent KH vortex. However, there is no obvious correlation between the locally measured E_|| and the field-aligned energy flux of 250–500 eV electrons in this region, or between E_|| and the field-aligned ion energy flux in the 2–3 keV range.

Figure 8I indicates a very intense current density layer with a maximum J∼1.3 μA/m² at the time of the E_||<0 observation at 1028:43 UT. This intense current layer, which is primarily associated with a very localized decrease of the in-plane magnetic field from By = 40 nT to By = 15 nT (Figure 2H) and a Jz_GSM = −1.1 μA/m² component of the FPI current density (not shown), cannot be supported by the enhancement of bi-directional electrons in the 250–500 eV range alone, due to the well-balanced nature of the energy flux in both directions along this magnetic field at this time. The 250–500 eV electrons have a different source than the Jz < 0 current itself. Moreover, the intriguing ∼1.5-s period of parallel electrons and ions at 1028:46.0–1028:47.5 UT is not associated with any significant current density or E_||, despite a significant decrease of the anti-parallel electron energy flux and the disappearance of the anti-parallel ion beam. The current density measured across the leading edge of the subsequent KH vortex period, as shown in Figure 9I, is rather benign and mostly weaker than ∼0.5 μA/m² when the two distinct ion beams are observed streaming in opposite directions along the magnetic field.

The detailed energy flux descriptions of ions at 2–3 keV and electrons at 250–500 eV as observed inside the warm leading edges of two adjacent KH vortex regions are not unique to this pair of KH vortices at 1028:29–1030:34 UT on 8 Sept 2015. The signature of fast counter-streaming ions along the magnetic field, although not clearly present in the ion VDFs of all the KH vortices, have been confirmed using the ion VDF observations for 17 such KH vortex regions of this post-noon event. Each KH vortex may also be associated with several individual bursts of sustained counter-streaming ion beam signatures in an uninterrupted series of 150-ms ion VDFs, as seen along the MMS-3 and MMS-4 example trajectories of Figure 6, as the MMS satellites travel across the initial, warm ion temperature region of any given KH vortex. Table 1 lists a total of 26 such MMS-1 periods distributed across the 17 KH vortices, with durations ranging from Δt = 0.75-s to Δt = 5.25-s (column 3, Table 1) and a median Δt = 1.95-s. The focused bursts of two ion beams are almost exclusively present in a warm Ti_||∼490 eV, intermediate density Ne ∼ 12 cm⁻³ (Table 1 median values) leading edge of the KH vortex region of this post-noon event, and before MMS moved into the high-temperature LLBL section of the KH vortex, which is mostly characterized by isotropic ion temperatures (Figures 2C,F). In contrast, the 26 intervals of two ion beams analyzed here typically reflect very anisotropic ion temperatures due to a presence of these field-aligned beams with an average T_R = Ti_||/Ti_perp that ranges from 0.94 to 1.62 with a median T_R = 1.24 value (Table 1). In using the ion VDF observations recorded by the MMS-1 and MMS-2 satellites, which are essentially aligned along the northward-pointing magnetic field, it is clear that the maximum PSD of the parallel ion beam is higher than the maximum PSD of the anti-parallel ion beam in 16 of the 26 intervals. These intervals are indicated using a “+” symbol in the last column of Table 1. There were only four periods when MMS-1 and MMS-2 indicated a higher PSD in the anti-parallel ion beam than in the PSD of the parallel ion beam (c.f. “−” symbol in last column of Table 1), and in six intervals (no symbols in last column of Table 1), the PSDs were essentially of equal magnitude in the two ion beams. The energy flux of bi-directional electrons often display a clear enhancement in the 250–500 eV energy range when the ion VDFs display the two counter-streaming ion beams. Moreover, when one of the two ion beams, with observed speeds in a range 350 < V_B < 775 km/s (Table 2), is absent or displaying a highly suppressed PSD before or after the times listed in Table 1, resulting in one single ion beam, then so too does the energy flux of the bi-directional electron signature tend to change, and often in such a way that more electron energy flux will be observed in the same direction along the magnetic field as the remaining field-aligned ion beam.

A pair of two off-equatorial magnetic reconnection regions, which may capture a significant volume of magnetosheath plasma onto newly closed magnetic fields [e.g., (Faganello and Califano, 2017; Ma et al., 2017; Ma et al., 2021)], may also be associated with accelerated field-aligned ions and accelerated bi-directional electrons [e.g., (Nykyri et al., 2006; Nishino et al., 2007; Bavassano Cattaneo et al., 2010; Faganello et al., 2014; Vernisse et al., 2016)]. The two numerically predicated magnetopause reconnection regions have either been proposed to be located very far from the KH wave observations near the equatorial plane, such as a high-latitude lobe region tailward of the cusp (Bavassano Cattaneo et al., 2010), or located in a relatively closer mid-latitude region to the KH vortices from a reported presence of field-aligned electron observations [e.g., (Faganello et al., 2014; Vernisse et al., 2016)].

Let us first assume a presence of two mid-latitude reconnection (MLR) regions following some recent numerical advances (Faganello and Califano, 2017; Ma et al., 2017; Fadanelli et al., 2018; Sisti et al., 2019). The two MLR regions may be expected at a minimum λ_KH-distance from the region of maximum KHI growth (Ma et al., 2014). In the KHI case of 8 Sept 2015, Eriksson et al. (2016a) estimated λ_KH∼2.6 R_E and Vernisse et al. (2020) obtained a maximum KHI growth region near the GSM latitude location of the MMS satellites. We, therefore, assume two symmetrically located MLR regions at an equal distance L = λ_KH to the south of MMS, and L = λ_KH to the north of MMS at (x,y,z)_GSM = (5.0, 7.5, −4.6) R_E. This MMS location corresponds to a polar θ = −24.4^o angle at radius R_GSM = 10.1 R_E, while the distance L = λ_KH along an assumed circular field-line segment translates to a polar angle separation of only θ = 14.7^o from MMS. The two assumed MLR regions would then be located at polar angles θ_N = −9.7^o and θ_S = −39.2^o corresponding to Z_GSM = −1.7 R_E for the NMLR region and Z_GSM = −6.4 R_E for the SMLR region. An ion moving at a field-aligned speed V_B = 525 km/s, which corresponds to the median of the observed distribution (Table 2), would cover this L = λ_KH distance in ∼32 s. This corresponds to 0.50T_KH, where T_KH = 63.3 s is the estimated KH time period (Eriksson et al., 2016a). A very fast field-aligned ion travelling at the maximum V_B = 775 km/s speed observed at a peak PSD in any of these ion beams, would cover that same distance in only ∼21 s or 0.33T_KH. The slowest V_B = 350 km/s field-aligned ions observed here would reach MMS in ∼47 s or 0.75T_KH.

A similar exercise for a northern HLR region, assumed to be present in a cusp region [e.g., (Song and Russell, 1992; Fuselier et al., 2014)] at θ = 80^o on the same post-noon side as MMS (Luhmann et al., 1984), and consistent with the observed IMF By > 0 and IMF Bz > 0 (Nakamura et al., 2017), would result in a polar angle θ = 104^o separation from MMS. This separation translates into an 18.4 R_E field-aligned distance from MMS if we assume a circular magnetic field line through the location of the MMS satellites. In comparison, one would obtain a ∼20.2 R_E distance to the surface of the Earth from the MMS satellite along an unperturbed dipole magnetic field line (Schulz and Lanzerotti, 1974) assumed to exist in this KH region. A more realistic field-aligned distance of the perturbed closed field line through the KH region could be longer still, since it is also associated with a stressed, tailward-extended geomagnetic field, as shown in Figure 10. If we assume a northern HLR region ∼2 R_E off the surface of the Earth along this dipole field, we obtain a ∼18.2 R_E distance in general agreement with the simplistic, circular field line. A field-aligned ion travelling at V_B = 525 km/s would cover a 18.4 R_E circular field-line distance in 3.5T_KH, assuming that it will not pitch-angle scatter off that field line before reaching MMS. The fast V_B = 775 km/s ions would reduce that travel time to 2.4T_KH. We note that an assumed HLR in the southern cusp region is expected in a pre-noon sector for the observed IMF conditions (Luhmann et al., 1984), thus requiring more involved modeling analysis to estimate rough ion travel times from a southern HLR region to MMS.

The probability appears to be low for a double HLR process to explain why two mostly D-shaped ion beams would be measured almost exclusively in a warm leading region of the KH vortex as suggested from Table 1. The typical, much longer travel times T > 3T_KH expected from a northern HLR as compared with T < T_KH from two symmetric MLR regions clearly suggest that two counter-streaming ion beams associated with two HLR regions, even if they remain well-collimated along the field, would be more distributed throughout the closed field region of the entire KH vortex. One would also expect a more banana-shaped ion velocity distribution about V_BxV = 0 for ions measured by MMS this far from a HLR entry region due to a conservation of the first adiabatic moment of ions, if we also assume that the ions entered the magnetosphere in a region of lower magnetic field strength near the two cusps compared with a higher magnetic field strength measured in an equatorial region (Fuselier et al., 2014). A double HLR process, which is independent from a KHI process near the equator, does not appear to explain the presence of the two counter-streaming ion beams with a mostly D-shaped distribution in a warm leading region of the KH vortices.

Direct ion-beam evidence in support of one or two KH-related MLR regions has not commonly been discussed in the literature, which is rather focused on electron observations at different energies to deduce the magnetic field topologies that may be present across the dynamic KH vortex region in its various phases of temporal evolution [e.g., (Faganello et al., 2014; Vernisse et al., 2016)]. However, ion observations may be less challenging to utilize in understanding the immediate domain around the KH vortices due to the lower speed of accelerated ions along the magnetic field as compared with accelerated 250–500 eV electrons. A 250 eV electron would travel between a magnetic mirror point at R_M = 1.1 R_E in the northern ionosphere at 72.92^o latitude to the mirror point in the southern ionosphere along a closed dipole magnetic field through the MMS location at (x,y,z)_GSM = (5.0, 7.5, −4.6) R_E in only T_B/2 = 7.25 s (Schulz and Lanzerotti, 1974). Here, T_B is the full bounce period of that electron on a closed field line for an estimated L = 12.75 drift-shell MMS location. A fast 500 eV electron would travel that distance in T_B/2 = 5.25 s. A one-way travel time from one HLR region to the MMS location would be shorter still for 250–500 eV electrons. This means that 250–500 eV electrons could sample several important geomagnetic domains as compared with 2–3 keV ions along the magnetic field in the same time, including two double HLR regions. In assuming that the two D-shaped ion beams are associated with accelerated magnetosheath ions in two MLR ion exhaust regions, then it is also likely that the enhanced energy flux of 250–500 eV electrons, as often recorded by MMS in the same time periods, correspond to accelerated magnetosheath electrons from the same MLR regions. However, due to their fast speed, it is possible that the background of bi-directional 250–500 eV electrons, existing nearly throughout the KH vortex regions on 8 Sept 2015 (Figure 2B) may have a different source farther from the MLR regions, such as magnetosheath electrons entering onto new closed field lines formed by two HLR regions.

Sisti et al. (2019) performed a two-fluid 3-D numerical simulation for the observed MMS conditions of the 8 Sept 2015 event to suggest (their Figure 3) how the warm leading KH vortex region and the associated vortex “arm” are both expected to support once-reconnected field-lines (open field topology) and twice-reconnected field-lines (newly closed field topology) in very limited regions of the KH vortex in the early nonlinear phase of the KH evolution encountered by MMS. The results in Sisti et al. (2019) with spatially limited regions of twice-reconnected fields in the warm leading edge of the KH vortex support a MLR process closer to the KH vortex rather than double-reconnected magnetic fields associated with HLR near the cusps. However, we note that the predictions by Sisti et al. (2019) should be viewed as the expected locations of field-lines associated with one or two active reconnection regions in close proximity to the 3-D KH vortex due to the absence of any HLR regions in their fluid simulation that we understand to be present in a real system for similar conditions of a northward interplanetary magnetic field [e.g., (Gosling et al., 1991; Song and Russell, 1992; Øieroset et al., 2005; Fuselier et al., 2014)].

The time durations of the counter-streaming ion beams of Table 1 may be used together with an average tailward V_KH∼258 km/s velocity of the KH vortices (Eriksson et al., 2016a) to estimate a range of in-plane spatial scales (ΔS) that we associate with twice-reconnected magnetic fields connecting two MLR regions. The statistical widths for the 26 events of Table 1 would correspond to a range of spatial scales 3<ΔS<22 di along the trajectory of MMS with an in-plane median 8 di dimension, if we assume a constant di = 61 km ion inertial scale for the average plasma density N∼14 cm⁻³ that MMS-1 measured at the time of the two periods of counter-streaming ion beams in Figure 2. This spatial dimension compares well with the narrow regions that Sisti et al. (2019) predicted for this MMS KH event. A straight path through a simulated KH vortex, taken along the y-axis of their Figure 3 (right) and consistent with a tailward KH vortex propagation, also suggests that a region of twice-reconnected MLR fields should be narrower at the very first ion leading edge of the warm KH vortex region as compared with a thicker such region along the vortex arm that stretches in toward the KH vortex center at the boundary between a pre-existing LLBL of hot, isotropic ion temperature and the inner-most region of the warm plasma domain of the KH-mixing region. This is also consistent with the two examples of counter-streaming ion beams measured by MMS and shown in Figures 2, 8, 9 with a narrow ΔS∼4 di layer present at the very leading ion edge of the first KH vortex, starting at 1028:42.950 UT (Table 1), and a thicker ΔS∼17 di layer of counter-streaming ion beams starting at 1029:51.849 UT near the inner edge with the isotropic LLBL. In this second, warm inner region event of the subsequent KH vortex, MMS actually observed a short-duration layer with a single D-shaped parallel ion beam (see Figure 7C and Figures 9C,D) sandwiched between this region of twice-reconnected fields and the LLBL-proper. In contrast, Sisti et al. (2019) predicts that such once-reconnected open magnetic fields (their Figure 3, right) associated with just one MLR region to the south of MMS should be present before the twice-reconnected fields, suggesting that KH events may be more complicated. The presence of two or three individual bursts of sustained counter-streaming ion beam signatures in a given warm KH-vortex region (Table 1) also suggests a more layered structure of magnetic field topologies with “twice-reconnected” (DMLR) regions occurring not just at the very leading edge and at the subsequent inner vortex arm as predicted by Sisti et al. (2019). However, this does not change the overall agreement between these MMS observations and the Sisti et al. (2019) predictions of expected widths and locations of “twice-reconnected” magnetic fields that we associate with two active MLR regions to generate new closed fields in a KH vortex.

Eriksson et al. (2020) reported similar ion VDFs observed by the THEMIS satellites that also consisted of two counter-propagating magnetosheath ion populations, but in a region between two converging dayside magnetopause reconnection exhausts in the early flux rope formation stage. Eriksson et al. (2020) also performed a two-dimensional particle-in-cell numerical simulation for the THEMIS conditions to show how the ion particles of the two ion beams originated as colder upstream particles in the adjacent magnetosheath that drifted toward the magnetopause, where they were picked-up by the magnetic fields and accelerated up to the ExB drift of the reconnection exhausts near the two reconnection X-lines. This well-known entry mechanism of magnetosheath ions associated with magnetic reconnection at the magnetopause was first predicted by Cowley (1982), whereby a parallel cutoff-velocity forms below which no magnetosheath ions may enter onto the open magnetic fields earthward of the magnetopause. This cutoff velocity is clearly present in the D-shaped ion VDFs of Figure 4. A similar ion entry process likely accelerated a cold magnetosheath ion population, as observed by MMS on the same field-lines as the two counter-streaming ions, in two mid-latitude regions to the north and south of MMS. A difference between the 8 Sept 2015 KH-case and the sub-solar observations reported by Eriksson et al. (2020) is the magnetic topology with the latter case displaying Bz_GSM < 0 in the adjacent dayside magnetosheath and a north-south directed pair of Vz_GSM jets. The KH-case, however, displayed a significant Bz_GSM > 0 guide magnetic field and weaker Bx_GSM > 0 and By_GSM > 0 components of the magnetic field (Table 1) when the two ion beams were observed. A similar B _GSM was also observed in the magnetosheath-proper after 1130 UT. Indeed, Figure 1G demonstrates how MMS observed a generally positive By_GSM > 0 at nearly twice the magnitude of a mostly positive Bx_GSM > 0 throughout this KHI period, including in the tenuous and hot magnetosphere before 0920 UT. In considering two MLR regions roughly 15^o north and south of MMS, it would seem plausible that similar By_GSM > Bx_GSM > 0 conditions may have existed adjacent the two MLR regions. However, a KH-dynamic shearing-motion of magnetic fields associated with a tailward propagation of the KH vortex against the stress of the geomagnetic field is likely more important to sustain a MLR process (Faganello and Califano, 2017) than the in-plane components of a magnetic field direction in a nearby magnetosheath. This shearing-process of magnetic fields in the magnetosphere and in the adjacent magnetosheath is clearly illustrated in Figure 10 for a dedicated 3-D MHD simulation that we performed for this MMS KH event (Ma et al., 2021). The simulated NMLR CS is directed northward (Jz > 0) and the SMLR CS is directed southward (Jz < 0) as a result of this KH-shearing action on the magnetic fields. Figure 10 implies that two mostly in-plane (XY_GSM) ion exhaust regions will form in the vicinity of both MLR regions, with the ion jets directed typically sunward and tailward from each X-line reconnection region.

The mostly in-plane ion ExB reconnection exhausts thus predicted by numerical simulations to be present near the two remote mid-latitude regions will be dominated by their in-plane Vx_GSM and Vy_GSM components of the ion outflow, and perpendicular to a dominant Bz_GSM > 0 guide magnetic field. However, in considering individual gyrating ion particles, one must consider the total magnetic field, including this dominant Bz_GSM > 0 guide magnetic field observed on 8 Sept 2015. A cold magnetosheath proton above some cutoff velocity (Cowley, 1982) may enter the locally opened magnetic field (either MLR, north or south) and, in the case of a plasma density asymmetry with a higher density in the adjacent magnetosheath and a lower density earthward of the MLR magnetopause, the cold magnetosheath ions will most likely cross the mid-plane of the Jz CS onto the geomagnetic field (Cassak and Shay, 2007; Birn et al., 2008; Pritchett, 2008). That is, we assume that most of the ion reconnection outflow supports a significant velocity component along the geomagnetic field direction on the earthward side of the remote MLR magnetopause regions, as we suggest in the Figure 11 schematic with a few ion trajectories from a high-density magnetosheath into a low-density magnetosphere with thin lines and associated arrows displaying the directions of the in-plane components of the KH-sheared magnetic field in agreement with Figure 10. MMS measured a magnetic field strength B₂∼85 nT and plasma density N₂∼20 cm⁻³ in the adjacent magnetosheath (Figures 2E,H). The dynamic equatorial LLBL region supported a similar field strength B∼75 nT and a density N∼12 cm⁻³ (Figure 2), while MMS sampled an outer magnetosphere plasma sheet before ∼0920 UT characterized by a field strength B₁∼70 nT and a density N₁∼2 cm⁻³ (Figure 1). If we assume that similar plasma sheet conditions existed earthward of the two MLR regions at a small 15^o separation to the north and south of MMS, and with similar conditions expected in an adjacent remote magnetosheath as those measured at MMS, we may estimate a magnetic field ratio B₁/B₂∼0.8 and a plasma density ratio N₂/N₁∼10 across the remote MLR regions. A similar case (B₁/B₂ = 0.7 and N₂/N₁ = 10) was simulated by Birn et al. (2008) with a region 2 corresponding to our magnetosheath and a region 1 corresponding to our magnetosphere. This case predicts a bulk exhaust outflow on a magnetosphere-side with higher Alfvén speed, in basic agreement with the Figure 11 schematic, with this outflow primarily aligned with the magnetic field direction earthward of the magnetopause.

The Figure 11 schematic ion entry process is viewed from above the NMLR region, and from above the SMLR region, with a dominant Bz_GSM > 0 pointing outward and the symbols at Y_GSM = 0 indicating the direction of the Jz_GSM CSs, again consistent with Figure 10. We also note that the two X-lines of the schematic may be associated with a tailward deHoffmann-Teller drift along this flank magnetopause location. This means that the bulk of the adjacent magnetosheath ion velocity population, which supports a finite field-aligned drift centered near V_B ∼ −75 km/s (Figure 3A), may experience a shift toward V_B∼0 km/s in the assumed tailward moving frame of reference of the schematic with magnetosheath ions expected to move in both directions of the magnetic field in Figure 11.

There are four cases to consider for a possible explanation of the two counter-streaming, accelerated magnetosheath ion beams along the magnetic field that we propose that MMS observed on 8 Sept 2015. In Case 1 (NMLR sunward jet), a cold magnetosheath ion is assumed to enter the magnetosphere along the open magnetic field onto a sunward-directed in-plane component of a KH-sheared magnetic field on the earthward side of the Jz_GSM > 0 CS. However, we note that the locally open magnetic field earthward of the MLR magnetopause is directed mostly northward (Bz > 0 dominant guide-field) with a smaller sunward tilt. The guiding-center of this cold gyrating ion is accelerated by the drift of the reconnected field lines, and it will be measured along that magnetic field as a faster parallel ion beam, but only in a region to the north of the NMLR jet. In Case 2 (NMLR tailward jet), a cold magnetosheath ion enters the magnetosphere and it obtains a fast exhaust speed directed along the geomagnetic field, but this time opposite the open magnetic field onto a sunward-directed (KH tilted) in-plane component of the magnetic field earthward of the Jz_GSM > 0 CS. The cold gyrating ion is accelerated tailward by the reconnected field lines, and it will be measured as a faster anti-parallel ion beam along this mostly northward magnetic field line with a sunward tilt, but only in a region to the south of this tailward NMLR jet. In Case 3 (SMLR sunward jet), a cold magnetosheath ion enters the magnetosphere opposite the open magnetic field onto a tailward-directed (KH-tilted) in-plane component of the magnetic field earthward of the Jz_GSM < 0 CS. The guiding-center of this cold gyrating ion is accelerated sunward by the reconnected field lines, and it will be measured along that mostly northward-directed magnetic field line as a fast anti-parallel ion beam, but only in a region to the south of the SMLR jet. Finally, in Case 4 (SMLR tailward jet), a cold magnetosheath ion enters the magnetosphere along the open magnetic field onto a tailward-directed (KH tilted) in-plane component of the field earthward of the Jz_GSM < 0 CS. As before, the locally open magnetic field is directed mostly northward with a tailward tilt. The guiding-center of the cold ion is accelerated tailward by the reconnected field lines, and it will be measured along that geomagnetic field line as a faster parallel ion beam as compared with its initial magnetosheath speed, but only in a region to the north of the SMLR jet.

The proposed incoming magnetosheath ion particles on 8 Sept 2015 will only be guided toward the equatorial plane of the KH-vortex from the tailward exhaust of the SMLR region, and from the tailward exhaust of the NMLR region, by the dominant Bz_GSM > 0 magnetic field upon entering the locally open magnetopause. We emphasize the expected importance of a higher Alfvén speed on the earthward side of the MLR regions (Birn et al., 2008) to align the ion exhaust with the geomagnetic field. If the conditions of a given KH case are such that the higher Alfvén speed shifts to the magnetosheath-side of the MLR CSs, then the primary difference should be two counter-streaming magnetosheath ion beams associated with two sunward exhausts in the tailward moving MLR X-line frame of reference, assuming a northward Bz_GSM > 0 guide-field on the magnetosheath-side and a DMLR process that captures magnetosheath plasma onto newly closed magnetic field lines. A rotation of the in-plane exhausts about the Bz_GSM > 0 guide-field of the X-line by local KH-vortex action will not affect this simple scenario. What matters is the direction of the normal magnetic field across the magnetopause in the vicinity of the X-line, and that the geomagnetic field is stretched tailward (sunward) near the SMLR (NMLR) X-line, while the KH-entrained mostly northward-directed magnetosheath magnetic field is tilted sunward (tailward) near the SMLR (NMLR) X-line in agreement with Figure 10. We should note that individual ion particles upon entering the two MLR exhaust regions will also experience a small reconnection electric field E _r = −VxB as, e.g., associated with a guiding-center outflow motion on the order of |V|∼100 km/s in an in-plane (normal) magnetic field on the order of |B|∼5 nT that would correspond to an electric field E_r∼0.5 mV/m. This E_r electric field is directed away from the equatorial plane at both MLR regions with Ez < 0 at the SMLR X-line and exhaust, and Ez > 0 at the NMLR X-line and exhaust, such that J·E > 0 associated with the strong Jz currents of Figure 10. However, the two poleward diverging Ez electric fields will unlikely affect the bulk population of the incoming magnetosheath ion particles in their attempt to reach the guiding-center ion exhaust speed before they exit the tailward exhaust regions along the dominant Bz_GSM > 0 guide magnetic field near the two MLRs and travel toward the equator.

Vernisse et al. (2016) presented a statistical study focused on MMS observations of field-aligned, heated electrons in the magnetosheath adjacent to the trailing magnetopause CSs of the KH spine region that we associate with “type-I” vortex-induced magnetic reconnection ion exhaust signatures on 8 Sept 2015 (Eriksson et al., 2016a). However, Vernisse et al. (2016) also displayed one important MMS-1 ion velocity distribution averaged over a 1.5-s period at 1044:53.500–1044:55.000 UT near the leading edge of one KH vortex that appears to show two weak ion beams. They concluded that “additional electron and ion populations are shown to be present in the magnetosheath, and those are suggested to come from mid-latitude reconnection driven by the twisting of the field lines away from the KH waves in the northern and southern hemispheres.” In the next several paragraphs, we review the MMS observations in and around this single ion VDF measurement using the same format that we employed in Figures 4, 8, 9 to further our understanding of these important ion observations in the immediate 3-D spatial domain of the KH vortex region.

Figure 12 shows a 21-s period around this leading edge region. The 2.6-s interval at 1044:54.000–1044:56.600 UT (two dotted vertical lines) marks the time that Vernisse et al. (2016) associated with a presence of two counter-streaming ion beams in MMS-1 observations, and possibly due to a remote presence of two MLR regions. They referred to this region as an ion boundary layer (IBL) (Gosling et al., 1990; Onsager et al., 2001) in an “interval where the spacecraft is in the magnetosheath.”

Figure 13 displays the 150-ms ion VDFs as recorded by MMS-1, MMS-2 and MMS-3 around the same time at 1044:54.349 UT and in the same 2-D plane format as shown in Figure 4. We marked this time in Figure 12 as a pink, solid vertical line inside the 2.6-s interval. The chosen time is close to a local maximum of the parallel ion temperature (Ti_||). The corresponding 1-D ion cuts at V_BxV = 0 in Figure 13 appear to show two ion beams, but with a significantly lower PSD than the ion beams shown in Figure 4. The average <Ti_||> = 164 eV during this 2.6-s interval within the IBL region is correspondingly lower as compared with the values listed in Table 1. The Ti_||/Ti_perp ratio only reached a 0.84 maximum with an average <Ti_||/Ti_perp> = 0.67 ratio in this same period. These ion temperature signatures, together with an average <Ne> = 13.5 cm⁻³ electron plasma density, are consistent with a magnetosheath-like domain adjacent to the ion leading edge of the KH vortex. In comparing the MMS-1 ion observations of Figures 12C,D with the corresponding ion observations of the two events of counter-streaming ion beams shown in Figures 8, 9, it is clear that MMS-1 recorded these weaker ion beam signatures in a magnetosheath-like region farther from the warm ion temperature domain of the KH vortex region itself as shown between two solid vertical lines at 1044:57.8–1045:05.8 UT in Figure 12.

We note how both MMS-1 and MMS-2, which were located nearly along the same magnetic flux tubes, did not display a D-shaped ion beam distribution in either a parallel or anti-parallel direction. The two MMS satellites rather measured fast parallel and anti-parallel ions with a significant drift in one perpendicular BxV-direction as compared with the ion VDFs of Figure 4. This finite V_BxV drift of the beam ions may reflect a magnetosheath-like domain of the ions, or ion entry potentially farther from the MMS satellites, whereby some parallel motion at the entry location may have changed into perpendicular motion at the satellite due to a conservation of the first adiabatic invariant (Fuselier et al., 2014). Hardly any of the 17 individual ion VDFs that MMS-1 sampled at 150-ms cadence at 1044:54.000–1044:56.600 UT displayed a D-shape distribution of the parallel and anti-parallel streaming ions in contrast with the ion VDFs of Figure 4 and most of the individual counter-streaming ion beam events listed in Table 1. However, Figures 13C,F show that MMS-3, with an earthward ΔY_GSM ∼ −156 km displacement from MMS-1 and with only a small earthward ΔY_GSM ∼ −71 km separation from MMS-2, in fact recorded a mostly D-shaped parallel ion beam and an anti-parallel ion beam with a much smaller V_BxV drift at the same time as the two ion VDFs at MMS-1 and MMS-2. MMS-3 measured very similar D-shaped distributions of the parallel ion beam mostly throughout this 2.6-s period inside a variable IBL region adjacent to the KH vortex (not shown). This more earthward MMS-3 location was also associated with relatively warmer ion temperatures during this same 2.6-s period with a higher average <Ti_||> = 208 eV and a higher Ti_||/Ti_perp ratio that peaked at 0.97 with an average <Ti_||/Ti_perp> = 0.78 ratio.

The presence of two D-shaped ion beams with very weak PSD as observed by MMS-3 in a magnetosheath-like IBL region, and just before it entered a KH vortex region, could indicate a reflection of earthward-drifting magnetosheath ions (Onsager et al., 2001) along the open magnetic field near two MLR regions to the south and to the north of the satellite, and on the magnetosheath-side of the two MLR CSs (Figure 11). Another possibility is a leakage of magnetosphere ions, and electrons, from two MLR regions as suggested in Vernisse et al. (2016). The simultaneous presence of a dominant magnetosheath ion core population and a general absence of hot LLBL ions (Figures 3, 13C,F) would seem to support a magnetosheath ion reflection scenario. The D-shaped nature of the ion beam distributions at MMS-3 also supports a more local MLR region and an open magnetopause as, e.g., compared with more banana-shaped ion distributions associated with a more distant ion entry location relative the satellite (Fuselier et al., 2014).

Figure 4 shows how MMS-3 recorded a faster parallel ion beam speed V_B for a lower PSD as compared with the V_B speed and PSD of the parallel ion beams measured by the other MMS satellites at the same time. This appears to be a typical trend in terms of the field-aligned ion speed at the maximum PSD when these ion beams are observed on 8 Sept 2015, whereby a lower PSD of the ion beam is often reflected in a faster ion speed along the magnetic field (Table 2). That is, fewer and fewer ions are measured the faster the ions are observed to move. This observation suggests the presence of a velocity filter effect for the DMLR process that may be explained in terms of the actual distance to the proposed MLR ion exhaust source region (Eriksson et al., 2020) with only the very fastest ions being able to cover a longer distance as compared with slower ions of a similar ion velocity distribution.

Let us assume as a baseline scenario that two symmetric MLR locations exist at nearly equal latitude distances from a region of maximum KHI growth, which is not far from the predicted locations of the MMS satellites on 8 Sept 2015 (Vernisse et al., 2020). The observation of a typically higher PSD associated with the parallel ion beam of the Table 1 events, as compared with a lower PSD in the anti-parallel ion beam, would then indicate a more active or steady reconnection process near the SMLR region, perhaps accelerating more ions in a parallel direction than a less-active NMLR region producing fewer ions in the anti-parallel direction. This appears to be consistent with the north-south asymmetry prediction in Sisti et al. (2019) for the observed in-plane magnetic fields of this KH event whereby the number of SMLR regions tends to dominate over the number of NMLR regions. The alternative scenario of two asymmetrically located MLR regions of similar reconnection activity relative a region of maximum KH growth would suggest that MMS could have been closer to the SMLR region than the NMLR region to explain the larger number of ions collected from that direction. Either scenario appears to explain the observed PSD differences with 62% of the 26 cases in Table 1 typically favoring a higher PSD in the parallel direction than the anti-parallel direction of the two ion beams, with the opposite PSD observation seen in only 15% of the 26 cases.

MMS mostly observed the counter-streaming ion beams in the warm, intermediate ion temperature region (Ti_w) of the KH vortex, which is defined as the KH-mixing region where Ti_MSH < Ti_w < Ti_MSP. Here, Ti_MSP corresponds to the high-temperature region of the pre-existing LLBL-proper and Ti_MSH is the cold ion temperature of the adjacent magnetosheath. Sisti et al. (2019) reproduced these three regions in their Figure 3 on the basis of the plasma density, where Ti_MSP corresponds to the highest-density LLBL region of their simulated KH vortex. However, there is not much of a difference in the observed plasma density of the two KH vortex regions (Figure 2) that we associate with Ti_w and Ti_MSP. Moreover, the regions of two distinct counter-streaming ion beams in individual ion VDFs typically correspond to Ti_||>Ti_prp. This is very rarely, if ever, observed in the LLBL-proper, where the characteristic ion temperature is mostly isotropic Ti_||∼Ti_prp.

Sorriso-Valvo et al. (2019) explored the MMS observations of the 8 Sept 2015 KH event and reported a presence of bi-directional ion beams with an ion VDF example presented at 1007:45.820 UT. This ion VDF is part of a longer 3.3-s period of 22 individual 150-ms cadence ion burst measurements with sustained counter-streaming ion beams (Table 1). The pair of two coherent ion beams presented in Sorriso-Valvo et al. (2019) was proposed to be a result of the observed plasma turbulence first reported in Stawarz et al. (2016) of this same KH vortex region. However, it remains unclear how an extended region of plasma turbulence in the KH vortex region of this event would result in such organized and focused periods of counter-streaming ion beams, and only toward the warm leading edge of the KH vortices. One would expect much more extended intervals of such bi-directional ion beams throughout the KH vortex region, as also expected from a double HLR source discussed earlier, if they were a direct result of plasma turbulence. Indeed, it appears that the two-fluid 3-D numerical simulation (Sisti et al., 2019), which is able to reproduce the observed loci and dimensions of two distinct counter-streaming ion beams reported here, provides a more straightforward explanation of the origin of the two ion beams in terms of twice-reconnected MLR magnetic field lines to the north and south of MMS during the early non-linear phase of the KH instability at the Earth’s flank magnetopause.

Finally, we should mention that is not impossible that MMS may have sampled a Jz < 0 CS region of one SMLR region at 1028:43 UT when it observed the intense J∼1.3 μA/m² current layer with a dominant Jz_GSM = −1.1 μA/m² component and E_|| = −6 mV/m at the start of the 0.90-s interval of counter-streaming ions (Figure 8) that we associate with “twice-reconnected” fields and a presence of two MLRs to the south and north of the region of maximum KHI growth. However, the equal energy flux of bi-directional 250–500 eV electrons did not support this current per se. It is very likely that the ∼1.5-s period of parallel 250–500 eV electrons and parallel 2–3 keV ions at 1028:46.0–1028:47.5 UT inside the warm region of this first KH vortex (Figure 8) may be explained as magnetosheath particles still entering a tailward reconnection exhaust from one active MLR to the south of MMS, while the decrease of the anti-parallel flux of said electrons and ions at this time suggests that MMS was no longer connected to a northern MLR. Either it ceased to be active, or MMS simply moved away from it onto fields with a different topology.