Multipoint Cluster Observations of Kinetic Alfvén Waves, Electron Energization, and O+ Ion Outflow Response in the Mid‐Altitude Cusp Associated With Solar Wind Pressure and/or IMF BZ Variations

We report the properties of low frequency (LF) electromagnetic fluctuations (≤11 Hz) in relation to input electron and ion outflow response observed by Cluster in the mid‐altitude cusp during high solar wind dynamic pressure PSW and active magnetospheric conditions (Kp = 4+). The multipoint observations reveal the dynamic interplay between the spatial‐temporal properties of the wave and electron inputs and the ion outflow response enabling an assessment of causal connections. The LF waves are identified as ingoing traveling Alfvén waves that become dispersive at the ion gyroradius scale (i.e., kinetic Alfvén waves KAWs). The KAWs are collocated with ingoing field‐aligned electrons and ion outflow at keV energies and below. The KAWs are associated with earthward directed Poynting fluxes and energy densities with peak amplitudes occurring at multiple energy enhancements (“step‐ups”) exhibited in the electrons and ions, attributed to IMF BZ and/or PSW variations. Indicative of a causal connection, KAW Poynting fluxes and energy densities are strongly correlated with precipitating electron energy fluxes and outflowing O+ energies and energy fluxes. These yield mid‐altitude cusp empirical relationships that can be incorporated into or constrain cusp transport models. These results demonstrate the important role played by KAWs in enhancing electron precipitation into the cusp ionosphere and subsequent O+ energization upward along the magnetic field into the mid‐altitude cusp and beyond. The results also suggest the importance of PSW and/or IMF BZ variations in driving/controlling the reconnection source Alfvén wave and electron inputs into the cusp that significantly impact the ion outflow process.

HULL ET AL.

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2 of 14 Studies based on low-altitude cusp observations have revealed that ion outflow fluxes are strongly correlated with input electromagnetic energy flux (direct current (DC) Poynting flux from convection and very low frequency (LF) Alfvén waves), and the precipitating electron density (Strangeway et al., 2005;Zheng et al., 2005).These correlations are indicative of two important mechanisms that affect ionospheric ion outflow.The ion outflow flux correlation to Poynting flux is indicative of Joule dissipation of enhanced electromagnetic energy to the ionosphere, which effectively increases the upwelling ion scale height.This process enables more ions to access altitudes where wave-particle heating is effective, thus gaining sufficient energy to escape via the magnetic mirror force.The correlation with electron density is interpreted to result from enhanced precipitation of low energy (soft) electrons, which leads to enhanced electron heating in the ionosphere, and subsequent enhancement of electron outflow and ambipolar electric fields that effectively increase the upwelling ion scale height (Chaston et al., 2015;Sydorenko & Rankin, 2013;Wahlund et al., 1992).These factors are a necessary, but not sufficient, step in the ion outflow process.Additional wave-particle processes are subsequently required to effectively accelerate ions transverse to the magnetic fields in order for them to escape gravity and to obtain the energies observed with the help of the mirror force.Candidates include ion cyclotron waves, lower-hybrid, and dispersive Alfvén waves (DAWs).
The Poynting flux and plasma that get deposited into the ionosphere are seeded in the cusp at higher altitudes by reconnection processes at the magnetopause (Chaston, Phan, et al., 2005;Zhang et al., 2012).In addition to Poynting flux associated with gross convection of large scale fields, significant contributions are carried by Alfvén waves (Chaston, Peticolas, et al., 2005;Keiling et al., 2003;Sundkvist, Krasnoselskikh, et al., 2005;Sundkvist, Vaivads, et al., 2005), which can occur over a spectrum of spatial scales encompassing large scale shear Alfvén waves to DAWs.Because they have no parallel electric field, the Poynting fluxes of large-scale Alfvén waves can be transmitted to the ionosphere, where they can be dissipated to enhance ion outflow (Strangeway et al., 2005).In contrast, Poynting fluxes of DAWs get dissipated into parallel electron energization/heating processes prior to reaching the ionosphere because these waves have a parallel electric field component (e.g., Chaston, Peticolas, et al., 2005).DAWs have perpendicular scales on the order of or less than the ion gyroradius (ρ i ), ion acoustic length (ρ s ), or the electron inertial length (λ e ) scales (Lysak & Lotko, 1996).At higher altitudes in the cusp, DAWs are in the kinetic regime (i.e., k ⊥ ρ i ≥ 1 or k ⊥ ρ s ≥ 1) and are generally referred to as KAWs.Much closer to Earth electron inertial effects dominate and the DAWs are generally referred to as inertial Alfvén waves.DAWs can affect ion outflow by enhancing "soft" electron precipitation and also through stochastic transverse ion acceleration (Chaston et al., 2015(Chaston et al., , 2016;;Johnson & Cheng, 2001).Observational evidence indicating the action of these effects in the dayside/cusp region was reported by Chaston, Peticolas, et al. (2005) who utilized measurements from a rare Cluster-Fast Auroral SnapshoT (FAST) conjunction to show that Poynting fluxes from broadband DAWs in the cusp at higher altitudes (∼5.4 R E ) get transferred to the plasma at low altitudes (∼3,500 km) through field-aligned electron acceleration, transverse ion acceleration, and Joule heating.These processes were shown to result in precipitating electron fluxes sufficient to drive bright aurora and cause outflows of energized electrons and O + ions from the ionosphere into the low-latitude boundary layer.
Though significant progress has been made, more work is needed to understand causal connections between input wave and plasma energy and ion outflow at higher altitudes in the cusp.Single spacecraft studies, which have been largely based on low orbiting satellite missions, have provided valuable insight into the processes that drive mass outflow.However, estimates of electromagnetic energy input via measurements from low orbiting satellite missions are incomplete, owing to the fact that a significant amount gets dissipated on transit to the ionosphere.Moreover, single spacecraft observations cannot be used to assess the spatial and temporal properties of the source input and consequential ion mass output responses.Resolving such complex interrelated processes requires multipoint observations at key locations within dayside/cusp region to better establish the spatial morphology of structures and how such structures evolve in time.The multipoint measurements provided by the Cluster mission enable an assessment of the ion outflow response to changes in the plasma and wave inputs within the cusp at mid-to high-altitudes.Past multipoint Cluster observational studies have made significant advances in our knowledge of the dayside cusp region, such as in cusp structure, location, and dynamics, and the spatial and temporal evolution of cusp plasma in relation to reconnection processes and solar wind variations (e.g., Bouhram et al., 2004;Cargill et al., 2005;Dunlop et al., 2005;Escoubet et al., 2006Escoubet et al., , 2013;;Pitout & Bogdanova, 2021;Pitout et al., 2006;Trattner et al., 2005Trattner et al., , 2008;;Zong et al., 2008, and references therein).However, the distribution and temporal evolution of the plasma and electromagnetic energy input and consequences to ion outflow are not fully understood.

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In this paper we report the results of our analysis of multipoint measurements from the Cluster mission sampled during a poleward crossing of the mid-altitude cusp region during variable high solar wind dynamic pressure and active magnetospheric conditions.Particular attention is focused on the spatial and temporal properties of Alfvén waves observed to occur throughout the cusp proper, and their relation to ingoing electrons and O + ion outflow.The paper is organized in the following manner.Section 2 provides a brief description of the Cluster instruments and data set used in this study.Section 3 presents the analysis of plasma and field observations from two of the Cluster spacecraft.Detailed analysis is presented that demonstrates LF waves at frequencies ≤11 Hz are comprised of a broad k-spectrum of earthward traveling Alfvén waves that become dispersive at the ion gyroradius scale (i.e., the waves at dispersive scales are KAWs).Examination of sequential measurements reveals correlations between space-time variations in the KAWs, the ingoing electrons, and O + ion outflow indicative of a causal relation.The correlated data is used to determine empirical relations in the mid-altitude cusp, that can be used to compare with O + outflow models.Finally, the discussion and summary and conclusions are given Sections 4 and 5, respectively.

Instrumentation and Experimental Data Set
This study is primarily based on measurements from the Cluster mission.Magnetic field measurements given at a rate of 22 Samples/s are from the Fluxgate Magnetometer instrument (Balogh et al., 1997).Electric field measurements given at a rate of 25 Samples/s are from the Electric Field and Wave (EFW) experiment (Gustafsson et al., 1997).The electric fields are measured only in the spacecraft spin plane.To quantify Poynting fluxes, the axial component is estimated by assuming E • B = 0, after matching spin plane electric field measurements to the magnetic field time tags via linear interpolation.This assumption is valid since the magnetic field is sufficiently off the spin plane with an angular departure ranging between 20° and 60°(median of 47°) in the interval of data used.It is also appropriate for assessing the properties of the KAWs examined in this paper, since E ‖ /E ⊥ ≪ 1 (e.g., Chaston, 2006) and that non-linear features associated with secondary effects that may lead to large E ‖ are not resolved by the EFW 25 S/s sampling rate.Electron data are from the Plasma Electron and Current Experiment (PEACE) (Johnstone et al., 1997), which measures electrons on two analyzers spanning the combined range of 0.7 eV-26 keV.Ion measurements are from the COmposition and DIstribution Function, which is part of the Cluster Ion Spectrometry experiment (Rème et al., 1997).CIS-CODIF measures ion composition in the range 5 eV q −1 -40 keV q −1 .Note, CIS-CODIF observations are only available on three Cluster spacecraft (SC1, SC3, and SC4).The PEACE and CIS-CODIF instruments typically provide electron and ion measurements down to 4 s spin resolution.
Data from the Wind spacecraft was also used to provide solar wind conditions.The plasma data at 24 s resolution used are from the Wind three-dimensional plasma (3DP) experiment (Lin et al., 1995).We also used 3 s resolution magnetic field measurements from the magnetic field investigation on Wind (Lepping et al., 1995).

Observations
To examine the spatial distribution and temporal evolution of plasma and electromagnetic fluctuations in the cusp, Figure 1 shows data from two of the Cluster spacecraft during a poleward transect of the mid-altitude cusp region on 23 September 2001.The incoming magnetosheath source protons in this event was the focus of the study by Trattner et al. (2005), who demonstrated that they exhibited signatures consistent with temporal changes in the reconnection rate (e.g., pulsed reconnection).This event occurred during active magnetospheric conditions Kp = 4 + and an auroral electrojet index reaching 495 nT at the beginning of a geomagnetic storm main phase (associated with a minimum Sym-H value of −90 nT).Upstream solar wind conditions for this event obtained from the Wind spacecraft are shown in Figure 2. The data shown have been propagated to the magnetopause using a delay time of 17.82 min reported in the study by Trattner et al. (2005).Figure 2a reveals that the solar wind dynamic pressure propagated to the magnetopause was quite variable with variations ranging from a typical value of 2.0 nPa to a fairly high value of 10.0 nPa.The pressure variations are due to plasma density variations embedded within a fairly steady high solar wind flow (see Figures 2b and 2c).The IMF has a strong B Y component (∼ −10 nT) and a preferential B Z southward component but with multiple northward excursions during the cusp crossing (Figure 2d).
The Cluster fleet was at a geocentric distance of 5 R E in a noon-midnight orbit when it encountered the cusp near local noon.The Cluster data shown in Figure 1 are displayed in the time ordered sequence in which each 10.1029/2023JA031982 4 of 14 spacecraft exited the plasma sheet and into the cusp region, with SC4 crossing into the cusp first near 1107 UT (dashed vertical line in Figures 1a and 1b), followed by SC1 essentially along the same track roughly 1 min later (dashed vertical line in Figures 1f and 1g).Shown for each spacecraft are the omnidirectional differential energy flux spectra of electrons (Figures 1a and 1f) and protons (Figures 1b and 1g).Also shown are the power spectral densities (PSD) of orthogonal transverse components of the magnetic field B xFAC (Figures 1c and 1h) and electric field E yFAC (Figures 1d and 1i) determined using a Morlet wavelet transformation (Torrence & Compo, 1998).Here, E yFAC is in the spin plane perpendicular to the background magnetic field B 0 approximately pointing in the magnetic westward direction, while B xFAC is out of the spin plane perpendicular to E yFAC and B 0 .Electric fields in geocentric solar ecliptic coordinates are depicted in Figures 1e and 1j from SC4 and SC1, respectively.As noted above, the E • B = 0 assumption was used to estimate the component of the electric field along the spin axis.
On SC4, the transition from closed field lines to open field lines at 1107 UT is characterized by an abrupt disappearance of electrons at keV energies and above in the omnidirectional differential energy flux spectrograms shown in Figure 1a.This is followed by the appearance of significantly enhanced differential energy fluxes of electrons at energies ≲1 keV (above the spacecraft potential indicated by the black curve) and protons at energies ≲10 keV (orange to red after 1107 UT in Figures 1a and 1b).The further poleward penetration of the spacecraft into the cusp is initially marked by the characteristic proton energy dispersion signatures expected for southward IMF conditions.Namely, lower-energy protons occur at higher latitudes (e.g., Reiff et al., 1977;Smith & Lockwood, 1996), owing to a velocity filter effect attributed to motion in the convecting magnetic field lines from the dayside magnetopause in association with magnetic reconnection.In this scenario, magnetic field lines are peeling off the reconnection site and convecting tailward over the polar cap.Consequently, the most energetic particles are on field-lines closest to the reconnection site because these travel the fastest along the field-line toward Earth, whereas lower energy protons are seen at a later time owing to time-of-flight effects.A similar energy-latitude dispersion signature is also initially observed in the suprathermal electrons collocated with the ions in the cusp.In this event, however, the characteristic decrease in energy of the plasma with increasing latitude is interrupted by multiple energy enhancements or "step-up" features, as indicated in Figures 1a and 1b.Similar energy dispersion signatures with multiple step-up features are seen in electrons and protons depicted in Figures 1f and 1g from SC1, which encounters the same latitudinal region roughly a minute later.Close inspection of Figure 2 reveals that these step-up features occur in association with pressure/density enhancements that occur in conjunction with multiple northward excursions of the IMF B Z from previous southward orientations.
Interspacecraft comparisons indicate significant differences in the electron and proton characteristics during the initial transect into cusp in the region between the plasma sheet boundary and just after the first step (time interval from ∼1108 UT to ∼1116 UT).Namely, the electrons and protons appear to extend over a broader energy range during SC4's transect than those seen on SC1.This suggests that the electrons and protons are hotter on SC4 than on SC1.Owing to the fact that these spacecraft basically follow the same track, these differences are interpreted as temporal changes.Subsequent to this interval (after ∼1116 UT) the electrons and protons exhibit similar variations among the spacecraft indicating that these are spatial in nature.
The PSDs of B xFAC and electric field E yFAC reveals that LF EM waves occur throughout the cusp.These waves appear as bursts of activity that are collocated with the step-up features in the electron and proton observations.The wave activity also appears to be more intense during the initial part of the cusp transect by SC4 in the interval from ∼1108 UT to ∼1116 UT.This is more apparent in the electric field observations given in Figure 1e, which are marked by the appearance of highly variable/modulated electric fields reaching 100 mV/m and magnetic fields (not shown).However, during SC1s crossing of the region a minute later, the electric fields shown in Figure 1j are significantly reduced relative to SC4 observations.These comparisons suggest a possible connection between the fluctuating fields and plasma constituents.
Close examination of Figures 1c and 1d from SC4 and Figures 1h and 1i from SC1 reveals that the E yFAC PSDs tend to extend to higher frequencies than their B xFAC PSD counterparts.This behavior is a hallmark of Alfvén waves that become dispersive in the higher frequency range of these figures.To verify that the LF EM fluctuations are Alfvén waves and assess their propagation characteristics, Figure 3 shows E yFAC /B xFAC ratios, coherencies, and the absolute value of the relative phases between E yFAC and B xFAC as a function of frequency from SC4 (Figures 3a-3c) and SC1 (Figures 3d-3f), respectively.The coherencies and relative phases were determined via a Morlet wavelet based cross-spectral analysis method (Torrence & Compo, 1998;Torrence & Webster, 1999).These examples are from the times indicated by the vertical lines in Figures 1c-1e and Figures 1h-1j for SC4 and SC1 observations, respectively.The E yFAC /B xFAC ratios in each set show the standard nonlinear rise from the Alfvén speed V A (indicated by the horizontal blue dotted line) with increasing frequency.This confirms that the LF waves are a spectrum of Alfvén waves that reach dispersive scales at higher frequencies.The solid blue curve is a fit to a generalized DAW theoretical estimate for the ratio given by Chaston et al. (2003): where V A is the local Alfvén speed, k ⊥ the perpendicular wave number,   = √ ∕ 2 the electron inertial length,   = √ ∕∕Ω the ion gyroradius, and   = √ ∕∕Ω the ion acoustic gyroradius, where T i is the ion temperature, T e the electron temperature, m i the ion mass, m e the electron mass, n the number density, and Ω i the ion gyrofrequency, respectively.The effects of ion composition (i.e., H + , He + , and O + ) were accounted for in 10.1029/2023JA031982 7 of 14 quantifying parameters for the fits.At the selected times, the He + to H + and O + to H + density fractions range from   He + ∕ H + ∼ 0.014-0.11and   O + ∕ H + ∼ 0.02-0.09(based on CIS-CODIF measurements), respectively.The total number density estimated from spacecraft potential measurements range from n ∼ 10-60 cm −3 , with a mean of < n > ∼ 31 cm −3 .The background magnetic field is 383 ± 47 nT.Based on these parameters, the Alfvén speeds range from V A ∼ 740-1,880 km/s, with a mean of V A ∼ 1,295 km/s.The electron and ion temperatures are estimated at T e = 42 ± 14 eV and T i = 550 ± 3,350 eV.The effective ion gyrofrequency is Ω i = 22 ± 6 rad/s.The effective ion gyroradius, ion acoustic gyroradius, and electron inertial length scales are estimated at ρ i = 8.4 ± 4.4 km, ρ s = 2.3 ± 0.5 km, and λ e = 1.0 ± 0.4 km.In the cusp, the Alfvén waves being LF are dominantly Doppler-shifted in the spacecraft frame and the perpendicular wavelength is related to the spacecraft frame frequency by the relation f SC = k ⊥ v r /2π, with v r being the relative velocity determined from fits to observed E yFAC /B xFAC ratios.The fit results for the relative velocities are noted in the first panel of each set of plots shown in Figure 3.The solid red line denotes where k ⊥ ρ i ∼ 1, which clearly delineates non-dispersive Alfvén waves from those at dispersive scales, which generally occurs at 0.2-0.4Hz in the examples shown in Figure 3, with one exception embedded in high flow (along track perpendicular flow of 90 km/s) reaching 1.2 Hz (Figure 3d).The reasonable agreement between the model fit and observed values indicates that Alfvénic fluctuations at dispersive scales are KAWs (Hasegawa, 1976;Lysak & Lotko, 1996).
The absolute phase provides information on the propagation and/or interference characteristics of the waves.Phases at 0°and 180°corresponds to outgoing and ingoing traveling waves, whereas phases at 90°corresponds to standing modes.Coherencies above 0.5 indicate where the phases are well-determined (Hull et al., 2023).Though there are exceptions, each example shows that the Alfvén waves from the non-dispersive and into the dispersive scale regime have characteristics of ingoing traveling waves.These results suggest that the waves are generated at a location along the magnetic field well above Cluster's altitude, most likely in association with magnetic reconnection processes at the magnetopause as indicated in previous studies (Chaston, Phan, et al., 2005;Zhang et al., 2012).
It is known that KAWs can energize electrons and ions (e.g., Johnson & Cheng, 2001;Stasiewicz et al., 2000;Wygant et al., 2002, and references therein).To identify evidence of this, Figure 4 shows electron, O + ion, and Alfvén wave observations from the same two Cluster spacecraft and time interval depicted in Figure 1.Shown, for each spacecraft, are the omnidirectional differential energy fluxes of electrons (Figures 4a and 4h) and the ion differential number flux spectra of outflowing O + ions (Figures 4b and 4i).For context, we include the PSDs of E yFAC (Figures 4c and 4j).Also shown for each spacecraft are Poynting fluxes parallel to the background magnetic field in two frequency ranges (Figures 4d and 4k).The LF wave component (red) spans frequencies f ≤ 0.2 Hz, which corresponds to the non-dispersive Alfvén wave regime as shown in Figure 3.The high frequency component (blue) spans frequencies f > 0.2 Hz, which corresponds to KAWs.Energy densities of magnetic and electric fields at f > 0.2 Hz (denoted U B and U E ) corresponding to KAWs are given in Figures 4e and 4f from SC4 and Figures 4l and 4m from SC1, respectively.Finally, integrated energy fluxes of downgoing electrons (red) and O + outflow (black) are shown in Figures 4g and 4n for SC4 and SC1, respectively.
The Alfvén waves at macro and kinetic scales carry sizable parallel Poynting fluxes (up to 1-2 mW/m 2 in situ or up to 125-250 mW/m 2 when mapped to the ionosphere) that are predominantly directed toward Earth (see Figures 4d and 4k).These have gross peak enhancements that coincide with the step-up features observed in the electron (Figures 4a and 4h) and proton (Figures 1b and 1g) observations.The energy densities of electric and magnetic fields of KAWs also show enhancements at step-up features followed by diminishing values with increasing latitude.This behavior may be due to the effects of the poleward convecting reconnected magnetic field-lines.Namely, the largest wave energy density and Poynting flux amplitudes are concentrated on the most recently reconnected field lines while wave activity decays with increasing latitude as these field-lines become more disconnected from the wave energy source.
The differential number flux spectra of outgoing O + shown in Figures 4b and 4i reveal that energized O + ion outflows at a few keV energies and below occur throughout the cusp (indicated by the red signatures).These outflows show energy enhancements and dispersion signatures similar to those observed in the electrons (see Figures 4a and 4h) and also the protons (see Figures 1b and 1g).
Further inspection suggests that the O + outflow is responding to spatial and temporal variations in the ingoing electrons and/or the KAW activity throughout the interval within a given spacecraft transect and among the spacecraft.Evidence of O + outflow temporally responding to wave and/or electron input is exhibited in the beginning HULL ET AL.

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8 of 14 of transect in the time interval from ∼1108 UT to ∼1116 UT.As shown previously in Figure 1, interspacecraft comparisons indicate significant differences in the KAW activity between SC4 and SC1 measurements in this focus interval.Here, we see that the previously aforementioned enhanced Alfvén wave activity seen in SC4 data are associated with enhanced KAW Poynting fluxes and energy densities (with peak values for S ‖ reaching 1-2 mW/m 2 , U B reaching 100-500 eV/cm 3 , and U E ∼ 0.01-0.02eV/cm 3 in Figures 4d-4f, respectively).Indicative of KAW control of electron energization and heating in the interval, an overall enhancement in the integrated energy fluxes of downgoing electrons is also observed with superposed factor of two to five modulations (Figure 4g) that generally vary in concert with modulations in the KAW energy densities.In response to the 10.1029/2023JA031982 9 of 14 KAW and electron input observed by SC4, upgoing oxygen ions O + exhibit enhanced integrated energy fluxes and energies in the focus interval.However, on SC1, which crosses nearly the same latitudinal region roughly a minute later, the KAW activity and associated Poynting fluxes and energy densities are to be significantly diminished in the focus interval (with peak values for S ‖ reducing to ∼ 0.2-0.5 mW/m 2 , U B reducing to ∼ 2-10 eV/cm 3 , and U E reducing to ∼ 0.0004-0.001eV/cm 3 in Figures 4k-4m, respectively).These diminished KAW quantities are accompanied by a significant reduction (factor of 6) in downgoing electron energy fluxes.The O + energy fluxes and energies are also reduced by over an order of magnitude.The drop in the input wave energy densities and fluxes is not due to deposition into the plasma at higher altitudes, otherwise we should see electron energy fluxes increase with decreasing Poynting fluxes.This behavior, however, is explainable as a temporal change in the input KAW energy with consequential changes to the input electron and O + outflow.Subsequent to this interval, the KAW, electron, and O + outflow quantities show similar spatially correlated variations among the spacecraft.These space-time correlations revealed in the multi-spacecraft observations provide strong evidence of a causal connection between input KAWs and electrons and the O + ion output in the cusp.
To better examine the extent to which the KAWs are impacting electrons, Figures 5c-5h show complementary sets of spin-period resolution electron velocity space distributions and differential energy fluxes as a function of energy and pitch-angle sampled by SC4 at times indicated by the vertical lines in Figures 5a and 5b.For context, the spectrogram of omnidirectional differential energy flux of electrons sampled by SC4 is depicted in Figure 5a.As a proxy for current sense, Figure 5b shows the spin-period averaged azimuthal component of the perturbation magnetic field ΔB west from SC4.The ΔB west is perpendicular to the magnetic meridional plane in the westward direction.Intervals in ΔB west associated with positive slopes correspond to upward current regions, while those associated with negative slopes indicate downward current regions.The variations in the slopes of ΔB west indicate that the currents are a nested series of alternating upward and downward field-aligned currents that appear at a typical cadence of 4.4 ± 2.1 s.Particularly noteworthy is that the cadence corresponds to the frequency at which the Alfvén waves in the interval become dispersive (where k ⊥ ρ i ∼ 1 in Figure 3a).This correspondence indicates that the short scale currents are supported by the KAWs in the interval.Consistent with energization in the KAW parallel electric fields, the electron distributions are shown to be preferentially magnetic field-aligned or field-opposed with unidirectional or counterstreaming signatures.As expected, the distributions exhibit parallel skews that vary in concert with the current sense.Namely, the electron distributions in Figures 5c, 5e, and 5g, which are sampled in upward current intervals, exhibit preferential field-opposed (downward directed or earthward) skews.In contrast, the electron distributions in Figures 5d, 5f, and 5h, which are sampled in downward current intervals, have preferential field-aligned (upward directed) skews.The dramatic variations/distortions within these short-scale currents demonstrated in Figure 5 confirm that the KAWs are not merely accompanying the electrons but are exerting significant control over the electron parallel energies and energy fluxes in the interval.
To quantify relationships, Figures 6a-6c   + , respectively.The data from SC4 and SC1 in these comparisons were sampled in the time interval from ∼1107-1138 UT and ∼1108-1139 UT, respectively.The electron and wave measurements were boxcar averaged and down-sampled to the resolution of the O + measurements to make these comparisons.
These comparisons reveal that input KAW and electron, and O + outflow quantities are strongly correlated, with linear coefficients r being ≥0.53 for the trends shown in Figure 6.The correlation ranges given to 99% confidence demonstrates that these correlations are statistically significant.The solid red lines in Figure 6 indicate the results of a log space linear regression analysis applied to the data.For comparisons between the KAW magnetic field energy densities and the downgoing electron energy fluxes, O + energies, and O + energy fluxes, the regression analysis yielded the power law relations   = 10

Discussion
The correlations together with the time sequences revealed by the multipoint Cluster observations strongly support the notion that the KAWs in the mid-altitude cusp are playing an important role in enhancing electron energy fluxes and O + outflow energies (and hence energy fluxes), the amount of which is controlled by the KAW energy densities and Poynting fluxes.The dependence of electron energy fluxes on KAW energy densities and Poynting fluxes is viewed to be indicative of KAW energy dissipation into electron heating.Figure 6g indicates that the electron energy fluxes are an order of magnitude larger than the corresponding averaged Poynting fluxes suggesting that a significant amount of KAW energy may have been deposited into the electrons by the time the incoming electrons have reached Cluster's altitude.The dependencies of O + outflow energies and energy fluxes on KAW energy densities is explainable as the result of non-adiabatic transverse energization of these ions in sufficiently thin perpendicular electric fields combined with the effects of magnetic mirroring.This energization is stochastic in nature (Johnson & Cheng, 2001) and comes into play when the criteria E ⊥ /B 0 > Ω i /k ⊥ (Chaston et al., 2004;Cole, 1976;Stasiewicz et al., 2000).This mechanism is more effective for heavier ions such as O + and can act to energize them all along Cluster's altitude and beyond, where the KAWs occur (Chaston, Peticolas,  et al., 2005).This is owing to the fact that the KAWs, though having thin transverse scales, have parallel wavelengths that extend over large distances along the field-line (≥1 R E ).In this scenario the amount of energy gained by the O + ions is expected to be related to the amplitude of the KAW transverse electric field (and thus energy density).
The correlations reported here are similar to those reported in previous studies in other contexts where Alfvén waves are observed (e.g., Chaston, 2006;Hull et al., 2019Hull et al., , 2020Hull et al., , 2023)).The studies by Hull et al. (2019Hull et al. ( , 2020) ) were based on Van Allen Probes observations in the nightside equatorial inner magnetosphere (L ∼ 3-6.6).These studies demonstrated that KAW energy densities and Poynting fluxes are strongly correlated with ingoing electron characteristic energies and energy fluxes and also outflowing O + energies and energy densities in the nightside equatorial magnetosphere.Inspection reveals that correlation counterparts are associated with different power law relations than reported here, which is likely a reflection of differing dayside and nightside conditions (e.g., high latitude vs. equatorial plane magnetic field location, plasma and wave parameters, and driving/reconnection rates).A positive correlation between Alfvénic Poynting fluxes and electron energy fluxes was reported in low altitude (<2 R E ) FAST observations in the nightside auroral zone (Chaston, 2006).Hull et al. (2023) also reported a similar positive correlation between O + outflow energies and the electric field energy density of KAWs in the high-altitude auroral region (4.5 R E geocentric distance) tied to substorm auroral beads near midnight.The novel results presented here demonstrate that such correlations are manifested in the mid-altitude cusp, as well.Moreover, the multipoint observations from Cluster revealed the complex interplay between space-time changes in the KAWs and the electron and O + responses that give rise to the correlations observed.
The empirical relations reported here are analogous to, but distinct from, relations determined from cusp/dayside observations at much lower altitudes (Strangeway et al., 2005;Zheng et al., 2005).In those studies, the observations are at an altitude where much of the DAW energy observed at Cluster's altitude is expected to be dissipated into plasma heating (Chaston, 2006).Moreover, comparisons were made with DC Poynting fluxes, which are at much lower frequencies than addressed here.Their results show a positive correlation between ion outflow fluxes and DC Poynting fluxes, which is consistent with Joule dissipation of Poynting flux into the ionosphere being an important controlling factor of ion outflow rates.However, ion and electron energy fluxes showed weak to no correlation with DC Poynting fluxes.These latter results are not contradictory to our results or those reported in previous studies in that the comparisons are distinctly different.Our results are interpreted to be a reflection of energization processes in DAWs occurring at altitudes further up along the field-line.In contrast, the weak or lack of correspondence reported in the studies by Strangeway et al. (2005) and Zheng et al. (2005) pertains to the effect, or lack thereof, of DC Poynting flux transmission and ionospheric deposition on electron and ion energy fluxes.

Summary and Conclusions
In this study, we utilized multipoint observations from the Cluster mission to assess the spatial and temporal properties of low-frequency waves (≤11 Hz), and their relation to electron input and O + ion outflow within Earth's mid-altitude cusp.The event occurred during high solar wind dynamic pressure and active magnetospheric conditions at the beginning of a geomagnetic storm main phase.Our results demonstrate that the LF waves are Alfvén waves that become dispersive at the ion gyroradius scale, which are characteristic of KAWs.Analysis of the phases between electric and magnetic field transverse components reveals that the Alfvén waves (over a broad range of frequencies encompassing non-dispersive to dispersive scales) observed throughout the cusp are predominantly earthward directed traveling waves.This result indicates that these waves are generated at a location along the magnetic field well beyond the Cluster satellites, most likely in association with magnetic reconnection processes at the magnetopause (Chaston, Phan, et al., 2005).The Alfvén waves were shown to carry sizable earthward directed Poynting fluxes (∼200 mW/m 2 mapped to ionospheric altitudes) at both macro-and kinetic scales.The KAWs are collocated with energy dispersed protons, electrons, and O + outflow at keV energies and below.The electrons embedded within the KAWs exhibit field-aligned signatures consistent with energization/heating in the KAW wave fields and have skews that vary with current sense.The Alfvén wave activity is bursty in nature, with spatial and temporal variations in the KAW Poynting fluxes and energy densities being strongly correlated with energy fluxes and/or energies of ingoing electrons and O + ion outflow.Upstream solar wind observations from the Wind spacecraft indicate that the enhancements in Alfvén wave activity and plasma in the cusp occurred in response to pres-

Figure 1 .
Figure 1.Omnidirectional differential energy flux spectra for (a and f) electrons, (b and g) protons H + , power spectral densities of (c and h) B xFAC and (d and i) E yFAC , and (e and j) the electric field in geocentric solar ecliptic coordinates from (a-e) SC4 and (f-j) SC1 observations.The black curve in (a) and (f) represents the spacecraft potential, above which corresponds to ambient electron measurements.The solid black vertical lines in (c)-(e) and (h)-(j) indicate selected times for E yFAC /B xFAC ratios and phases shown in Figure 3 below.The dashed vertical lines in (a) and (b) and (f) and (g) indicate where SC4 and SC1 enter into the cusp, respectively.

Figure 2 .
Figure 2. Wind 3DP and magnetic field investigation observations in solar wind propagated to magnetopause.Shows (a) Dynamic pressure, (b) density, (c) velocity vector in geocentric solar ecliptic coordinates and (d) magnetic field vector in geocentric solar magnetospheric coordinates.The solid vertical lines indicate the cusp entry times for SC4 and SC1.

Figure 3 .
Figure 3. Ratio between E yFAC from Electric Field and Wave and B xFAC from Fluxgate Magnetometer, coherency, and absolute value of the relative phase between E yFAC and B xFAC sampled by (a-c) SC4 and (d-f) SC1 at the times indicated by the vertical lines in Figures 1c-1e and Figures 1h-1j, respectively.The blue solid curves are the local dispersion relation fits to the E yFAC /B xFAC ratio.The solid red vertical line indicates where k ⊥ ρ i ∼1 (determined from the fits), with k ⊥ being the transverse wave number and ρ i the ion gyroradius.The dashed black vertical lines indicate the spin and half spin frequencies.The blue horizontal dotted lines indicate the Alfvén speed.

Figure 4 .
Figure 4. Shows (a and h) omnidirectional differential energy flux spectra for electrons, (b and i) differential number flux spectra for upgoing O + ions, (c and j) PSDs of E yFAC , (d and k) parallel Poynting fluxes for low frequency (red) and high frequency (blue) Alfvén wave components, energy densities of kinetic Alfvén wave (e and l) magnetic and (f and m) electric fields, and (g and n) integrated energy fluxes for downgoing electrons (red) and upgoing O + ions (black) from (a-g) SC4 and (h-n) SC1, respectively.Note, the energy fluxes of downgoing electrons (g and n) were divided by 10 for comparison purposes.The black curve in (a) and (h) represents the spacecraft potential, above which corresponds to ambient electron measurements.The black curve in (b) and (i) denotes the outflowing O + energy.

Figure 5 .
Figure 5. Observations from SC4. Shows (a) electron differential energy flux spectra and (b) the westward perturbation magnetic field component.Also shown are (c-h) sets of electron distribution functions in v ‖ -v ⊥ space and differential energy fluxes as a function of energy and pitch-angle sampled at the times indicated by labeled blue vertical lines in (a) and (b).The black curve in (a) indicates the spacecraft potential.

Figure 6 .
Figure 6.Data sampled by two Cluster spacecraft (SC1 and SC4) in the cusp on 23 September 2001.Compares magnetic field energy densities U B of kinetic Alfvén waves at frequencies f > 0.2 Hz with (a) downgoing electron energy fluxes, (b) O + outflow energy, and (c) O + outflow energy fluxes.Compares kinetic Alfvén wave electric field energy densities U E at f > 0.2 Hz with (d) downgoing electron energy fluxes, (e) O + outflow energy, and (f) O + outflow energy fluxes.Also compares the parallel Poynting fluxes at f > 0.2 Hz with (g) downgoing electron energy fluxes, (h) O + outflow energy, and (i) O + outflow energy fluxes.Correlation coefficients r with 99% confidence limits are given at the top of each plot.The solid red line indicates results of a regression analysis applied to the data.Fit slopes and intercepts are given in each panel.
compare magnetic field energy densities U B of KAWs above 0.2 Hz with downgoing electron energy fluxes   , O + outflow energies    + , and O + outflow energy fluxes    + observed in the cusp by SC1 and SC4, respectively.Similarly, comparisons between electric field energy densities U E of KAWs above 0.2 Hz with 1.5  0.64Similarly, for comparisons between the KAW electric field energy densities and the downgoing electron energy fluxes, O + energies, and O + energy fluxes, the regression analysis yielded the power law relations   = 10 4.8  1.0  , respectively. Fo comparisons between the KAW parallel Poynting fluxes and the downgoing electron energy fluxes, O + energies, and O + energy fluxes, the fits yielded the HULL ET AL.