Direct observations of cross-scale energy transfer driven by multiple-ion interactions in space plasmas

Domain: physics
Published: 2025-12-13
Editorial outcome: major_revision

Abstract
Astrophysical and space plasmas are inherently multi-scale in nature. Identifying the mechanisms responsible for transporting energy across different physical scales is an essential step in modeling the dynamics of these plasmas and their associated astrophysical and space systems. Traditionally, these mechanisms are examined within an electron-single ion framework, even in the presence of multiple ion species. This simplification is justified by the dominance of a single ion species in most observations. In this work, we present measurements from the Magnetospheric Multiscale mission in Earth’s magnetosphere that challenge this paradigm. Data analysis reveals that hydrogen and helium ions, which commonly coexist, behave differently in ion-scale waves, with hydrogen ions responding more like electrons and helium ions behaving more like ions. These differential responses then induce interactions between the two ion species, exciting lower-hybrid electrostatic waves and consequently driving energy cascading from the ion scale down to the lower-hybrid scale. This process remains efficient even when helium ions are present in very minor quantities. Our observations, therefore, provide direct experimental evidence for cross-scale energy transfer processes in plasmas through multiple-ion interactions.

Introduction
Plasmas are ubiquitous throughout the universe and play a critical role in the composition of many astrophysical and space systems1,2, such as stellar corona, astrophysical disks, and the magnetospheres of pulsars, dwarfs, and planets. These plasmas are characterized as multi-scale systems1–4, where processes across a wide range of physics scales occur simultaneously. The interaction of these multi-scale processes, along with the associated cross-scale energy transfer and field-particle energy redistribution (e.g., see review by ref. 4), governs the dynamics of plasmas and, consequently, the evolution of the astrophysical and space systems they constitute.

Understanding the interactions between different components of plasmas is essential for developing a comprehensive framework of plasma cross-scale physics. Plasmas are inherently heterogeneous, consisting of both negatively and positively charged species. Typically, electrons comprise the negatively charged species, while the positively charged species are more diverse, often including hydrogen, helium, oxygen, and metal ions5–8. These ions exhibit distinct dynamics, such as undergoing differential acceleration during interactions with plasma waves9 and contributing unequally to the growth of instabilities10. However, despite this known complexity, most classical theories of plasma cross-scale physics, particularly those (e.g., gyrokinetics turbulence theory11) that account for kinetic effects, are based on a simplified electron-single ion model. At first glance, this simplification seems reasonable, as in most observed plasmas, a single species (usually hydrogen ions) dominates both in number and energy density, while other ion species are present in much smaller quantities5–8. Thus, it has seemed natural to omit the existence of minor ions and interactions between different ion species (hereafter referred to as multiple-ion interactions) when considering plasma dynamics, at least as a first-order approximation.

However, several theoretical studies have indicated that minor ions may actively participate in cross-scale energy transfer processes in plasmas. For instance, during interactions with plasma waves, minor ions exhibit distinct responses compared to major species, resulting in velocity distribution functions (VDFs) characterized by different temperature, anisotropy, and drift speed9,12–15. The resulting differential VDFs may, in turn, serve as sources of free energy, potentially driving wave excitation at other scales16.

Here, we present observational evidence confirming the non-negligible role for multiple-ion interactions in cross-scale energy transfer in collisionless plasmas. Specifically, we focus on a process known as cross-scale wave-particle interactions17–20. This process can efficiently drive energy transfer across scales through the simultaneous interactions of waves of different scales with charged particles. Our analysis of data from NASA’s Magnetospheric Multiscale (MMS) mission21 (Methods, subsection MMS data) reveal that the interplay between hydrogen and helium ions with ion-scale waves can trigger further interactions between the two ions, which, in turn, excites electrostatic waves at the smaller lower-hybrid scale. This process couples ion-scale and lower-hybrid-scale dynamics, forming pathways for energy transfer between these scales. Our observations thus demonstrate that the coexistence and interaction of multiple ion species introduce an efficient mechanism for transporting energy across scales in plasmas, one not accounted for in traditional electron-single ion theories.

Results
Coupling between ion scale and lower-hybrid scale waves
On 29 December 2020, the MMS spacecraft traveled out of the magnetosphere through the dayside magnetopause at about [8.2, 0.6, 5.6] RE (Earth radii, about 6371 km) in the Geocentric Solar Ecliptic (GSE) coordinates. Just before it crossed the magnetopause, a cross-scale wave-particle interaction event was detected at approximately 18:18 UT (Fig. 1). This event occurred within an incompressible plasma flow (Fig. 1a, b), as evidenced by the nearly constant plasma number density (Nbg = 1.4 cm−3) derived from the upper-hybrid line observation (Supplementary Fig. 1a). Figure 1c zooms into this flow, showing the three components of ion bulk velocity in GSE. The ion bulk velocity can be decomposed into a baseline and a quasi-sinusoidal wave. The baseline, which remains relatively steady throughout the shown time period, represents the aforementioned plasma flow and is hereinafter referred to as background flow Vbg (= 59 × [0.33, −0.83, 0.44] km/s in GSE averaged over the shown time interval). Vbg is approximately perpendicular to the nearby magnetic field lines as <Vbg, Bbg> = 86°, where <,> denotes the angle between two vectors, and Bbg = 52 × [−0.66, 0.04, 0.75] nT in GSE represents the background magnetic field obtained by averaging the measured magnetic field over the same period as Vbg.

Superposed on Vbg is a quasi-sinusoidal wave at about 0.25 Hz, between the gyro-frequencies of hydrogen ions H+ (0.79 Hz) and helium ions He+ (0.20 Hz) evaluated at Bbg. Similar wavy signatures can also be observed in the magnetic field (Fig. 1d; see corresponding dynamical spectra in Supplementary Fig. 2a), electric field (Fig. 1e), and ion spectrogram detected by MMS/FPI-DIS (Fig. 1f; detailed later). A minimum variance analysis22 (MVA) of the magnetic field (see Methods, subsection EMIC wave) indicates that the wave propagates along k^ = [0.62, −0.08, −0.78] in GSE, which is approximately anti-parallel to Bbg with <k^, Bbg> = 176°. Hence, the 0.25 Hz wave fits the classification reserved for electromagnetic ion cyclotron (EMIC) waves, as presented in Supplementary Note 1 and Supplementary Fig. 4.

Besides the EMIC wave, wavy signatures are also observed near the lower hybrid frequency (flh = 34 Hz) in the dynamical spectra of the electric field (Fig. 1h). No corresponding signatures can be identified in the magnetic field (Supplementary Fig. 3a), suggesting these waves are electrostatic. These electrostatic waves can be further divided into two groups of different frequencies, ~35 and 12 Hz (termed as higher- and lower-frequency electrostatic waves hereinafter). Both groups appear in quasi-periodic wave packets, as shown in Fig. 1h as well as Fig. 1g, i, presenting the integrated power of the higher- and lower-frequency electrostatic waves, respectively. Interestingly, a direct comparison of Fig. 1g, i with Fig. 1d–f indicates that these lower-hybrid wave packets are in rhythm with the EMIC wave. This is further quantitatively confirmed by a cross-wavelet analysis25 of the integrated power of the electrostatic waves (Fig. 1g, i) and the EMIC wave electric field. For both the higher- and lower-frequency electrostatic waves, the resulting correlation coefficient (Supplementary Fig. 5a, b) peaks near the frequency of the EMIC wave and holds a significant value (~0.77 and ~0.66, respectively) over the timespan of interest. These results suggest that the electrostatic waves are modulated by the EMIC wave. In what follows, we will demonstrate that a cross-scale wave-particle interaction involving multiple-ion interactions is responsible for this modulation.

Hydrogen-helium ion counter drift induced by EMIC waves
We begin by examining the interaction between the EMIC wave and ions. Given the similarity of the EMIC wave fields across the four MMS spacecraft (Supplementary Fig. 2d), only MMS-1 observations are shown here. First, we note the EMIC wave is approximately linearly polarized, as the MVA reports a ratio of 4.5 between the maximum and intermediate eigenvalues. Therefore, we define a field-aligned coordinate (FAC) system (l, m, n), where the n axis is parallel to Bbg, the m axis aligns with the cross product of the n axis and the MVA eigenvector with the largest eigenvalue, and the l axis completes the right-handed coordinate system. As defined in this way, the EMIC wave approximately propagates in the −n direction and has magnetic and electric field oscillations primarily in the l and m directions, respectively. Figure 2a, b present the magnetic field (Bw = [Bl, Bm, Bn]) and electric field (Ew = [El, Em, En]) of the EMIC wave in this coordinate system, obtained with a 0.08–0.75 Hz bandpass filter (Methods, subsection EMIC wave). As expected, Bl and Em reach larger amplitudes than the other components, although finite Bm and El are also noted.

The EMIC wave significantly modulates low-energy ions, namely those with velocities v much smaller than the EMIC wave phase speed Vϕ, which is about 1017 km/s (corresponding to a kinetic energy of 5.4 keV for hydrogen ions and 21.6 keV for helium ions), as obtained in Methods, subsection EMIC wave. Figure 2c, which copies Fig. 1f, again shows the energy-time spectrogram of ion omnidirectional energy flux. A series of red arcs below ~100 eV, recurring at the period of the EMIC wave, is observed. Figure 2d, e show the reduced one-dimensional distribution functions along the l and m axes, respectively, derived by averaging the three-dimensional velocity distribution functions over the other two directions. Here, the kinetic energy is used as the vertical axis instead of velocity because the presence of multiple ion species makes it challenging to convert energy, the quantity directly measured by FPI-DIS, into velocity. The red arcs noted in Fig. 2c also appear in Fig. 2d, e, with the arcs in Fig. 2d (i.e., along the l axis) more significant.

These arcs manifest the response of low-energy ions to the EMIC wave. To show this, we derive the motion of low-energy ions in the EMIC wave field (see Methods, subsection low-energy ion dynamics)
Vi = 1/ (1 − (ω/Ωi)2) [ (Ew × Bbg)/Bbg2 + (1/Ωi) ∂Ew/∂t ], (1)
where ω and Ω represent wave angular frequency and the gyro-frequency of i-th ions. This formula is valid as a first-order approximation in the small parameter v=Vϕ. The first and second terms in the parentheses are the usual “E×B” drift velocity (VE) and polarization drift velocity (VP), respectively. The factor preceding the parentheses represents the effect of finite wave frequency and becomes infinite when ω approaches Ω, i.e., wave-ion resonance. The solid white curve in Fig. 2c presents the kinetic energy of hydrogen ions (H+) calculated with Eq. 1 and the observed EMIC wave field (Fig. 2a, b). The solid black curves in Fig. 2d, e give the components along the l and m axes, respectively. All the curves closely align with the arcs, suggesting that these arcs (henceforth referred to as hydrogen arcs) result from the EMIC wave modulation.

Besides the hydrogen arcs, a second group of arcs is observed between 100 and 1000 eV in Fig. 2c. Corresponding signals can be identified in Fig. 2d, e as well, although they are a bit faint as masked by the hydrogen arcs. These arcs are distinct from the hydrogen arcs in that they are in anti-phase. A straightforward hypothesis is that they represent another ion species. We then substitute the mass and charge of helium ions (He+) into Eq. 1 and plot the results as dashed curves in Fig. 2c–e. Evidently, these curves match the second group of arcs well. Therefore, we conclude the second group arcs are a manifestation of the EMIC wave-helium ion interaction.

The consistency between the theory and observations verifies Eq. 1. This equation indicates that hydrogen ions and helium ions respond distinctly. For hydrogen ions, the polarization drift is weak compared to the “E×B” drift (VP = VE × ω/ΩH = 0.31), and the factor arising from finite wave frequency is close to unity (1/ (1 − (ω/ΩH)2) = 1.1). Therefore, the overall response of hydrogen ions is almost the “E×B” drift and thus electron-like. This is more intuitively illustrated in Figs. 2b and 3a, which show that the drift velocity of hydrogen ions (dashed black curves) is close to that of electrons (solid grey curves). In contrast, the response of helium ions is more ion-like. Their polarization drift is comparable to the “E×B” drift (VP = VE × ω/ΩHe = 1.25) and the factor 1/ (1 − (ω/ΩHe)2) = −1.8 is smaller than unity. The latter fact further indicates that helium ions move in the opposite directions to hydrogen ions. Consequently, the overall response of helium ions deviates significantly from the “E×B” drift (see solid black curves in Figs. 2b and 3a). The differing responses between hydrogen and helium ions create a counter-drift configuration in the plane perpendicular to the magnetic field. This configuration, as shown below, is responsible for the electrostatic waves near the lower-hybrid frequency.

Electrostatic waves excited by hydrogen-helium ion counter drift
Here, we show a detailed analysis of the higher-frequency electrostatic waves, while the analysis of the lower-frequency electrostatic waves follows a similar approach. We select the five most significant wave packets of the higher-frequency electrostatic waves (marked by numbered dashed blue lines in Fig. 3c) for closer examination. We first note that all four MMS spacecraft observed these wave packets (Supplementary Fig. 3c). However, upon zooming into each wave packet, the waveform shows no coherence between different MMS spacecraft. This observation indicates that the wavelength of these waves is much smaller than MMS spacecraft separation (~50 km, primarily in the perpendicular plane), while the scale of the excitation region is comparable to the separation (Supplementary Fig. 3d). Consequently, we cannot use cross-spacecraft timing analysis or similar techniques to determine the wavenumber of these waves. Nevertheless, their propagation directions can be determined from an MVA of the observed electric fields (see Methods, subsection electrostatic waves). The results (Supplementary Table 1) indicate that these waves propagate obliquely, with a notable preference for the perpendicular direction. Figure 3e shows the projection of the propagation directions in the l-m plane. Evidently, the waves approximately propagate in the -m direction. Interestingly, when these waves are detected, hydrogen ions mainly move in the +m direction, while helium ions move in the -m direction as modulated by the EMIC wave (Fig. 3a, b). Figure 3e illustrates this configuration.

The counter drift between hydrogen and helium ions (Fig. 3e) could be unstable to the ion-ion cross-field instability26–29 and excite electrostatic waves near the lower-hybrid frequency. To verify this scenario, we conduct an analysis of the linear dispersion relation with parameters derived from the observations (Methods, subsection electrostatic waves and Supplementary Note 2). Figure 3f shows the obtained frequency (black curve) and growth rate (blue curve) in the rest frame of the spacecraft. A large, positive growth rate is obtained within the frequency-wavenumber space of interest. Particularly, the growth rate peaks at the frequency ~33 Hz, close to the frequency of the higher-frequency electrostatic waves. The corresponding wavenumber is 0.28 km−1, corresponding to a wavelength of about 3.6 km. This figure is much smaller than MMS spacecraft separation, as we expect. This analysis suggests that the EMIC wave-induced hydrogen-helium ion counter drift is responsible for the higher-frequency electrostatic waves.

A similar scenario applies to the lower-frequency electrostatic waves. These waves also propagate approximately along the hydrogen-helium ion counter drift, which is now in the −l direction (Fig. 3g). An analysis of the linear dispersion relation of the ion-ion cross-field instability reveals that this counter drift can account for these waves as well. As shown in Fig. 3h, positive growth rates occur near 14 Hz, where the lower-frequency electrostatic waves are observed. It is interesting to note that the hydrogen-helium ion relative drift speed is close to 170 km/s during both the higher- and lower-frequency electrostatic waves (see Fig. 3e, g). Therefore, in the rest frame of the plasma, the two electrostatic waves have almost identical frequencies, both close to flh. The observed differences in frequencies actually result from the Doppler shift induced by Vbg. This shift only significantly affects the lower-frequency electrostatic waves, since Vbg is approximately parallel to their propagation direction but approximately perpendicular to that of the higher-frequency electrostatic waves (see more details in Methods, subsection electrostatic waves).

A comparison between the electrostatic wave amplitude (Fig. 3c, d) and the helium-hydrogen relative drift speed (Fig. 3a, b) reveal that the two are not one-to-one correlated. This mismatch suggests that additional parameters, such as plasma composition and temperature, may influence wave growth (see Supplementary Note 3 for parameter studies detailing this influence). Future investigations that account for the modulation of these parameters by EMIC waves, as well as the temporal variations induced by the oscillating EMIC wave fields, may yield a more comprehensive understanding of the observed electrostatic wave amplitudes.

As a final remark, we would like to point out that, for symmetric reasons, the scenario proposed here would predict two additional groups of electrostatic waves, with one group propagating in the +m direction and the other in the +l direction. These waves may account for the spots of enhanced power in Fig. 1h that are not synchronized with either the higher- or lower-frequency electrostatic waves (some of these spots are marked by arrows in Fig. 1h). However, for reasons that remain unclear, these signals appear weaker and more sporadic compared to the two electrostatic wave populations analyzed above.

Methods
MMS data
Unless otherwise stated, the data presented in this paper were taken from MMS-1. The magnetic field and electric field were measured by the Fluxgate Magnetometers38 and the Electric Field Double Probe39,40, respectively. The ion data presented in Figs. 1, 2 were measured by the Fast Plasma Investigation-Dual Ion Spectrometers (FPI-DIS)41, which provide three-dimensional velocity distribution functions of ions from ~10 eV to 30 keV every 150 ms in burst mode. The FPI-DIS does not distinguish between ion species; however, the ion species (primarily hydrogen and helium ions) are distinguished by the Hot Plasma Composition Analyzer (HPCA)42. The relative abundances in terms of number density of H+, He+, He++, and O+ are 95.5%, 1.4%, 1.1%, and 2.0%, respectively, during our event (Supplementary Fig. 1b).

Survey mode data are used for Figs. 1d, 2a and S1b–d, S2, S7a. Fast mode data are used for Figs. 1a, b, e, 2b and S1a, S5a, b, S7b. Burst mode data are used for Figs. 1c, f–i, 2c–e and S3, S4a, S5, and S7c–f. (Here, “S” refers to Supplementary Figs.)

EMIC wave
Minimum variance analysis (MVA)22 of magnetic field determines the directions along which the magnetic field changes most and least. In the context of quasi-monochromatic waves, the former represents the primary axis of magnetic field oscillation, while the latter gives wave propagation direction k^ (since 0=∇·Bw/k^·Bw). We apply this technique to the magnetic field shown in Fig. 1d to determine the characteristics of the observed EMIC wave. The three resulting eigenvalues are λ1=18.6, λ2=4.1, λ3=1.0, with λ1/λ2=4.5. The n wave propagation direction k^ (the 180° ambiguity from MVA is solved by examining the Poynting flux derived from the measured magnetic and electric field). This result suggests that the EMIC wave propagates approximately anti-parallel to the background magnetic field.

Furthermore, the ratio λ1/λ2=4.5 suggests that the EMIC wave is approximately linearly polarized with a polarization axis along the FAC l axis. This is consistent with the observation that Bl oscillates more significantly than the other components (Fig. 2a) and the ellipticity (Supplementary Fig. 2c) derived from the aforementioned SVD analysis. However, a finite Bm is also observed, although its amplitude is less than half that of Bl. The finite Bm primarily arises from the inhomogeneity in the EMIC wave. For instance, in the first half of the time interval shown in Fig. 2a, Bl and Bm have equal amplitudes and are in anti-phase. Thus, the EMIC wave there is also linearly polarized, but with a polarization axis ~45° from the FAC l axis. Therefore, the MVA and the accordingly defined FAC only represent the average characteristics of the EMIC wave. Nevertheless, this inhomogeneity does not affect our analysis of the low-energy ions, as Eq. 1 only involves local field at any given time.

We further determine the parallel phase velocity (Vϕ) of the EMIC wave from the Faraday’s law: Vϕ= P(Em)/P(Bl)=1017 km/s, where P(B) and P(E) represent the power spectral density derived from a Fast Fourier transform of the EMIC wave field Bl and Em, respectively. We note that this value represents both the parallel phase velocity in the rest frame of the spacecraft and that in the rest frame of the plasma, as Doppler shift is expected to be negligible due to the orthogonal configuration of k^ and Vbg. The resulting Vϕ is within 24% of the local Alfvén speed VA=817 km/s estimated with Bbg, Nbg, and ion composition observed by HPCA.

Low-energy ion dynamics
We consider how low-energy ions respond to the EMIC wave. Here, for simplicity, we approximate the EMIC wave as a strictly anti-parallel propagating, linearly polarized wave. The field is modeled as
Bx = B? cos(ωt+kz)
Ez = E? cos(ωt+kz), (2)
By = Bx = Ez = 0
where E? =B?ω/k=Vϕ and all the symbols have their standard meanings. Then, the equations of motion of an ion with mass m and charge e are
v_x = Ωvy + ΩB cos(ωt+kz)
v_y = −Ωvx + ΩB cos(ωt+kz) (3)
v_z = 0
where Ω=eBbg/m represents gyro-frequency, ΩB=eB?/m, and z0 gives the initial z coordinate. A formal solution z(t)=z0 + v dt has been used to replace z in the argument of the cosine function. The low-energy assumption (v≪Vϕ) simplifies these equations to
v_x = −Ωvy + ΩB cos(ωt+kz0)
v_y = Ωvx + ΩB cos(ωt+kz0) (4)
v_z = 0
to a first-order approximation in the small parameter v=Vϕ. These equations represent a forced oscillation and can be solved straightforwardly,
vx = 1/(1 − (ω/Ω)2) B? cos(ωt+kz)
vy = 1/(1 − (ω/Ω)2) B? sin(ωt+kz), (5)
vz = 0
The solutions can be rewritten in a more general fashion,
v= 1/(1 − (ω/Ω)2) [ (Ew × Bbg)/Bbg2 + (1/Ω) ∂Ew/∂t ], (6)
which corresponds to Eq. 1 in the main text with E replaced by Ew. The first and second terms in the parentheses are “E×B” drift velocity and polarization drift velocity, respectively.

Consistent with our expectation, this formula reduces to the conventional “E×B” drift in the low-frequency limit (ω/Ω≪1). In the high-frequency limit, due to the prefactor 1/(1 − (ω/Ω)2), the resulting velocity approaches zero, indicating wave-particle decoupling. This latter case applies particularly to O+ ions in our study, for which 1/(1 − (ω/Ω)2) = −0.04 (for comparison, this factor for hydrogen and helium ions is 1.1 and −1.8). Therefore, we do not consider these ions when modeling the growth rate of the electrostatic waves.

Another commonly coexisting species is He++ ions. According to Eq. 6, these ions would be efficiently modulated by the EMIC wave. However, no relevant signatures at the predicted energies are observed (Supplementary Fig. 5c), even though HPCA does indicate their presence in this event (albeit with the lowest abundance). As a result, these ions are also excluded from the analysis presented in the main text.

We also point out that a formula similar to Eq. 6 can be obtained for waves of other polarization. For instance, the drift velocity induced by left-handed circularly polarized waves can be obtained by simply replacing the factor before the parentheses in Eq. 6 with 1/(1 − ω/Ω).

Finally, from Eq. 6, one may immediately observe that this type of response would not result in any net wave-particle energy exchange. This first term on the right-handed side is perpendicular to E and has a zero dot product with E. While the second term on the right-handed side is aligned with E, it is 90° out of phase with E. Consequently, the dot product of this term with E averages to zero over a wave period.

Electrostatic waves
The propagation of electrostatic waves can be determined from an MVA of the observed electric field, as these waves propagate along the direction of electric field oscillation according to Maxwell’s equations. Figure 3e, g show the propagation directions of the higher- and lower-frequency electrostatic waves obtained in this way. Strictly speaking, the propagation direction obtained by MVA has an intrinsic 180° ambiguity. However, an analysis of linear dispersion relation described below indicates that only the solutions presented here are supported. For the other branch of solutions, the theoretical growth rate is negative within the frequency range of interest, preventing waves from growing to an observable amplitude.

The geometry analysis presented in Fig. 3 support the association of these electrostatic waves to an ion-ion cross-field instability28,29 excited by the EMIC wave-induced hydrogen-helium ion counter drift. An analysis of the linear dispersion relation is conducted to provide further evidence. For simplicity, we consider a hydrogen-helium-electron plasma and neglect other species, such as O+. Parameter studies presented in Supplementary Fig. 6 and summarized in Supplementary Note 3 indicate that the impact of this approximation, as well as those made in the following two paragraphs, is moderate and does not affect our main conclusions. We also assume the electrostatic waves propagates strictly perpendicular to Bbg and along the hydrogen-helium ion counter drift. Expressed in the rest frame of hydrogen ions (which is approximately the rest frame of the plasma, given that hydrogen ions dominate the mass density), we have28,29.
(1 − k2vth,H2/ω2) + (ωp,He2/ω2) Z0(kvth,He/ω) + (ωp,e2/Ωe2) (1 − I0(b)e−b) = 0, (7)
where u denotes the drift speed of helium ions relative to hydrogen ions, ωp,i and vth,i with i=H,He,e are hydrogen ion, helium ion and electron plasma frequencies and thermal speeds, respectively, and Z0 is the plasma dispersion function. All parameters are estimated from the observations. Ωi is evaluated at Bbg = 52 nT. vth,i is derived from temperatures estimated from MMS observations (Supplementary Note 2): electrons ~10 eV, hydrogen ~3.3 eV, and helium ~3.8 eV. To calculate ωp,i, the density of each species is required. However, both FPI and HPCA slightly underestimate the density, as they observe particles only within a limited energy range (but the core populations should have been observed, as the FPI and HPCA densities are close to Nbg derived from the upper-hybrid line). Therefore, we estimate the densities of each species based on Nbg, along with species abundances adopted from HPCA observations: 98.6% for hydrogen and 1.4% for helium ions. All these parameters are applied uniformly to both the higher- and lower-frequency electrostatic waves.

The relative drift speed u is determined using Eq. 1 and the observed EMIC wave field. For both the higher- and lower-frequency electrostatic waves, we first extract the values of u at the local peaks of the corresponding wave amplitudes (marked by the dashed lines in Fig. 3a–d), and then set u as the average of the resulting values. The results are u=164 km/s (Fig. 3e) and 171 km/s (Fig. 3g) for the higher- and lower-frequency electrostatic waves, respectively.

The two speeds are very close, resulting in very similar frequency and growth rate profiles for the higher- and lower-frequency electrostatic waves in the rest frame of the plasma. For example, the frequencies at the maximum growth rates in the rest frame of plasma are 40.7 Hz and 42.7 Hz for the higher- and lower-frequency electrostatic waves, respectively. The observed frequency difference between the two waves actually arises from the Doppler shift transferring frequency in the rest frame of the plasma to the rest frame of the spacecraft. As shown in Fig. 3e, g the background flow (Vbg), the EMIC wave-induced hydrogen ion velocity (VH) and the electrostatic wave propagation direction form different configurations for the higher- and lower-frequency electrostatic waves. During the former, the background flow is approximately perpendicular to the wave propagation. Thus, the velocity for the Doppler shift is solely VH = 34 km/s. In contrast, during the latter, the background flow is approximately anti-parallel with the wave propagation, and the velocity for the Doppler shift is VH + Vbg = 109 km/s.

As an additional remark, we note that previous studies28 using a full version of the linear dispersion relation, without restriction on wave propagation direction, indicate that the growth rate of the ion-ion cross-field instability may peak at directions moderately deviating from relative drift when relative drift speed is large. This may explain the non-zero angles observed between the electrostatic wave propagation and the relative drift in our cases, if this deviation is not due to measurement errors.

Data availability
The magnetic field data from the Fluxgate Magnetometers (FGM) instruments, the electric field data from the Electric Field Double Probe (EDP) instruments, and the ion data from the Fast Plasma Investigation-Dual Ion Spectrometers (FPI-DIS) instruments are available in the MMS Science Data Center under accession code https://lasp.colorado.edu/mms/sdc/public/. The time interval of interest is December 29, 2020 18:17:48-18:18:18 UT. Source data are provided with this paper.

Code availability
The dispersion relation solver BO is available from ref. 44, as provided by its authors.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Review Report on Direct Observations of Cross-Scale Energy Transfer Driven by Multiple-Ion Interactions in Space\nPlasmas\nOverview:\nPaper proposes a compelling, new, cross-scale energy transfer mechanism in space plasmas, influenced by a minor\nspecies He+ ions. The ion-scale hydrogen-band EMIC waves impact hydrogen ions which follow “(cid:1) × (cid:2)” drift, while the\nresponse of helium ions are impacted by a significant polarization drift. The EMIC wave frequency lies between the\nhydrogen and helium gyrofrequencies, resulting in opposite motion of He+ and H+ in the plane perpendicular to the\nmagnetic field, creating a counter drift configuration. This gives rise to the electrostatic waves near the lower-hybrid\nfrequency via the ion-ion cross-field instability. These observations demonstrate that interactions between different ion\nspecies cannot be ignored when addressing the cross-scale physics.\nSummary Evaluation:\nPaper is an important new addition to the space plasma physics field in understanding the detailed physics of the cross-\nscale energy transport at different scales. I believe the paper is appropriate for Nature Communications after following\nrevisions.\nDetailed comments:\n1. Line 29/ Line46-47: I suggest adding citations to previous relevant works that address cross-scale energy transport from\nspace plasmas, e.g., between MHD-scale waves and ion scale waves, and associated ion and electron heating:\nMoore, T., Nykyri, K. & Dimmock, A. Cross-scale energy transport in space plasmas. Nature Physics 12, 1164–1169 (2016).\nhttps://doi.org/10.1038/nphys3869,\nNykyri, K., Ma, X. and Johnson, J. (2021). Cross-Scale Energy Transport in Space Plasmas. In Magnetospheres in the Solar\nSystem (eds R. Maggiolo, N. André, H. Hasegawa, D.T. Welling, Y. Zhang and L.J. Paxton).\nhttps://doi.org/10.1002/9781119815624.ch7\nNykyri, K., Ma, X., Burkholder, B., Rice, R., Johnson, J. R., Kim, E.-K., et al. (2021). MMS observations of the multiscale wave\nstructures and parallel electron heating in the vicinity of the southern exterior cusp. Journal of Geophysical Research: Space\nPhysics, 126, e2019JA027698. https://doi.org/10.1029/2019JA027698\n2. Lines 73-74\\Lines 220: Paper should show in supplementary information the HPCA measurements of the relative\nabundance of the number densities of the He++, He+ and H+. The He++ would have the gyro-frequency of ~ 0.5 of the\nproton cyclotron frequency.\n3. Figure 1d. As background magnetic field is quite strong, it Is difficult to see by eye the dB with an amplitude of ~ 5 nT. I\nrecommend extracting the background field and compare the dE/dB ratio to local Alfven speed to verify how electromagnetic\nor electrostatic the waves are. A panel of the wave polarization at each frequency and propagation angle would also be\ngood to show to assess how variable the wave properties are.\n4. A) Wave mode could be further checked by checking the velocity distribution functions and whether the dispersion\nsurfaces (when plugged into dispersion solvers) would give a positive growth for EMIC waves.\nB) To assess the free energy of the EMIC wave growth, test the temperature moment anisotropy condition for the H+ and\nHe+ and He++ wave growth by taking the perpendicular and parallel temperatures form HPCA data.\n5. Article needs to add information of the instrument mode used, e.g., burst mode, fast or survey mode. If the FGM survey\nmode data has been used the sampling rate is 16Hz. It appears the supplementary figure 1b has used 128 Hz burst mode\nFGM data. Shown this way, as the lower freuquencies have higher power, the color scale may mask any wave power at\nlower hybrid frequnecy ange. I suggest creating a combined spectrogram of the search coil magnetometer data,\nabove 16 Hz with sensitivity at higher frequencies and calculating the dE/dB spectrogram around lower hybrid frequency band,\nnormalized to the local wave Alfven speed to assess whether the lower-hybrid band waves are electro-static.\nSome of the extra analysis may be organized into supplementary information and reference in the main text to remain within\npage limits for Nature Communications.", "reviewer_2": "The manuscript deals with a cross-scale energy transfer driven by interactions between protons and alpha particles. In\nparticular, the authors presented an experimental evidence of cross-scale energy wave-particle interactions due to multiple-\nion interactions in the magnetosphere. By using high-resolution measurements of MMS spacecraft, the authors showed an\ninterplay between protons and alpha particles with electromagnetic ion cyclotron waves (a counter-drift configuration) which\ntrigger electrostatic waves near the lower-hybrid frequency. The results are very interesting since, as far as I know, it is the\nfirst time that multi-ion interactions in space have been directly observed to induce a transfer of energy between different\nscales. As the authors stated, this can be an essential mechanism responsible for transporting energy across scales in\nastrophysical and space systems.\nEven if I recognize the powerful of the MMS mission in the near-Earth environment, I’m wondering if the same mechanism\ncan be observed in other system explored by space missions, such as the solar wind. Indeed, the new solar missions, that is\nParker Solar Probe and Solar Orbiter, are investigating the solar wind from the near-Earth towards the Sun. In this sense, I\nwould like the authors to discuss this point. Indeed, electromagnetic measurements are available on these spacecraft and\nthe particle instruments, SPAN and PAS, work in a similar way. As DIS of FPI suite, they do not distinguish between ion\nspecies, but signatures of ion populations for both protons and alpha particles can be distinguished in the ion distribution\n(see McManus et al. 2022, 2025, De Marco et al. 2023, Bruno et al. 2024). Moreover, onboard Solar Orbiter, another\ninstrument of the SWA suite, that is HIS, can directly measure heavy ion distribution functions, but unfortunately a few\ndatasets are available.\nMoreover, this point should be also added to the Introduction since the authors did not discuss any numerical model neither\nobservational results about the contribution of heavy ions, and in particular alpha particles, to the cross-scale energy\ntransfer. Despite the above mentioned works which used Parker Solar Probe and Solar Orbiter particle data, there are\ndifferent numerical approaches that took into account the contribution of alpha particles, such as Ofman 2010, Maneva et al.\n2010, 2013, 2015, Perrone et al. 2011, 2013, Valentini et al. 2016).\nAnother point is about some missing figures that can help the reader to understand better the results and how they have\nbeen obtained. In particular, in my opinion the following two figures would be added in the supplementary information:\n- the cross-wavelet analysis as mentioned at pag 4\n- the 4 MMS signals for the wave packets as mentioned at pag. 6.\nVery minor points:\n- In fig 3f the growth rate is a blue curve, but in the text (pag 7 line 183) is referred as red curve\n- the arrows in fig 1h are not well visible.\n- in supplementary information, left panels of fig.2 are the same of left panel of fig. 3 panels e and g.\nTherefore, in my opinion, the manuscript is very interesting and deserve to be published but after additional discussions and\nclarifications.", "reviewer_3": "The paper provides direct observations of cross-scale energy transfer driven by cross-scale wave-particle interaction using\nunique dataset from MMS spacecraft. The paper showed that the interplay between hydrogen and helium ions with ion-scale\nwaves can further excites electrostatic waves at the smaller lower-hybrid scale. This topic is highly significant, as it\nhighlights the non-negligible role of multi-ion interactions in mediating energy transport across scales in space plasmas.\nHowever, further justification and clarification are needed before the manuscript can be considered for acceptance.\nMajor comments:\nThe paper presents a compelling agreement between EMIC wave-induced hydrogen-helium ion counter-drift and the\nobserved arc structures in the energy-time spectrogram. However, the relationship between the relative drift velocity and the\namplitude of electrostatic waves remains unclear—particularly when comparing peaks 2 and 3 in the lower-frequency\nelectrostatic wave (Figure 3d) with the corresponding l-component of the drift velocity (Figure 3a). This raises the question of\nwhether additional factors such as plasma compositions or temperature may significantly influence wave growth.\nFurthermore, prior studies (e.g., Khazanov et al., 2016) have reported cross-scale wave-particle interactions involving lower\nhybrid waves driven by ion polarization drift in the presence of EMIC waves. The authors should cite this work and clarify\nhow the current study offers new or substantially different insights.\nKhazanov, G. V., S. Boardsen, E. N. Krivorutsky, M. J. Engebretson, D. Sibeck, S. Chen, and A. Breneman (2017), Lower\nhybrid frequency range waves generated by ion polarization drift due to electromagnetic ion cyclotron waves: Analysis of an\nevent observed by the Van Allen Probe B, J. Geophys. Res. Space Physics, 122, 449–463, doi:10.1002/2016JA022814.\nMinor comments:\n1. Given that O+ are often coexist with H+ and He+ in the magnetosphere, what is expected the drift speed of O+ and how do\nthey influence the generation of the lower hybrid electrostatic waves? To what extent would the presence of O+ modify the\nwave frequency and growth rate profiles?\n2. Line 350-351: should the ~99% abundance refer to hydrogen ions rather than helium ions? I commend that the authors\nprovide the FPI-DES plus HPCA measurements in the supplemental material to support the parameters used in estimating\nthe wave growth, as well as the O+ energy-time spectrogram mentioned in the above comment.\n3. Line 365: Please explicitly provide the value of the lower –frequency electrostatic wave frequency in the rest frame of the\nplasma (i.e., without Doppler shift) at the end of this paragraph.\n4. Lines 231-233: The authors state that the proposed mechanism relies on two essential elements—EMIC waves and minor\nions—which are said to exist almost ubiquitously in the magnetosphere. This would imply that lower hybrid waves, EMIC\nwaves, and the associated relative ion drift should be commonly observed together. To support this claim, could the authors\nprovide at least one additional event, possibly in the supplemental material?\nLines 352-354: I found the calculation of the relative drift speed u somewhat unclear. The manuscript states that u is\ndetermined at the time when the electrostatic wave amplitude peaks. However, there are multiple peaks—five for the higher-\nfrequency and four for the lower-frequency electrostatic waves—yet only a single value of u is provided for each case. Could\nthe authors clarify how u was selected in light of the multiple peaks? Additionally, would variations in the relative drift speed\nat different peak times impact the wave frequency and growth rate profiles? How is this approach consistent with the\nobserved modulation of electrostatic wave frequency and amplitude?", "reviewer_4": "Review report\non Paper\n\"Direct Observations of Cross-Scale Energy Transfer Driven by Multiple-Ion Interactions in Space Plasmas\"\nby Z.-Y. Liu, Q.-G. Zong, S. Wang, X.-Z. Zhou, Y. Chao\nsubmitted to Nature Communications\nThe paper describes a case study which relies on 30 seconds of plasma and electromagnetic field measurements by a\nsingle MMS spacecraft. The authors conclude that this observation provides direct experimental evidence for cross-scale\nenergy transfer processes in plasmas with multiple ion species. This conclusion is based on measurements of low-\nfrequency waves, drifting hydrogen and helium ions, and Doppler shifted waves close to the lower hybrid frequency in the\nplasma frame. I can recommend the paper for publication only after a major revision is done, according to my specific\ncomments listed below.\nSpecific comments\nl. 45 \"experimental evidence\" is probably a strong wording provided that a very limited set of single point measurements is\nused\nl. 59-62 It is rather shocking that, in a paper on cross-scale coupling, the multipoint capabilities of the MMS mission are left\nunexplored\nl. 80 The theory of propagation of electromagnetic waves in cold plasmas containing multiple ion species seems to be\ncompletely ignored by the authors. Multi-ion cross-over, cutoff and hybrid frequencies define the wave mode structure and\nshould be estimated in the context of the presented observations. The mode structure should be described and discussed in\norder to properly interpret the measurements. Rigorously identifying the observation with the electromagnetic ion cyclotron\n(EMIC) mode would require a more thorough analysis and comparison with cold plasma theory.\nl. 94 it is a rather weak evidence that the electrostatic waves are modulated based just on 3-5 periods of the low frequency\nelectromagnetic wave\nl. 100 A single-mode quasiparallel wave should be nearly circularly polarized in the plasma frame, either in the left handed\nor in the right handed sense. However, the cold homogeneous plasma theory in fact predicts the presence of both left-and\nright-hand polarized modes in the frequency range between the multi-ion L-mode cutoff and H+ cyclotron frequency. Hence,\nthe observed linear polarization can be still well consistent with the theory if both modes are present.\nl. 102, 103 wave propagation in the inhomogeneous, hot plasma is mentioned as a possible cause of the observed linear\npolarization. This needs to be explained. Mechanisms which would be responsible for it should be described.\nl. 342-343, 351 the abundance of helium ions~99% contradicts the statement that hydrogen ions dominate the mass density\nl. 344 The approximate dispersion relation 7 should be verified with publicly accessible numerical dispersion solvers in\nmulticomponent plasmas like WHAMP"}, "author_response": "Response to Reviewer #1\nOverview: Paper proposes a compelling, new, cross-scale energy transfer mechanism in space\nplasmas, influenced by a minor species He+ ions. The ion-scale hydrogen-band EMIC waves\nimpact hydrogen ions which follow “𝐸 × 𝐵” drift, while the response of helium ions are impacted\nby a significant polarization drift. The EMIC wave frequency lies between the hydrogen and\nhelium gyrofrequencies, resulting in opposite motion of He+ and H+ in the plane perpendicular to\nthe magnetic field, creating a counter drift configuration. This gives rise to the electrostatic waves\nnear the lower-hybrid frequency via the ion-ion cross-field instability. These observations\ndemonstrate that interactions between different ion species cannot be ignored when addressing the\ncross-scale physics.\nSummary Evaluation: Paper is an important new addition to the space plasma physics field in\nunderstanding the detailed physics of the cross-scale energy transport at different scales. I believe\nthe paper is appropriate for Nature Communications after following revisions.\nWe sincerely appreciate Reviewer #1 for his/her time and effort in evaluating our manuscript, as\nwell as for the constructive feedback provided. We have carefully considered the comments and\nrevised the manuscript accordingly. Specifically, as suggested, we have now cited the\nrecommended references (thank you for these excellent papers!) and discussed our results in the\ncontext of these works. We have also added additional observations and analyses, including an\nSVD analysis of the EMIC wave, the theoretical dispersion relation of the EMIC wave, and the\nratio of magnetic to electric power for the lower-hybrid frequency waves. Furthermore, we have\nrefined the presentation in accordance with the reviewer’s suggestions. We hope these revisions\naddress the reviewer’s concerns and clarify any ambiguities in the previous version of the\nmanuscript.\nPlease note that the numbering of supplementary figures may differ from that in the previous\nversion of the manuscript. Any such changes are noted in our response where relevant. The line\nnumbers referenced below correspond to the text marked with track changes.\nBefore addressing the detailed comments below, we would like to first clarify our treatment of\nelectron temperature, which is used in the theoretical analysis of the dispersion relation of the\nlower-hybrid electrostatic waves. In the previous version of the manuscript, the electron\ntemperature was estimated by fitting FPI-DES measurements. However, during this round of\nrevision, we realized that FPI-DES measurements in the low-energy channels may not be reliable\ndue to the spacecraft potential (~4 V) and photoelectron contamination. As a result, the previously\nadopted value of 10 eV may not accurately reflect the true electron temperature. Moreover, this\nmeasurement limitation may imply that the exact electron temperature cannot be determined with\nconfidence. Nevertheless, an analysis suggests that 10 eV remains a reasonable representative\nvalue. To see this, we first note that the total electron density is 1.4 cm−3, as determined from the\nupper-hybrid line. On the other hand, FPI-DES detects a partial density of approximately 0.2 cm−3\nabove 32.8 eV (the 6th energy channel), where the influence of spacecraft potential and\nphotoelectrons is minimal. A comparison of the two numbers indicates that the majority of\nelectrons have energies below 32.8 eV. Therefore, adopting 10 eV—roughly one-third of 32.8\neV—as a representative temperature may remain a reasonable approximation. Furthermore, we\nconducted a parameter study (see Supplementary Note 3), which demonstrates that the dispersion\nrelation of lower-hybrid electrostatic waves is not highly sensitive to variations in electron\ntemperature. For instance, the waves exhibit a substantial growth rate as long as the electron\ntemperature remains below 44 eV. Accordingly, the impact of uncertainty in the electron\ntemperature on our results is expected to be moderate, and our main conclusion—the EMIC wave-\ninduced hydrogen-helium relative drift can excite electrostatic waves at the lower-hybrid scales—\nstill holds. Thus, we continue to use 10 eV as the electron temperature in the theoretical analysis\npresented in this version of the manuscript. This issue and our treatment are now described in line\n184-196 of the Supplementary Information:\nDue to the spacecraft potential (~4 V) and photoelectron contamination47, FPI-DES measurements in the\nlow-energy channels may not be reliable for deriving the electron temperature. Nevertheless, we can still\nconstrain the electron temperature based on observations. First, we note that the total electron density is\n𝑁 =1.4 cm-3, as determined from the upper-hybrid line. Next, FPI-DES suggests a partial density of ~0.2\n𝑏𝑔\ncm-3 above 32.8 eV (the 6th energy channel of FPI-DES), where the effects of spacecraft potential and\nphotoelectrons are weak. A comparison of these two values indicates that the majority of electrons have\nenergies below 32.8 eV. Therefore, as a rough estimate, we adopt an electron temperature of 10 eV (i.e.,\nabout one-third of 32.8 eV). A parameter study presented in Supplementary Note 3 indicates that the\ndispersion relation of lower-hybrid electrostatic waves is not highly sensitive to electron temperature. For\ninstance, the waves maintain a sizeable growth rate as long as the electron temperature remains below 44 eV.\nTherefore, the impact of uncertainty in the electron temperature on our results is expected to be moderate.\nDetailed comments:\n1. Line 29/ Line46-47: I suggest adding citations to previous relevant works that address cross-\nscale energy transport from space plasmas, e.g., between MHD-scale waves and ion scale waves,\nand associated ion and electron heating: (1) Moore, T., Nykyri, K. & Dimmock, A. Cross-scale\nEnergy transport in space plasmas. Nature Physics 12, 1164–1169 (2016).\nhttps://doi.org/10.1038/nphys3869. (2) Nykyri, K., Ma, X. and Johnson, J. (2021a). Cross-Scale\nEnergy Transport in Space Plasmas. In Magnetospheres in the Solar System (eds R. Maggiolo, N.\nAndré, H. Hasegawa, D.T. Welling, Y. Zhang and L.J. Paxton).\nhttps://doi.org/10.1002/9781119815624.ch7. (3) Nykyri, K., Ma, X., Burkholder, B., Rice, R.,\nJohnson, J. R., Kim, E.-K., et al. (2021b). MMS observations of the multiscale wave structures\nand parallel electron heating in the vicinity of the southern exterior cusp. Journal of Geophysical\nResearch: Space Physics, 126, e2019JA027698. https://doi.org/10.1029/2019JA027698\nWe sincerely thank the reviewer for recommending these papers. Indeed, these studies have\nclearly demonstrated that wave-particle interactions can mediate energy exchange between\nMHD/fluid-scale waves and ion-scale waves. Our observations further reveal that ion-scale waves\ncan transfer energy down to lower-hybrid-scale waves. Taken together, these studies highlight a\ncoherent picture in which the interplay between waves of different scales plays a critical role in\ncross-scale energy transfer in space plasmas. Hence, we have cited Moore et al. (2016) as ref. 19,\nNykyri et al. (2021a) as ref. 4, and Nykyri et al. (2021b) as ref. 20 in the revised manuscript, and\nhave introduced them in lines 30-33:\nThe interaction of these multi-scale processes, along with the associated cross-scale energy transfer and\nfield-particle energy redistribution (e.g., see review by ref.4), governs the dynamics of plasmas and,\nconsequently, the evolution of the astrophysical and space systems they constitute.\nAnd lines 56-59:\nSpecifically, we focus on a process known as cross-scale wave-particle interactions18-21. This process can\nefficiently drive energy transfer across scales through the simultaneous interactions of waves of different\nscales with charged particles.\nAnd lines 275-281:\nNevertheless, recent observations18-21 have clearly shown that these interactions can efficiently transfer\nenergy from fluid-scale waves to ion-scale waves. Our results further reveal that ion-scale waves can transfer\nenergy down to low-hybrid scales. Together, these studies demonstrate that cross-scale wave-particle\ninteractions do happen in space and could play an important role in mediating energy exchange between\ndifferent scales in various astrophysical and space plasma phenomena.\n2. Lines 73-74\\Lines 220: Paper should show in supplementary information the HPCA\nmeasurements of the relative abundance of the number densities of the He++, He+ and H+. The\nHe++ would have the gyro-frequency of ~ 0.5 of the proton cyclotron frequency.\nThanks for this valuable suggestion. Now, the relative abundances in terms of number density for\nH+, He+, He++, and O+ are now shown in Supplementary Fig. 1b. Lines 291-293 in the main text\nsummarize these observations.:\nInformation on ion composition was obtained from the Hot Plasma Composition Analyzer42 (HPCA): The\nrelative abundances in terms of number density of H+, He+, He++, and O+ are 95.5%, 1.4%, 1.1%, and 2.0%,\nrespectively, during our event (Supplementary Fig. 1b).\n3. Figure 1d. As background magnetic field is quite strong, it is difficult to see by eye the dB with\nan amplitude of ~ 5 nT. I recommend extracting the background field and compare the dE/dB ratio\nto local Alfven speed to verify how electromagnetic or electrostatic the waves are. A panel of the\nwave polarization and propagation angle at each frequency would also be good to assess how\nvariable the wave properties are.\nAs suggested, the revised Fig. 1d shows the magnetic field measurement with the background\nfield 𝐵⃗ =52×[−0.66,0.04,0.75] nT in GSE removed. Now, the signatures corresponding to\n0\nthe EMIC wave can be seen clearly.\nThe comparison of the dE/dB ratio (i.e., phase speed) to local Alfven speed is given in lines 324-\n330:\nWe further determine the parallel phase velocity (𝑉 ) of the EMIC wave from the Faraday’s law: 𝑉 =\n𝜙 𝜙\n√𝑃(𝐸 )/𝑃(𝐵)=1017 km/s, where 𝑃(𝐵) and 𝑃(𝐸 ) represent the power spectral density derived from\n𝑚 𝑙 𝑙 𝑚\na Fast Fourier transform of the EMIC wave field 𝐵 and 𝐸 , respectively..……The resulting 𝑉 is within\n𝑙 𝑚 𝜙\n24% of the local Alfvén speed 𝑉 =817 km/s estimated with 𝐁 , 𝑁 , and ion composition observed by\n𝐴 𝑏𝑔 𝑏𝑔\nHPCA.\nThis result verifies the observed ~0.25 Hz wave is electromagnetic in nature. By the way, please\nnote that we have re-calculated the local Alfvén speed using a more accurate ion composition\nderived from HPCA observations. The updated Alfvén speed is slightly lower than that presented\nin the previous version of the manuscript (817 km/s versus 959 km/s), which was based on a\nproton-electron plasma.\nIn the revised manuscript, Supplementary Fig. 2b and 2c now present the frequency-time\nspectrograms of the wave normal angle and ellipticity, respectively, derived from a singular value\ndecomposition (SVD) analysis (Santolík et al., 2003, cited as ref. 43) of the magnetic field. These\nfigures show that the wave properties are approximately uniform within the frequency-time\ndomain where the wave power spectral density is large. Furthermore, when averaged over this\ndomain, the wave normal angle is approximately 13∘ and the ellipticity is −0.04, which are\nconsistent with our previous conclusion of approximately field-aligned propagation and linear\npolarization. We note that the approximately field-aligned propagation of the observed wave rules\nout the possibility that it is a kinetic Alfvén wave, which is another common mode near the ion\ncyclotron frequency in the magnetosphere but typically propagates quasi-perpendicularly. The\nresults of the SVD analysis are also discussed in the Methods section, subsection EMIC waves.\nIn addition, Supplementary Fig. 2a shows the dynamic spectrum of the magnetic field in the\nfrequency range corresponding to the EMIC wave, illustrating the approximately monochromatic\nnature of the wave.\n4. A) To assess the free energy of the EMIC wave growth, test the temperature moment anisotropy\ncondition for the H+ and He+ and He++ by taking the perpendicular and parallel temperatures\nform HPCA data.\nHPCA observations of ion anisotropy, defined as the ratio of perpendicular to parallel temperature,\nare now presented in Supplementary Fig. 1c. Averaged over the entire event, the anisotropies of\nH+, He+, He++, and O+ are 1.71, 1.05, 1.53, and 1.02, respectively.\nIn addition, we note that previous studies have suggested that EMIC waves in the magnetosphere\nare primarily excited by anisotropic hot H+ ions. Their effects will be incorporated into the\ndispersion relation analysis presented in the following response. To derive their parameters, we\nspecifically consider FPI-DIS measurements above 2 keV. This energy threshold is chosen to\navoid contamination from He+, which primarily appears below 1 keV (Fig. 2c), and to eliminate\nthe influence of low-energy hydrogen arcs. The resulting distribution function is shown in\nSupplementary Fig. 3a, where a clear anisotropy is evident, with the perpendicular PSDs\nexceeding the parallel PSDs. We fit a bi-Maxwellian distribution to the data and obtain a number\ndensity of 0.23 cm-3, a parallel temperature of 3148 eV, and a perpendicular temperature of 5506\neV.\nThis information is now included in Supplementary Note 1. Please refer to the response to the\nfollowing comment.\nB) Wave mode could be further checked by checking the velocity distribution functions and\nwhether the dispersion surfaces (when plugged into dispersion solvers) would give a positive\ngrowth for EMIC waves.\nWe sincerely appreciate this insightful suggestion. In response, we calculated the dispersion\nrelation within the frequency range corresponding to EMIC waves using a Maxwellian H+-He+-\nHe++-O+-electron plasma model and the dispersion relation solver BO developed by Xie (2019;\ncited as ref. 44). To account for the effects of hot H+ ions, which play a critical role in EMIC wave\nexcitation, we divided the H+ ions into a cold core population and a hot population in this part,\nwith the parameters of the latter provided in the above response. Supplementary Fig. 3b presents\nthe resulting wave frequency as a function of wavenumber. We also plot the observed dispersion\nrelation of the EMIC wave as a black square, with a frequency~0.25 Hz and a\nwavenumber~2.46×10-4 km-1 (=0.25 [Hz] / 1017 [km/s]). This data point lies close to the\ntheoretical dispersion relation for EMIC waves (red curve), supporting our identification of the\n0.25 Hz wave as an EMIC wave.\nSupplementary Fig. 3c further presents the corresponding growth rates as functions of\nwavenumber for different branches. The red branch exhibits positive growth rates near the\nwavenumber of the observed waves, indicating that this EMIC mode can indeed grow under the\ngiven plasma conditions. This result reinforces our conclusion.\nThese results, together with how the plasma model is set, are now presented in the Supplementary\nNote 1, lines 107-140 in the Supplementary Information:\nWe further verify that the observed ~0.25 Hz wave corresponds to the EMIC mode by comparing its\nproperties with the theoretical dispersion relation of EMIC waves. To this end, we employ a bi-Maxwellian\nH+-He+-He++-O+-electron plasma. The densities of these species are set based on 𝑁 =1.4 cm-3\n𝑏𝑔\n(Supplementary Fig. 1a) and HPCA measurements of ion compositions (Supplementary Fig. 1b):\nelectrons~1.4 cm-3, H+~1.337 cm-3, He+~0.0196 cm-3, He++~0.0154 cm-3, and O+~0.028 cm-3. Previous\nstudies have shown that EMIC waves in the magnetosphere are mainly excited by anisotropic hot H+. To\naccount for this, we here divide the H+ ions into a cold core population and a hot population. The parameters\nof the latter are determined from FPI-DIS measurements above 2 keV. This energy threshold is chosen to\navoid contamination by He+, which primarily appears below 1 keV (Fig. 2c). It also eliminates the influence\nof low-energy hydrogen arcs. Supplementary Fig. 3a shows the FPI-DIS phase space densities (PSDs) above\n2 keV in the parallel and perpendicular directions. Evidently, the distribution is anisotropic, with the\nperpendicular PSDs exceeding the parallel PSDs. We fit a bi-Maxwellian distribution to the data and obtain a\nnumber density of 0.23 cm-3, a parallel temperature of 3148 eV, and a perpendicular temperature of 5506 eV.\nAccordingly, the number density of the cold core H+ population is set to 1.107 cm-3. The cold core H+, He+,\nHe++, O+, and electrons are also modeled as bi-Maxwellian. Their parallel temperature 𝑇 = 3 𝑇 and\n∥ 1+2𝛼 𝑒𝑓𝑓\n3𝛼\nperpendicular 𝑇 = 𝑇 are derived from the effective temperature 𝑇 and temperature anisotropy\n⊥ 1+2𝛼 𝑒𝑓𝑓 𝑒𝑓𝑓\n𝛼. For simplicity, 𝑇 is set to 10 eV for electrons and 3 eV for all ion species. The anisotropy 𝛼 is set to\n𝑒𝑓𝑓\nunity for electrons and to the values of 𝑇 /𝑇 obtained from HPCA measurements (Supplementary Fig. 1c)\n⊥ ∥\naveraged over the entire event for ions: H+ ~1.71, He+ ~1.05, He++ ~1.53, and O+ ~1.02. (A test actually\nindicates that the non-zero temperature and anisotropy of these particles have little impact on the resulting\ndispersion relation.)\nThis plasma model is then input into the dispersion relation solver BO44. Supplementary Fig. 3b shows the\nresulting wave frequency as a function of wavenumber. We also plot the observed dispersion relation of the\nEMIC wave as a black square: frequency~0.25 Hz and wavenumber~2.46×10-4 km-1 (=0.25 [Hz] / 1017\n[km/s]). The observation lies close to the theoretical dispersion relation (red curve), supporting our\nidentification of the ~0.25 Hz wave as an EMIC wave. This conclusion is further supported by the\ncorresponding growth rates. As shown in Supplementary Fig. 3c, the red branch exhibits positive growth\nrates near the wavenumber of the observed wave, indicating that this EMIC mode can indeed grow under the\ngiven plasma conditions.\nA reference to this result is provided in lines 91-94 of the main text:\nHence, the 0.25 Hz wave fits the classification reserved for electromagnetic ion cyclotron (EMIC) waves24,25,\na typical ion-scale wave mode. This conclusion is further supported by an analysis of the theoretical\ndispersion relation for EMIC waves, as presented in Supplementary Note 1 and Supplementary Fig. 3.\n5. Article needs to add information of the instrument mode used, e.g., burst mode, fast or survey\nmode. If the FGM survey mode data has been used the sampling rate is 16Hz. It appears the\nsupplementary figure 1b has used 128 Hz burst mode FGM data. Shown this way, as the lower\nfreuquencies have higher power, the color scale may mask any wave power at lower hybrid\nfrequnecy range. I suggest creating a combined spectrogram of the search coil magnetometer data,\nabove 16 Hz with sensitivity at higher frequencies and calculating the dE/dB spectrogram around\nlower hybrid frequency band, normalized to the local wave Alfven speed to assess whether the\nlower-hybrid band waves are electro-static.\nWe sincerely appreciate these great comments and suggestions. The instrument modes used are\nnow described in lines 294-296 of the revised manuscript:\nSurvey mode data are used for Fig. 1d, 2a, S1b-1d, S2a-S2c. Fast mode data are used for Fig. 1a, 1b, 1e, 2b,\nS1a, S4a, S4b. Burst mode data are used for Fig. 1c, 1f-1i, 2c-2e, , S2d-S2f, S3a, S4a-S4c. (Here, “S” refers\nto supplementary figures.)\nAs suggested, Supplementary Fig. 2e now shows the dE/dB/VA spectrogram in the frequency\nrange corresponding to lower-hybrid electrostatic waves. It can be seen that this parameter reaches\nvalues around 100 or even higher when wave-like signals appear near the lower-hybrid frequency\nin the electric field spectrogram, confirming the electrostatic nature of these waves.\nAs described above, FGM survey mode data are used for analyzing the EMIC waves (e.g., Fig. 1d\nand 2a), and FGM burst mode data are used for the lower-hybrid frequency waves (e.g.,\nSupplementary Fig. 2d, which was labeled as Supplementary Fig. 1b in the previous version).\nThe sampling frequency of the FGM burst mode data, 128 Hz, is sufficient to resolve wave activity\nwithin the lower-hybrid frequency range (~5-40 Hz). It might be unnecessary to invoke the search\ncoil magnetometer data. Additionally, please note that Supplementary Fig. 2d starts from 3 Hz;\nthus, the real lower-frequency components are not shown in this figure. In particular, this lower\ncutoff is significantly higher than the frequency of the EMIC wave (~0.25 Hz). Therefore, the\ncolor-scale effect suggested by the reviewer is unlikely to affect our analysis much in this case.\nFurthermore, the electrostatic nature of the waves under consideration is quantitatively supported\nby the dE/dB/VA plot described above.\nSome of the extra analysis may be organized into supplementary information and reference in the\nmain text to remain within page limits for Nature Communications.\nOnce again, we would like to express our sincere gratitude to Reviewer #1 for the comprehensive\nreview and insightful comments, which have undoubtedly helped improve our manuscript. We\nhope that our revisions have adequately addressed these comments and clarified any ambiguities\npresent in the previous version.\nResponse to Reviewer #2\nThe manuscript deals with a cross-scale energy transfer driven by interactions between protons\nand alpha particles. In particular, the authors presented an experimental evidence of cross-scale\nenergy wave-particle interactions due to multiple-ion interactions in the magnetosphere. By using\nhigh-resolution measurements of MMS spacecraft, the authors showed an interplay between\nprotons and alpha particles with electromagnetic ion cyclotron waves (a counter-drift\nconfiguration) which trigger electrostatic waves near the lower-hybrid frequency. The results are\nvery interesting since, as far as I know, it is the first time that multi-ion interactions in space have\nbeen directly observed to induce a transfer of energy between different scales. As the authors\nstated, this can be an essential mechanism responsible for transporting energy across scales in\nastrophysical and space systems.\nWe sincerely appreciate Reviewer #2 for his/her time and effort in evaluating our manuscript, as\nwell as for the constructive feedback provided. We have carefully considered the comments and\nrevised the manuscript accordingly. In particular, we have discussed the possibility of observing\ncross-scale wave-particle interactions in the solar wind. Relevant numerical simulations are now\nintroduced in the revised manuscript (thank you for suggesting these excellent papers). We have\nalso added additional figures presenting the cross-wavelet analysis and the four MMS\nobservations of the electrostatic waves, as suggested. We hope these revisions address the\nreviewer’s concerns and clarify any ambiguities in the previous version of the manuscript.\nPlease note that the numbering of supplementary figures may differ from that in the previous\nversion of the manuscript. Any such changes are noted in our response where relevant. The line\nnumbers referenced below correspond to the text marked with track changes.\nBefore addressing the detailed comments below, we would like to first clarify our treatment of\nelectron temperature, which is used in the theoretical analysis of the dispersion relation of the\nlower-hybrid electrostatic waves. In the previous version of the manuscript, the electron\ntemperature was estimated by fitting FPI-DES measurements. However, during this round of\nrevision, we realized that FPI-DES measurements in the low-energy channels may not be reliable\ndue to the spacecraft potential (~4 V) and photoelectron contamination. As a result, the previously\nadopted value of 10 eV may not accurately reflect the true electron temperature. Moreover, this\nmeasurement limitation may imply that the exact electron temperature cannot be determined with\nconfidence. Nevertheless, an analysis suggests that 10 eV remains a reasonable representative\nvalue. To see this, we first note that the total electron density is 1.4 cm−3, as determined from the\nupper-hybrid line. On the other hand, FPI-DES detects a partial density of approximately 0.2 cm−3\nabove 32.8 eV (the 6th energy channel), where the influence of spacecraft potential and\nphotoelectrons is minimal. A comparison of the two numbers indicates that the majority of\nelectrons have energies below 32.8 eV. Therefore, adopting 10 eV—roughly one-third of 32.8\neV—as a representative temperature may remain a reasonable approximation. Furthermore, we\nconducted a parameter study (see Supplementary Note 3), which demonstrates that the dispersion\nrelation of lower-hybrid electrostatic waves is not highly sensitive to variations in electron\ntemperature. For instance, the waves exhibit a substantial growth rate as long as the electron\ntemperature remains below 44 eV. Accordingly, the impact of uncertainty in the electron\ntemperature on our results is expected to be moderate, and our main conclusion—the EMIC wave-\ninduced hydrogen-helium relative drift can excite electrostatic waves at the lower-hybrid scales—\nstill holds. Thus, we continue to use 10 eV as the electron temperature in the theoretical analysis\npresented in this version of the manuscript. This issue and our treatment are now described in line\n184-196 of the Supplementary Information:\nDue to the spacecraft potential (~4 V) and photoelectron contamination47, FPI-DES measurements in the\nlow-energy channels may not be reliable for deriving the electron temperature. Nevertheless, we can still\nconstrain the electron temperature based on observations. First, we note that the total electron density is\n𝑁 =1.4 cm-3, as determined from the upper-hybrid line. Next, FPI-DES suggests a partial density of ~0.2\n𝑏𝑔\ncm-3 above 32.8 eV (the 6th energy channel of FPI-DES), where the effects of spacecraft potential and\nphotoelectrons are weak. A comparison of these two values indicates that the majority of electrons have\nenergies below 32.8 eV. Therefore, as a rough estimate, we adopt an electron temperature of 10 eV (i.e.,\nabout one-third of 32.8 eV). A parameter study presented in Supplementary Note 3 indicates that the\ndispersion relation of lower-hybrid electrostatic waves is not highly sensitive to electron temperature. For\ninstance, the waves maintain a sizeable growth rate as long as the electron temperature remains below 44 eV.\nTherefore, the impact of uncertainty in the electron temperature on our results is expected to be moderate.\nEven if I recognize the powerful of the MMS mission in the near-Earth environment, I’m\nwondering if the same mechanism can be observed in other system explored by space missions,\nsuch as the solar wind. Indeed, the new solar missions, that is Parker Solar Probe and Solar\nOrbiter, are investigating the solar wind from the near-Earth towards the Sun. In this sense, I\nwould like the authors to discuss this point. Indeed, electromagnetic measurements are available\non these spacecraft and the particle instruments, SPAN and PAS, work in a similar way. As DIS of\nFPI suite, they do not distinguish between ion species, but signatures of ion populations for both\nprotons and alpha particles can be distinguished in the ion distribution (see McManus et al. 2022,\n2025, De Marco et al. 2023, Bruno et al. 2024). Moreover, onboard Solar Orbiter, another\ninstrument of the SWA suite, that is HIS, can directly measure heavy ion distribution functions,\nbut unfortunately a few datasets are available.\nThank you for the comments. Overall, we are optimistic about the possibility of observing the\nsame (or similar) mechanisms in the solar wind. In general, cross-scale wave-particle interactions\nmanifest as coupling between two waves of different scales in electromagnetic measurements: the\ngrowth of smaller-scale waves is modulated by larger-scale waves, resulting in periodic wave\npackets of the former that are synchronized with the fields of the latter. Field instruments onboard\nthe Parker Solar Probe and Solar Orbiter are capable of identifying such events. To uncover the\nphysical mechanisms underlying these electromagnetic signatures, particle data with sufficiently\nhigh energy, angular, and temporal resolution are essential. While such observations are\nchallenging, they are not necessarily infeasible. For instance, the PAS instrument onboard Solar\nOrbiter can resolve three-dimensional particle velocity distribution functions. Its burst-mode data,\nwith a sampling frequency of up to 0.25 Hz and above the proton cyclotron frequency (~0.1 Hz or\nlower), is capable of capturing wave-particle interactions near the ion cyclotron frequency.\nMoreover, as the reviewer noted, techniques have been developed to distinguish ion species,\nincluding minor ions. Therefore, in principle, PAS is capable of detecting cross-scale wave-\nparticle interactions like that investigated in our study.\nWe also note that results from MMS can inform investigations involving other instruments.\nTheoretical models may be developed based on physical mechanisms identified through MMS\nobservations (e.g., the one presented in our manuscript). By comparing model outputs, such as\nwave frequency and polarization, with spacecraft measurements of the electromagnetic field, it is\npossible to assess whether a proposed mechanism aligns with observations, even in the absence of\nparticle data with the required resolution. For these reasons, we aim to examine MMS\nobservations in great detail.\nIn summary, while observing cross-scale wave-particle interactions in the solar wind remains\nchallenging, we do not consider it impossible. Further work is certainly needed, and results from\nMMS may serve as a valuable guide in this effort. Since a detailed discussion of this topic falls\nbeyond the scope of the present study, we would prefer not to include it in the manuscript.\nNevertheless, we sincerely appreciate the recommended papers, which provide additional useful\nmaterials to our discussion. Accordingly, we have cited De Marco et al. (2023) as ref. 8, Bruno et\nal. (2024) as ref. 9, and McManus et al. (2024) as ref. 10, and have introduced their findings in\nlines 36-40:\nTypically, electrons comprise the negatively charged species, while the positively charged species are more\ndiverse, often including hydrogen, helium, oxygen, and metal ions5-8. These ions exhibit distinct dynamics,\nsuch as undergoing differential acceleration during interactions with plasma waves9 and contributing\nunequally to the growth of instabilities10.\nMoreover, this point should be also added to the Introduction since the authors did not discuss any\nnumerical model neither observational results about the contribution of heavy ions, and in\nparticular alpha particles, to the cross-scale energy transfer. Despite the above mentioned works\nwhich used Parker Solar Probe and Solar Orbiter particle data, there are different numerical\napproaches that took into account the contribution of alpha particles, such as Ofman 2010,\nManeva et al. 2010, 2013, 2015, Perrone et al. 2011, 2013, Valentini et al. 2016).\nWe sincerely appreciate the reviewer for recommending the nice references. Indeed, these\nnumerical studies provide valuable context for our observations and help us better position our\nresults within the existing literature. Accordingly, we have cited Ofman (2010) as ref. 12, Perrone\net al. (2012) as ref. 13, Maneva et al. (2013, 2015) as ref. 14 and 15, and Valentini et al. (2016) as\nref. 16. Their key findings have been introduced in lines 49-54:\nHowever, several theoretical studies have indicated that minor ions may actively participate in cross-scale\nenergy transfer processes in plasmas. For instance, during interactions with plasma waves, minor ions exhibit\ndistinct responses compared to major species, resulting in velocity distribution functions (VDFs)\ncharacterized by different temperature, anisotropy, and drift speed9,12-15. The resulting differential VDFs may,\nin turn, serve as sources of free energy, potentially driving wave excitation at other scales16.\nAnother point is about some missing figures that can help the reader to understand better the\nresults and how they have been obtained. In particular, in my opinion the following two figures\nwould be added in the supplementary information: (1) the cross-wavelet analysis as mentioned at\npage 4, and (2) the 4 MMS signals for the wave packets as mentioned at page 6\nWe appreciate these comments. As suggested, Supplementary Fig. 4a and 4b now present the\ncross-wavelet analysis between the integrated power of the electrostatic waves and the electric\nfield of the EMIC wave. The results show a strong correlation between the two quantities (lines\n103-109). The four MMS observations of the electrostatic wave packets, including both the\ndynamic spectra of the electric field and the corresponding integrated power, are shown in\nSupplementary Fig. 2f. Lines 178-179 in the main text refer to this figure.\nVery minor points:\n- In fig 3f the growth rate is a blue curve, but in the text (pag 7 line 183) is referred as red curve\nThanks for identifying this mistake. It has been corrected. Please find lines 196-197:\nFig. 3f shows the obtained frequency (black curve) and growth rate (blue curve) in the rest frame of the\nspacecraft.\n- the arrows in fig 1h are not well visible.\nWe have enlarged the arrows. Hope they are now more visible. Thanks for the suggestion.\n- in supplementary information, left panels of fig.2 are the same of left panel of fig. 3 panels e and\ng.\nWe are sorry for the confusing presentation. The left panels of the original Supplementary Fig. 2\nwere indeed duplicated from the left panels of Fig. 3e and 3g to help illustrate the results shown in\nthe tables on the right side of the original Supplementary Fig. 2. However, to avoid potential\nconfusion, we have now removed these panels and moved the tables to Supplementary Table 1.\nTherefore, in my opinion, the manuscript is very interesting and deserve to be published but after\nadditional discussions and clarifications.\nOnce again, we would like to express our sincere gratitude to Reviewer #2 for the comprehensive\nreview and insightful comments, which have undoubtedly helped improve our manuscript. We\nhope that our revisions have adequately addressed these comments and clarified any ambiguities\npresent in the previous version.\nResponse to Reviewer #3\nThe paper provides direct observations of cross-scale energy transfer driven by cross-scale wave-\nparticle interaction using unique dataset from MMS spacecraft. The paper showed that the\ninterplay between hydrogen and helium ions with ion-scale waves can further excites electrostatic\nwaves at the smaller lower-hybrid scale. This topic is highly significant, as it highlights the non-\nnegligible role of multi-ion interactions in mediating energy transport across scales in space\nplasmas. However, further justification and clarification are needed before the manuscript can be\nconsidered for acceptance.\nWe sincerely thank Reviewer #3 for his/her time and effort in evaluating our manuscript, as well\nas for the constructive feedback provided. We have carefully considered the comments and revised\nthe manuscript accordingly. In particular, we conducted a parameter study to assess the effects of\nion composition, particle temperature, and the relative drift speed between helium and hydrogen\non the properties of the electrostatic waves near the lower-hybrid frequency. We have also\ndiscussed the modulation of O+ and He++ ions by the EMIC wave and included additional figures\nillustrating how the parameters used in our dispersion relation analysis are determined.\nFurthermore, we compared our findings with those of Khazanov et al. (2016) (thank you for\nrecommending this insightful paper) and discussed how our unique observations contribute new\nperspectives on the physics of cross-scale wave-particle interactions. We hope these revisions\nadequately address the reviewer’s concerns and help clarify the ambiguities present in the\nprevious version of the manuscript.\nPlease note that the numbering of supplementary figures may differ from that in the previous\nversion of the manuscript. Any such changes are noted in our response where relevant. The line\nnumbers referenced below correspond to the text marked with track changes.\nBefore addressing the detailed comments below, we would like to first clarify our treatment of\nelectron temperature, which is used in the theoretical analysis of the dispersion relation of the\nlower-hybrid electrostatic waves. In the previous version of the manuscript, the electron\ntemperature was estimated by fitting FPI-DES measurements. However, during this round of\nrevision, we realized that FPI-DES measurements in the low-energy channels may not be reliable\ndue to the spacecraft potential (~4 V) and photoelectron contamination. As a result, the previously\nadopted value of 10 eV may not accurately reflect the true electron temperature. Moreover, this\nmeasurement limitation may imply that the exact electron temperature cannot be determined with\nconfidence. Nevertheless, an analysis suggests that 10 eV remains a reasonable representative\nvalue. To see this, we first note that the total electron density is 1.4 cm−3, as determined from the\nupper-hybrid line. On the other hand, FPI-DES detects a partial density of approximately 0.2 cm−3\nabove 32.8 eV (the 6th energy channel), where the influence of spacecraft potential and\nphotoelectrons is minimal. A comparison of the two numbers indicates that the majority of\nelectrons have energies below 32.8 eV. Therefore, adopting 10 eV—roughly one-third of 32.8\neV—as a representative temperature may remain a reasonable approximation. Furthermore, we\nconducted a parameter study (see Supplementary Note 3), which demonstrates that the dispersion\nrelation of lower-hybrid electrostatic waves is not highly sensitive to variations in electron\ntemperature. For instance, the waves exhibit a substantial growth rate as long as the electron\ntemperature remains below 44 eV. Accordingly, the impact of uncertainty in the electron\ntemperature on our results is expected to be moderate, and our main conclusion—the EMIC wave-\ninduced hydrogen-helium relative drift can excite electrostatic waves at the lower-hybrid scales—\nstill holds. Thus, we continue to use 10 eV as the electron temperature in the theoretical analysis\npresented in this version of the manuscript. This issue and our treatment are now described in line\n184-196 of the Supplementary Information:\nDue to the spacecraft potential (~4 V) and photoelectron contamination47, FPI-DES measurements in the\nlow-energy channels may not be reliable for deriving the electron temperature. Nevertheless, we can still\nconstrain the electron temperature based on observations. First, we note that the total electron density is\n𝑁 =1.4 cm-3, as determined from the upper-hybrid line. Next, FPI-DES suggests a partial density of ~0.2\n𝑏𝑔\ncm-3 above 32.8 eV (the 6th energy channel of FPI-DES), where the effects of spacecraft potential and\nphotoelectrons are weak. A comparison of these two values indicates that the majority of electrons have\nenergies below 32.8 eV. Therefore, as a rough estimate, we adopt an electron temperature of 10 eV (i.e.,\nabout one-third of 32.8 eV). A parameter study presented in Supplementary Note 3 indicates that the\ndispersion relation of lower-hybrid electrostatic waves is not highly sensitive to electron temperature. For\ninstance, the waves maintain a sizeable growth rate as long as the electron temperature remains below 44 eV.\nTherefore, the impact of uncertainty in the electron temperature on our results is expected to be moderate.\nMajor comments:\nThe paper presents a compelling agreement between EMIC wave-induced hydrogen-helium ion\ncounter-drift and the observed arc structures in the energy-time spectrogram. However, the\nrelationship between the relative drift velocity and the amplitude of electrostatic waves remains\nunclear—particularly when comparing peaks 2 and 3 in the lower-frequency electrostatic wave\n(Figure 3d) with the corresponding l-component of the drift velocity (Figure 3a). This raises the\nquestion of whether additional factors such as plasma compositions or temperature may\nsignificantly influence wave growth.\nThank you very much for identifying this issue. As demonstrated in the parameter study presented\nin Supplementary Note 3, the growth of electrostatic waves is indeed influenced by several other\nparameters. To conduct this study, we first reproduced the dispersion relation derived from Eq. 7\nin the manuscript using the dispersion relation solver BO developed by Xie (2019, cited as ref. 44)\n(this is also requested by reviewer #4). The newly obtained dispersion relation closely resembles\nthat shown in Fig. 3f, thereby validating our approximate formulation in Eq. 7. The results are\nsummarized in Supplementary Fig. 5a and discussed in lines 199-217 in the Supplementary\nInformation:\nWe utilize the dispersion relation solver BO44 to validate the approximate dispersion relation Eq. 7 (see\nFig. 3f and 3h). The parameters for the higher- and lower-frequency electrostatic waves differ only in the\nrelative drift speed (164 km/s versus 171 km/s). Therefore, for simplicity, we do not perform calculations for\nthe two cases separately. Instead, we consider a representative case in which helium ions drift relative to\nhydrogen ions at the average speed of 167.5 km/s. All other parameters, including magnetic field strength,\nnumber density, and temperature, are the same as those listed in the Methods, subsection electrostatic waves.\nAdditionally, Doppler shift effects are not included in this calculation. (Hereinafter, this model is referred to\nas the standard model.)\nSupplementary Fig. 5a presents the results. The trends of both the frequency and growth rate curves closely\nresemble those in Fig. 3f (where the Doppler shift effect is weak). The wavenumber, frequency, and growth\nrate at the maximum growth are 0.22 km-1, 32.7 Hz, and 2.8 Hz, respectively. These values are slightly\ndifferent but still consistent with the values derived from Eq. 7 (e.g., 0.28 km-1, 40.7 Hz, and 1.4 Hz for the\nhigher-frequency electrostatic waves). This agreement indicates that our approximate dispersion relation Eq.\n7 captures the primary characteristics of the instability. Furthermore, it once again demonstrates that the\nEMIC wave-induced relative drift between hydrogen and helium ions provides free energy for the growth of\nelectrostatic waves near the lower-hybrid frequency (=34 Hz).\nUsing this dispersion relation solver, we investigated the influence of ion composition, the relative\ndrift speed between helium and hydrogen ions, the temperatures of helium, hydrogen, and\nelectrons, as well as the temperature anisotropy of helium ions. The detailed results are presented\nin lines 232-272 of the Supplementary Information and copied below. In summary, the inclusion of\noxygen ions does not significantly alter the dispersion relation. The frequency at which the\nmaximum growth rate occurs remains largely unchanged across these parameter variations, except\nin the case of electron temperature. The maximum growth rate decreases with decreasing helium\nabundance and relative drift speed, and with increasing helium, hydrogen, or electron temperature.\nNevertheless, as long as these parameters do not deviate substantially from the values used in the\nmain manuscript, the maximum growth rate remains sufficiently high to allow the electrostatic\nwaves to grow to an observable amplitude. More importantly, these results demonstrate that,\nwithin a reasonable parameter range, the helium-hydrogen relative drift can robustly excite\nelectrostatic waves consistent with those observed, thereby reinforcing our main findings.\nNevertheless, the effects of these parameters should not be overlooked, and they may explain the\nreviewer’s observation that the amplitude of the electrostatic waves is not one-to-one correlated\nwith the relative drift speed. A brief discussion on this point has been added in lines 216-220 in the\nmain text:\nA comparison between the electrostatic wave amplitude (Fig. 3c and 3d) and the helium-hydrogen relative\ndrift speed (Fig. 3a and 3b) reveals that the two are not one-to-one correlated. This mismatch suggests that\nadditional parameters, such as plasma composition and temperature, may influence wave growth (see\nSupplementary Note 3 for parameter studies detailing this influence). Future investigations that account for\nthe modulation of these parameters by EMIC waves, as well as the temporal variations induced by the\noscillating EMIC wave fields, may yield a more comprehensive understanding of the observed electrostatic\nwave amplitudes.\nThe results of the aforementioned parameter study are provided below for the reviewer’s\nreference:\nNext, we consider the effects of O+ ions, which are the most abundant minor species. Given that the EMIC\nwave-induced drift of O+ ions is rather weak (Methods, subsection low-energy ion dynamics), we assume\nthem to be stationary. Their abundance is taken from HPCA measurements, that is ~2.0% (accordingly, the\nabundance of H+ ions reduces to to 96.6%). The temperature is set to 3 eV. Supplementary Fig. 5c shows the\ndispersion relation for this case. The results closely resemble those of the standard model. At the maximum\ngrowth rate, the wavenumber, frequency, and growth rate are 0.19 km-1, 32.5 Hz, and 2.7 Hz, respectively.\nThese results indicate that O+ ions can be safely neglected in our analysis. (O+ ions are not considered in the\nrest of this note.)\nThe effects of helium ion abundance are also examined. Supplementary Fig. 5d presents the maximum\ngrowth rate (hereafter denoted as 𝛾 ) and the corresponding frequency (𝑓 ) as functions of helium ion\n𝑚 𝑚\nabundance. 𝑓 is relatively insensitive to the abundance, decreasing slightly from approximately 34 Hz to\n𝑚\n𝑚\nabundance and approaches zero as the abundance tends toward zero. However, it remains greater than half\nthe 𝛾 value in the standard model (i.e., 1.4 Hz, hereafter denoted as 𝛾 and regarded as a standard in the\n𝑚 𝑐\nfollowing comparison) as long as the abundance exceeds 0.36%. These results indicate that, provided the\nhelium ion abundance is not too low, the considered electrostatic waves can still grow to an observable\namplitude\nSupplementary Fig. 5e illustrates the influence of the relative drift speed 𝑢 between helium and hydrogen\nions. As 𝑢 increases from 90 km/s to 300 km/s, the corresponding frequency 𝑓 first rises to a peak of\n𝑚\n𝑚\nHowever, it remains above 𝛾 when 𝑢 decreases to 100 km/s. Notably, for 𝑢>110 km/s, 𝛾 exhibits little\n𝑐 𝑚\nsensitivity to further increases in u; for instance, it increases by only 0.1 Hz as u increases from 167.5 km/s to\n300 km/s.\nThe dependence on helium temperature 𝑇 is shown in Supplementary Fig. 5f. 𝑓 is relatively insensitive\nHe 𝑚\nto this parameter, increasing only slightly from 32.6 Hz to 34.4 Hz as 𝑇 increases from 0.1 to 60 eV. 𝛾\nHe 𝑚\ndecreases with increasing 𝑇 , but remains above 𝛾 as long as 𝑇 is below 19 eV. Supplementary Fig. 5g\nHe 𝑐 He\nshows the effects of hydrogen temperature 𝑇 . Similar to 𝑇 , 𝑓 is relatively insensitive to 𝑇 . 𝛾 also\nH He 𝑚 H 𝑚\ndecreases with increasing 𝑇 , but remains above 𝛾 as long as 𝑇 e is below 26 eV. Supplementary Fig. 5h\nH 𝑐 He\npresents 𝑓 and 𝛾 as functions of electron temperature 𝑇. 𝑓 initially increases to a peak of\n𝑚 𝑚 e 𝑚\napproximately 40 Hz and then decreases to 18.1 Hz as 𝑇 rises from 1 to 100 eV. 𝛾 remains around 2.8 Hz\ne 𝑚\nfor 𝑇<30, and subsequently decreases to 0.35 Hz as 𝑇 increases to 100 eV. It remains above 𝛾 for\ne e 𝑐\n𝑇<44 eV.\ne\nThe effects of helium ion temperature anisotropy are shown in Supplementary Fig. 5i. Both 𝑓 and 𝛾\n𝑚 𝑚\nare insensitive to this parameter. As the anisotropy varies over two orders of magnitude from 0.1 to 10, 𝑓\n𝑚\nchanges by less than 1.5%, and 𝛾 varies by no more than 20%.\n𝑚\nFurthermore, prior studies (e.g., Khazanov et al., 2016, doi:10.1002/2016JA022814) have reported\ncross-scale wave-particle interactions involving lower hybrid waves driven by ion polarization\ndrift in the presence of EMIC waves. The authors should cite this work and clarify how the current\nstudy offers new or substantially different insights.\nWe sincerely thank the reviewer for bringing this excellent work to our attention. The topic of this\npaper indeed overlaps with that of ours. However, due to limitations in the resolution of the Van\nAllen Probes data, the referenced paper was unfortunately unable to provide particle observations\nthat are essential for investigating the underlying physics. In contrast, our study presents the\nrequired particle measurements, which not only unambiguously confirm the role of minor ions in\nthis cross-scale wave-particle interaction but also offer new insight into the underlying\nmechanism: The excitation of lower-hybrid electrostatic waves by the EMIC wave is primarily\nmediated through its finite-frequency effect on ion motion, rather than through the induced ion\npolarization drift (at least for this event). To clarify this, we recall the motion of low-energy ions\nin EMIC wave fields (Eq. 1): 𝑉⃗ = 1 ( 𝐸⃗ 𝑤×𝐵⃗ 𝑏𝑔+ 1 𝜕𝐸⃗ 𝑤), where the first term in the\n𝑖 1−(𝜔/Ω𝑖 )2 𝐵\n𝑏\n2\n𝑔\n𝐵𝑏𝑔Ω𝑖 𝜕𝑡\nparentheses is the “𝐸×𝐵” drift and the second term represents the polarization drift, and the\n1\nprefactor , captures the finite-frequency effect of the EMIC wave. The counter-drift\n1−(𝜔/Ω𝑖 )2\nbetween helium and hydrogen ions primarily arises from this factor: it evaluates to 1.1 for\nhydrogen and −1.8 for helium, thereby causing the two ions to move in opposite directions and\nproducing a significant relative drift. Notably, this means that even the “𝐸×𝐵” drift term alone can\nlead to relative motion between hydrogen and helium ions, which could subsequently drive lower-\nhybrid wave growth.\nWe have added a brief discussion of this point, along with a citation to Khazanov et al. (2016;\ncited as ref. 31) in lines 231-242:\nFigure 4 summarizes the cross-scale wave-particle interaction studied here. Modulated by the ion-scale\nEMIC wave, hydrogen ions behave similarly to electrons and primarily follow the “𝐸×𝐵” drift, whereas\nhelium ions exhibit a more ion-like response, showing significant polarization drift in addition to the “𝐸×\n𝐵” drift. This polarization drift, as indicated by ref.31, can provide free energy for electrostatic waves near\n𝑓 . But more importantly, our observations and analysis reveal that the finite-frequency effect of the EMIC\n𝑙ℎ\nwave—through the factor [1−(𝜔/Ω)2]−1 in Eq. 1—can cause hydrogen and helium ions to move in\n𝑖\nopposite directions in the plane perpendicular to the magnetic field, creating a counter drift configuration.\nThis counter drift subsequently excites electrostatic waves near the lower-hybrid frequency via the ion-ion\ncross-field instability.\nTherefore, we respectfully suggest that our study offers novel observations and physical insights\nthat potentially advance our understanding of cross-scale wave-particle interactions.\nMinor comments:\n1. Given that O+ are often coexist with H+ and He+ in the magnetosphere, what is expected the\ndrift speed of O+ and how do they influence the generation of the lower hybrid electrostatic\nwaves? To what extent would the presence of O+ modify the wave frequency and growth rate\nprofiles?\nAs shown in the manuscript, the motion of low-energy ions in EMIC wave fields can be modeled\nas 𝑉⃗ = 1 ( 𝐸⃗ 𝑤×𝐵⃗ 𝑏𝑔+ 1 𝜕𝐸⃗ 𝑤) (Eq. 1 in our manuscript). For O+ ions, the prefactor\n𝑖 1−(𝜔/Ω𝑖 )2 𝐵\n𝑏\n2\n𝑔\n𝐵𝑏𝑔Ω𝑖 𝜕𝑡\n1\nis only −0.04 (for comparison, this prefactor for hydrogen and helium ions are 1.1 and\n1−(𝜔/Ω𝑖 )2\n−1.8, respectively), as the wave frequency (~0.25 Hz) is approximately five times the cyclotron\nfrequency of O+ (~0.049 Hz). Therefore, the EMIC wave-induced drift for O+ is rather weak,\nindicating O+ can be approximated as decoupled to the EMIC wave (this once again highlights the\nrole of the finite-frequency effect in EMIC wave modulation of low-energy ions). We now\ndiscussed this point in lines 353-356:\nIn the high-frequency limit, due to the prefactor 1/[1−(𝜔/Ω)2], the resulting velocity approaches zero,\nindicating wave-particle decoupling. This latter case applies particularly to O+ ions in our study, for which\n1/[1−(𝜔/Ω)2]=−0.04 (for comparison, this factor for hydrogen and helium ions are 1.1 and −1.8).\nAs detailed in our response to Major Comment #1, the presence of O+ does not significantly affect\nthe properties of the lower-hybrid electrostatic waves when its abundance is set to the value\nmeasured by HPCA. For instance, it only reduces the wavenumber, frequency, and growth rate at\nthe maximum growth rate by 14%, 0.6%, and 3.6%, respectively. The relevant results have been\nincluded in lines 232-240 of the Supplementary Information, which is attached to our response to\nMajor Comment #1.\n2. Line 350-351: should the ~99% abundance refer to hydrogen ions rather than helium ions?\nI commend that the authors provide the FPI-DES plus HPCA measurements in the supplemental\nmaterial to support the parameters used in estimating the wave growth, as well as the O+ energy-\ntime spectrogram mentioned in the above comment.\nThank you very much for identifying this mistake. It has been corrected. The revised lines 397-\n405 now provide the details of the particle parameters used in our dispersion relation analysis of\nthe lower-hybrid electrostatic waves:\nAll parameters are estimated from the observations. Ω is evaluated at 𝐵 =52 nT. 𝑣 is derived from\n𝑖 𝑏𝑔 𝑡ℎ,𝑖\ntemperatures estimated from MMS observations (Supplementary Note 2): electrons ~10 eV, hydrogen\n~3.3 eV, and helium ~3.8 eV. To calculate 𝜔 , the density of each species is required. However, both FPI\n𝑝,𝑖\nand HPCA slightly underestimate the density, as they observe particles only within a limited energy range\n(but the core population should have been observed, as the FPI and HPCA densities are close to 𝑁\n𝑏𝑔\nderived from the upper-hybrid line). Therefore, we estimate the densities of each species based on 𝑁 ,\n𝑏𝑔\nalong with species abundances adopted from HPCA observations: 98.6% for hydrogen and 1.4% for helium\nions. All these parameters are applied uniformly to both the higher- and lower-frequency electrostatic waves.\nAs suggested, we now present observations of these parameters in Supplementary Fig. 1. In\nparticular, Supplementary Fig. 1d shows the velocity distribution functions from which the\ntemperatures of hydrogen and helium ions are derived. Lines 159-196 in the Supplementary\nInformation provide a detailed description:\nA Maxwellian H+-He+-electron plasma is used to assess whether the EMIC wave-induced relative drift\nbetween H+ and He+ is unstable to electrostatic waves in the lower-hybrid frequency range. The parameters\nof this model are set according to observations. In this note, we show how temperatures of these particles are\nestimated.\nTo obtain a set of parameters representative of the overall conditions, we average the observations over the\nentire event, i.e., from 18:17:48 to 18:18:18 UT. This averaging is especially necessary for He+, as HPCA\nobservations suffer from low count statistics at any given time; only by averaging over a relatively long\nperiod can we obtain a robust velocity distribution function (VDF). However, the perpendicular bulk\noscillations induced by the EMIC wave would significantly broaden the average VDFs of H+ and He+ in the\nperpendicular plane, resulting in an apparently higher temperature than the actual one. To mitigate this effect,\nwe assume an isotropic VDF for each species in the dispersion relation analysis, and set the temperature as\nthat derived from the measured VDF in the parallel direction. A parameter study (see Supplementary Note 3)\nlater shows that the anisotropy of the VDFs has only a minor influence on the theoretical dispersion relation.\nSince FPI-DIS provides much better count statistics than HPCA and primarily detects H+ ions, we derive H+\ntemperature from it. The black crosses in the left panel of Supplementary Fig. 1d show the measured parallel\nVDFs. By fitting a Maxwellian distribution, we obtain a temperature of 3.3 eV. For He+, we use HPCA\nobservations. The black crosses in the middle panel of Supplementary Fig. 1d show the corresponding VDF,\nand a Maxwellian fit yields a temperature of 3.8 eV.\nDue to the spacecraft potential (~4 V) and photoelectron contamination47, FPI-DES measurements in the\nlow-energy channels may not be reliable for deriving the electron temperature. Nevertheless, we can still\nconstrain the electron temperature based on observations. First, we note that the total electron density is\n𝑁 =1.4 cm-3, as determined from the upper-hybrid line. Next, FPI-DES suggests a partial density of ~0.2\n𝑏𝑔\ncm-3 above 32.8 eV (the 6th energy channel of FPI-DES), where the effects of spacecraft potential and\nphotoelectrons are weak. A comparison of these two values indicates that the majority of electrons have\nenergies below 32.8 eV. Therefore, as a rough estimate, we adopt an electron temperature of 10 eV (i.e.,\nabout one-third of 32.8 eV). A parameter study presented in Supplementary Note 3 indicates that the\ndispersion relation of lower-hybrid electrostatic waves is not highly sensitive to electron temperature. For\ninstance, the waves maintain a sizeable growth rate as long as the electron temperature remains below 44 eV.\nTherefore, the impact of uncertainty in the electron temperature on our results is expected to be moderate.\nIon composition measured by HPCA is presented in Supplementary Fig. 1b. A summary of the\nobservations can be found in lines 292-293 in the main text:\nThe relative abundances in terms of number density of H+, He+, He++, and O+ are 95.5%, 1.4%, 1.1%, and\n2.0%, respectively, during our event (Supplementary Fig. 1b).\nThe number density derived from the upper-hybrid line, which is used to define the background\nnumber density 𝑁 , is shown in Supplementary Fig. 1a. (This figure was already included in the\n𝑏𝑔\nprevious version of the manuscript.).\nAs detailed in our response to the above comment, low-energy O+ ions are approximately\ndecoupled from the EMIC wave due to their low cyclotron frequency. We also did not identify\nany arc-like signatures representing their interaction with the EMIC wave in the FPI and HPCA\nobservations. Therefore, we do not show their energy-time spectrogram here. For completeness,\nwe note that HPCA also suggests the coexistence of He++ ions. However, we do not find any\nrelevant signatures either. (see Supplementary Fig. 4c for a comparison between FPI-DIS\nobservations and the predicted energy of He++ arcs). This may be due to the fact that the wave-\nparticle interaction dynamics considered here apply only to low-energy ions, as detailed in the\nmanuscript, whereas He++ ions, which presumably originate from the solar wind, are expected to\nbe relatively hot. Since He++ arcs do not appear in the observations, we did not consider them\nwhen investigating the growth of the electrostatic waves. A brief discussion of this point has been\nadded to lines 357-362:\nAnother commonly coexisting species is He++ ions. According to Eq. 6, these ions would be efficiently\nmodulated by the EMIC wave. However, no relevant signatures at the predicted energies are observed\n(Supplementary Fig. 4c), even though HPCA does indicate their presence in this event (albeit with the lowest\nabundance). As a result, these ions are also excluded from the analysis presented in the main text.\n3. Line 365: Please explicitly provide the value of the lower–frequency electrostatic wave\nfrequency in the rest frame of the plasma (i.e., without Doppler shift) at the end of this paragraph.\nThis information can now be found in lines 415-418:\nThe two speeds are very close, resulting in very similar frequency and growth rate profiles for the higher-\nand lower-frequency electrostatic waves in the rest frame of the plasma. For example, the frequencies at the\nmaximum growth rates in the rest frame of plasma are 40.7 Hz and 42.7 Hz for the higher- and lower-\nfrequency electrostatic waves, respectively.\nFor reference, the lower-hybrid frequency is about 34 Hz.\n4. Lines 231-233: The authors state that the proposed mechanism relies on two essential\nelements—EMIC waves and minor ions—which are said to exist almost ubiquitously in the\nmagnetosphere. This would imply that lower hybrid waves, EMIC waves, and the associated\nrelative ion drift should be commonly observed together. To support this claim, could the authors\nprovide at least one additional event, possibly in the supplemental material?\nThanks for this great suggestion! Supplementary Fig. 6 provides another example of such events.\nDuring this event, an EMIC wave with a frequency of ~0.11 Hz and nearly parallel propagation is\ndetected (panels a and b). Simultaneously, two groups of arc-like signatures appear in the energy-\ntime spectrograms of ions measured by FPI-DIS (panel c). We calculated the kinetic energies\ncorresponding to the EMIC wave-induced drift of hydrogen (H+) and helium (He+) ions, and the\nresults are overlaid in panel c. These theoretical predictions closely match the observed arc-like\nstructures, supporting our interpretation. Panel e presents the electric field power near the lower-\nhybrid frequency (~25.4 Hz), while panel d shows the integrated power in the 5-50 Hz range,\nencompassing the lower-hybrid frequency. Quasi-periodic enhancements, synchronized with the\narc-like signatures in panel c, are clearly observed in panels c and d, indicating coupling between\nthe EMIC wave and lower-hybrid-scale waves. Furthermore, panel f displays the ratio of magnetic\nto electric field power, normalized by the local Alfvén speed (~296 km/s). When enhancements in\nelectric field power occur, this ratio is around 100, highlighting the electrostatic nature of the\nwaves near the lower-hybrid frequency. This event further demonstrates the connection between\nlower-hybrid waves, EMIC waves, and the associated relative ion drift. Lines 254-258 in the main\ntext refer to this event:\nIn contrast, the mechanism presented here does not have such restrictions in principle, as both the two\nessential elements—EMIC waves (particularly hydrogen-band EMIC waves)24,25 and minor ions5,6,36,37—\nexist essentially everywhere in magnetospheres (see Supplementary Fig. 6 for another example of such\nevents).\n5. Lines 352-354: I found the calculation of the relative drift speed u somewhat unclear. The\nmanuscript states that u is determined at the time when the electrostatic wave amplitude peaks.\nHowever, there are multiple peaks—five for the higher-frequency and four for the lower-\nfrequency electrostatic waves—yet only a single value of u is provided for each case. Could the\nauthors clarify how u was selected in light of the multiple peaks? Additionally, would variations in\nthe relative drift speed at different peak times impact the wave frequency and growth rate profiles?\nHow is this approach consistent with the observed modulation of electrostatic wave frequency and\namplitude?\nWe sincerely apologize for the lack of clarity in our previous statements. The relative drift speed\n𝑢 is set as the average of the identified peaks, with the higher- and lower-frequency electrostatic\nwaves treated separately. This is now described more clearly in lines 406-410:\nThe relative drift speed 𝑢 is determined using Eq. 1 and the observed EMIC wave field. For both the\nhigher- and lower-frequency electrostatic waves, we first extract the values of 𝑢 at the local peaks of the\ncorresponding wave amplitudes (marked by the dashed lines in Fig. 3a-3d), and then set 𝑢 as the average of\nthe resulting values. The results are 𝑢=164 km/s (Fig. 3e) and 171 km/s (Fig. 3g) for the higher- and\nlower-frequency electrostatic waves, respectively.\nVariations in 𝑢 do affect the properties of the electrostatic waves, as detailed in our response to\nMajor Comment #1 regarding the parameter study presented in Supplementary Fig. 5. (To save\nspace, we do not repeat those details here.) However, as the reviewer correctly noted, there is no\nstrong one-to-one correspondence between the observed wave amplitude and the relative drift\nspeed, suggesting that other plasma parameters, such as temperature and helium ion abundance,\nalso play a role. Due to limitations in observational resolution and associated uncertainties, we are\nunable to examine their effects in detail based on the available data. Nevertheless, our theoretical\nevaluation using representative parameters support the main conclusion that the EMIC wave-\ninduced helium-hydrogen relative drift can excite electrostatic waves near the lower-hybrid\nfrequency.\nOnce again, we would like to express our sincere gratitude to Reviewer #3 for the comprehensive\nreview and insightful comments, which have undoubtedly helped improve our manuscript. We\nhope that our revisions have adequately addressed these comments and clarified any ambiguities\npresent in the previous version.\nResponse to Reviewer #4\nThe paper describes a case study which relies on 30 seconds of plasma and electromagnetic field\nmeasurements by a single MMS spacecraft. The authors conclude that this observation provides\ndirect experimental evidence for cross-scale energy transfer processes in plasmas with multiple\nion species. This conclusion is based on measurements of low-frequency waves, drifting hydrogen\nand helium ions, and Doppler shifted waves close to the lower hybrid frequency in the plasma\nframe. I can recommend the paper for publication only after a major revision is done, according to\nmy specific comments listed below.\nWe sincerely thank Reviewer #4 for his/her time and effort in evaluating our manuscript, as\nwell as for the constructive feedback provided. We have carefully considered the comments and\nrevised the manuscript accordingly. In particular, we have verified our approximate dispersion relation for\nthe electrostatic waves near the lower-hybrid frequency using a public dispersion relation solver.\nWe have also added four MMS observations of the electrostatic waves and refined the presentation\nas suggested. We hope these revisions adequately address the reviewer’s concerns and help clarify\nthe ambiguities present in the previous version of the manuscript.\nPlease note that the numbering of supplementary figures may differ from that in the previous\nversion of the manuscript. Any such changes are noted in our response where relevant. The line\nnumbers referenced below correspond to the text marked with track changes.\nBefore addressing the detailed comments below, we would like to first clarify our treatment of\nelectron temperature, which is used in the theoretical analysis of the dispersion relation of the\nlower-hybrid electrostatic waves. In the previous version of the manuscript, the electron\ntemperature was estimated by fitting FPI-DES measurements. However, during this round of\nrevision, we realized that FPI-DES measurements in the low-energy channels may not be reliable\ndue to the spacecraft potential (~4 V) and photoelectron contamination. As a result, the previously\nadopted value of 10 eV may not accurately reflect the true electron temperature. Moreover, this\nmeasurement limitation may imply that the exact electron temperature cannot be determined with\nconfidence. Nevertheless, an analysis suggests that 10 eV remains a reasonable representative\nvalue. To see this, we first note that the total electron density is 1.4 cm−3, as determined from the\nupper-hybrid line. On the other hand, FPI-DES detects a partial density of approximately 0.2 cm−3\nabove 32.8 eV (the 6th energy channel), where the influence of spacecraft potential and\nphotoelectrons is minimal. A comparison of the two numbers indicates that the majority of\nelectrons have energies below 32.8 eV. Therefore, adopting 10 eV—roughly one-third of 32.8\neV—as a representative temperature may remain a reasonable approximation. Furthermore, we\nconducted a parameter study (see Supplementary Note 3), which demonstrates that the dispersion\nrelation of lower-hybrid electrostatic waves is not highly sensitive to variations in electron\ntemperature. For instance, the waves exhibit a substantial growth rate as long as the electron\ntemperature remains below 44 eV. Accordingly, the impact of uncertainty in the electron\ntemperature on our results is expected to be moderate, and our main conclusion—the EMIC wave-\ninduced hydrogen-helium relative drift can excite electrostatic waves at the lower-hybrid scales—\nstill holds. Thus, we continue to use 10 eV as the electron temperature in the theoretical analysis\npresented in this version of the manuscript. This issue and our treatment are now described in line\n184-196 of the Supplementary Information:\nDue to the spacecraft potential (~4 V) and photoelectron contamination47, FPI-DES measurements in the\nlow-energy channels may not be reliable for deriving the electron temperature. Nevertheless, we can still\nconstrain the electron temperature based on observations. First, we note that the total electron density is\n𝑁 =1.4 cm-3, as determined from the upper-hybrid line. Next, FPI-DES suggests a partial density of ~0.2\n𝑏𝑔\ncm-3 above 32.8 eV (the 6th energy channel of FPI-DES), where the effects of spacecraft potential and\nphotoelectrons are weak. A comparison of these two values indicates that the majority of electrons have\nenergies below 32.8 eV. Therefore, as a rough estimate, we adopt an electron temperature of 10 eV (i.e.,\nabout one-third of 32.8 eV). A parameter study presented in Supplementary Note 3 indicates that the\ndispersion relation of lower-hybrid electrostatic waves is not highly sensitive to electron temperature. For\ninstance, the waves maintain a sizeable growth rate as long as the electron temperature remains below 44 eV.\nTherefore, the impact of uncertainty in the electron temperature on our results is expected to be moderate.\n1. 45 \"experimental evidence\" is probably a strong wording provided that a very limited set of\nsingle point measurements is used\nThanks a lot! Lines 55-56 have been revised as follows:\nHere, we present observational evidence confirming the non-negligible role for multiple-ion interactions in\ncross-scale energy transfer in plasmas.\n2. 59-62 It is rather shocking that, in a paper on cross-scale coupling, the multipoint capabilities of\nthe MMS mission are left unexplored.\nWe sincerely appreciate this comment. Supplementary Fig. 2f now presents the four MMS\nobservations of electrostatic waves near the lower-hybrid frequency. These observations are\ndiscussed in lines 178-183:\nWe first note that all four MMS spacecraft observed these wave packets (Supplementary Fig. 2f). However,\nupon zooming into each wave packet, the waveform shows no coherence between different MMS spacecraft.\nThis observation indicates that the wavelength of these waves is much smaller than MMS spacecraft\nseparation (~50 km in this event), while the scale of the excitation region is comparable to or larger than the\nseparation.\nRegarding the EMIC wave, the four MMS observations are nearly identical and do not provide\nsignificant additional information. Therefore, we do not include all four observations in the\nmanuscript.\n3. 80 The theory of propagation of electromagnetic waves in cold plasmas containing multiple ion\nspecies seems to be completely ignored by the authors. Multi-ion cross-over, cutoff and hybrid\nfrequencies define the wave mode structure and should be estimated in the context of the\npresented observations. The mode structure should be described and discussed in order to properly\ninterpret the measurements. Rigorously identifying the observation with the electromagnetic ion\ncyclotron (EMIC) mode would require a more thorough analysis and comparison with cold plasma\ntheory.\nThank you very much for this constructive comment. To illustrate the wave mode structure in a\nplasma containing multiple ion species, we performed a dispersion relation calculation using the\ndispersion relation solver BO, developed by Xie (2019, cited as ref. 44 and also used in response\nto Comment #8). This calculation includes five ion species, cold core H+, hot H+, He+, He++,\nand O+, with parameters adopted from MMS observations. The resulting dispersion relation,\nshown in Supplementary Fig. 3, exhibits the expected multiple band structures. For comparison, we also\nplot the observed EMIC wave in the same figure. The wave properties derived from observations\nalign well with the theoretical dispersion relation, supporting our identification of the observed\nwave as an EMIC wave. These results are discussed in lines 107-140 in the Supplementary\nInformation:\nWe further verify that the observed ~0.25 Hz wave corresponds to the EMIC mode by comparing its\nproperties with the theoretical dispersion relation of EMIC waves. To this end, we employ a bi-Maxwellian\nH+-He+-He++-O+-electron plasma. The densities of these species are set based on 𝑁 =1.4 cm-3\n𝑏𝑔\n(Supplementary Fig. 1a) and HPCA measurements of ion compositions (Supplementary Fig. 1b):\nelectrons~1.4 cm-3, H+~1.337 cm-3, He+~0.0196 cm-3, He++~0.0154 cm-3, and O+~0.028 cm-3. Previous\nstudies have shown that EMIC waves in the magnetosphere are mainly excited by anisotropic hot H+. To\naccount for this, we here divide the H+ ions into a cold core population and a hot population. The parameters\nof the latter are determined from FPI-DIS measurements above 2 keV. This energy threshold is chosen to\navoid contamination by He+, which primarily appears below 1 keV (Fig. 2c). It also eliminates the influence\nof low-energy hydrogen arcs. Supplementary Fig. 3a shows the FPI-DIS phase space densities (PSDs) above\n2 keV in the parallel and perpendicular directions. Evidently, the distribution is anisotropic, with the\nperpendicular PSDs exceeding the parallel PSDs. We fit a bi-Maxwellian distribution to the data and obtain a\nnumber density of 0.23 cm-3, a parallel temperature of 3148 eV, and a perpendicular temperature of 5506 eV.\nAccordingly, the number density of the cold core H+ population is set to 1.107 cm-3. The cold core H+, He+,\nHe++, O+, and electrons are also modeled as bi-Maxwellian. Their parallel temperature 𝑇 = 3 𝑇 and\n∥ 1+2𝛼 𝑒𝑓𝑓\n3𝛼\nperpendicular 𝑇 = 𝑇 are derived from the effective temperature 𝑇 and temperature anisotropy\n⊥ 1+2𝛼 𝑒𝑓𝑓 𝑒𝑓𝑓\n𝛼. For simplicity, 𝑇 is set to 10 eV for electrons and 3 eV for all ion species. The anisotropy 𝛼 is set to\n𝑒𝑓𝑓\nunity for electrons and to the values of 𝑇 /𝑇 obtained from HPCA measurements (Supplementary Fig. 1c)\n⊥ ∥\naveraged over the entire event for ions: H+ ~1.71, He+ ~1.05, He++ ~1.53, and O+ ~1.02. (A test actually\nindicates that the non-zero temperature and anisotropy of these particles have little impact on the resulting\ndispersion relation.)\nThis plasma model is then input into the dispersion relation solver BO44. Supplementary Fig. 3b shows the\nresulting wave frequency as a function of wavenumber. We also plot the observed dispersion relation of the\nEMIC wave as a black square: frequency~0.25 Hz and wavenumber~2.46×10-4 km-1 (=0.25 [Hz] / 1017\n[km/s]). The observation lies close to the theoretical dispersion relation (red curve), supporting our\nidentification of the ~0.25 Hz wave as an EMIC wave. This conclusion is further supported by the\ncorresponding growth rates. As shown in Supplementary Fig. 3c, the red branch exhibits positive growth\nrates near the wavenumber of the observed wave, indicating that this EMIC mode can indeed grow under the\ngiven plasma conditions.\nLines 91-94 in the main text refer to these supplementary materials:\nHence, the 0.25 Hz wave fits the classification reserved for electromagnetic ion cyclotron (EMIC) waves24,25,\na typical ion-scale wave mode. This conclusion is further supported by an analysis of the theoretical\ndispersion relation for EMIC waves, as presented in Supplementary Note 1 and Supplementary Fig. 3.\n4. 94 it is a rather weak evidence that the electrostatic waves are modulated based just on 3-5\nperiods of the low frequency electromagnetic wave\nThe correlation between the electrostatic wave packet structure and the EMIC wave field\ndiscussed here provides the first indication of coupling between the two wave modes. Subsequent\nparticle observations, which reveal the modulation of hydrogen and helium ions by the EMIC\nwave, along with a dispersion relation analysis demonstrating that the modulated particle\ndistributions are unstable to electrostatic waves like the ones observed, together establish the\nphysical link between the two waves and complete our proposed scenario. Our conclusion is thus\nsupported by multiple lines of consistent evidence, rather than wave field observations alone.\n5. 100 A single-mode quasiparallel wave should be nearly circularly polarized in the plasma\nframe, either in the left handed or in the right handed sense. However, the cold homogeneous\nplasma theory in fact predicts the presence of both left-and right-hand polarized modes in the\nfrequency range between the multi-ion L-mode cutoff and H+ cyclotron frequency. Hence, the\nobserved linear polarization can be still well consistent with the theory if both modes are present.\nWe sincerely appreciate the reviewer for this valuable insight. We fully agree that the\nsuperposition of left-hand and right-hand polarized waves could account for the observed\npolarization of the EMIC wave. Accordingly, we have incorporated this suggested mechanism into\nthe manuscript. However, we would like to remark that our analysis and main conclusions do not\nrely on the specific generation mechanism of the polarization of the EMIC wave. Rather, they are\nbased solely on the observed polarization at the time of detection, which has been determined\nfrom the measured EMIC wave fields. We included this discussion primarily to provide a more\ncomplete analysis; it does not serve as the basis for our subsequent results. Therefore, we moved\nthis discussion—along with an extension of our original scenario and a consideration of the\nmechanism proposed by the reviewer—to the Supplementary Information (lines 142-158):\nHowever, a discrepancy is noted in the polarization. The theoretical calculation predicts a left-hand circular\npolarization, whereas our analysis of the observed EMIC wave field suggests a linear polarization. Such a\ndiscrepancy is common in previous studies24,25 and may result from several factors. For instance, cold plasma\ntheory predicts the coexistence of both left-hand and right-hand polarized modes within the frequency range\nof interest. The superposition of these modes can lead to linearly polarized waves. Indeed, right-hand\npolarized waves near ion cyclotron frequencies are possible in the magnetosphere. For example, the full-\nwave ray tracing simulations by ref.45 suggest that a reversal from left-hand to right-hand polarization may\noccur at the crossover frequency as EMIC waves propagate through a multi-ion, inhomogeneous\nmagnetosphere, providing a mechanism for right-hand polarized waves near ion cyclotron frequencies.\nPropagation in the compressed dayside outer magnetosphere may also directly cause mode conversion from\nleft-hand to linearly polarized waves at the ion-ion hybrid resonance46. At present, the dominant mechanism\nresponsible for the observed wave polarization remains unclear. Nevertheless, we note that our analysis and\nconclusions do not rely on the specific generation mechanism of the polarization. They depend only on the\nobserved polarization at the time of detection, which has been robustly determined from the measured\nEMIC wave fields.\n6. 102, 103 wave propagation in the inhomogeneous, hot plasma is mentioned as a possible cause\nof the observed linear polarization. This needs to be explained. Mechanisms which would be\nresponsible for it should be described.\nThank you! We have expanded our discussion in lines 142-158 of the Supplementary Information.\nA copy of the revised text is included in the above response.\n7. 342-343, 351 the abundance of helium ions~99% contradicts the statement that hydrogen ions\ndominate the mass density\nSorry for this mistake. Lines 403-404 have been corrected:\nWe estimate the densities of each species based on 𝑁 , along with species abundances adopted from HPCA\n𝑏𝑔\nobservations: 98.6% for hydrogen and 1.4% for helium ions.\n8. 344 The approximate dispersion relation 7 should be verified with publicly accessible numerical\ndispersion solvers in multicomponent plasmas like WHAMP\nWe sincerely appreciate the valuable suggestion. We have now verified Eq. 7and our results using\nthe dispersion relation solver BO, developed by Xie (2019, cited as Ref. 44). (If we understand\ncorrectly, WHAMP does not support velocity distribution functions with perpendicular drift, and\nthus it was not used in this analysis.) The results, presented in Supplementary Fig. 5a, are\nconsistent with the dispersion relation derived from Eq. 7 (Fig. 3f and 3h). Supplementary Note 3\n(see lines 198-217 in the Supplementary Information) provides a detailed description of the\nsettings and results:\nWe utilize the dispersion relation solver BO44 to validate the approximate dispersion relation Eq. 7 (see\nFig. 3f and 3h). The parameters for the higher- and lower-frequency electrostatic waves differ only in the\nrelative drift speed (164 km/s versus 171 km/s). Therefore, for simplicity, we do not perform calculations for\nthe two cases separately. Instead, we consider a representative case in which helium ions drift relative to\nhydrogen ions at the average speed of 167.5 km/s. All other parameters, including magnetic field strength,\nnumber density, and temperature, are the same as those listed in the Methods, subsection electrostatic waves.\nAdditionally, Doppler shift effects are not included in this calculation.\nSupplementary Fig. 5a presents the result. The trends of both the frequency and growth rate curves closely\nresemble those in Fig. 3f (where the Doppler shift effect is weak). The wavenumber, frequency, and growth\nrate at the maximum growth are 0.22 km-1, 32.7 Hz, and 2.8 Hz, respectively. These values are slightly\ndifferent but still consistent with the values derived from Eq. 7 (e.g., 0.28 km-1, 40.7 Hz, and 1.4 Hz for the\nhigher-frequency electrostatic waves). This agreement indicates that our approximate dispersion relation\nEq. 7 captures the primary characteristics of the instability. Furthermore, it once again demonstrates that the\nEMIC wave-induced relative drift between hydrogen and helium ions provides free energy for the growth of\nelectrostatic waves near the lower-hybrid frequency (=34 Hz).\nOnce again, we would like to express our sincere gratitude to Reviewer #4 for the comprehensive\nreview and insightful comments, which have undoubtedly helped improve our manuscript. We\nhope that our revisions have adequately addressed these comments and clarified any ambiguities\npresent in the previous version.\nResponse to Reviewer #1\nThe authors have performed significant revisions and additional analysis which is placed into\nsupplementary information as requested by this reviewer. The authors also addressed the points of\nthe other reviewers. I am happy with the revised version and recommend the manuscript for\npublication in Nature Communications after the following minor correction: the reference number\n4 and 20 are the same, they are both by the same first author (Nykyri) but the other one should be\na JGR-Space Physics paper focusing on electron heating, the other is an AGU monograph-chapter.\nWe sincerely appreciate Reviewer #1 for his/her continued efforts in reviewing our manuscript. In\nresponse to the remaining comment, we have corrected ref. 20, which now refers to the JGR-\nSpace Physics paper, while ref. 4 refers to the AGU monograph chapter. We thank the reviewer for\nidentifying this mistake!\nResponse to Reviewer #2\nIn my opinion, the revisions made to the manuscript are satisfactory. The additional discussions\nand clarifications provided by the authors significantly enhance the reader's understanding of the\nstudy's findings and contribute to placing the results within the appropriate scientific context.\nTherefore, the revised manuscript is now suitable for publication.\nAs a final suggestion, I recommend including the cone of influence in the frequency-time\nspectrograms presented in the Supplementary Figures. This addition would clarify the regions\nwhere wavelet coefficients are affected by edge effects. In particular, the red areas at the edges of\npanel (d) in Figure S2 appear to be non-physical and could be misleading without such an\nindication.\nWe sincerely appreciate Reviewer #2 for his/her continued efforts in reviewing our manuscript. In\nresponse to the remaining comment, we have added the cone of influence as shaded areas in the\nspectrograms of Fig. 1h, Supplementary Figs. 3a–c, and 7e–f, to indicate where edge effects are\nsignificant. In particular, one can see that the high-value areas in Supplementary Fig. 3a\n(originally Supplementary Fig. 2d) lie within the cone of influence, indicating they are non-\nphysical, as pointed out by the reviewer. We thank the reviewer for this great suggestion!\nResponse to Reviewer #3\nThe authors have thoroughly addressed my concerns, and I am pleased to recommend this\nmanuscript for publication.\nWe sincerely appreciate Reviewer #3 for his/her continued efforts in reviewing our manuscript.\nResponse to Reviewer #4\nI appreciate the work of the authors on the major revision of this manuscript. They satisfactorily\nanswered all my questions and comments that I raised in my first review. I therefore recommend\nthis revised version for publication. I have two minor follow-up comments that the authors may\nwant to consider.\nWe sincerely appreciate Reviewer #4 for his/her continued efforts in reviewing our manuscript and\nthank for the feedback. We have revised the manuscript accordingly, as detailed in our following\nresponses. Please note that the line numbers refer to the change-tracked manuscript.\n1. While the authors did plausibly respond to my expressive comment concerning the unexplored\nmultipoint capabilities of the MMS mission by adding a reference to the Supplementary Figure 2f,\nI still feel that more details might improve the quality of the paper. For example, showing (perhaps\nin an additional Supplementary Figure) how the correlation of electrostatic power in the two bands\ndepends on the separation vector of the 6 spacecraft pairs (similarly as in\ndoi:10.1029/2002GL016178) might show some degree of organization along a preferred direction\nand bring additional insight into these cross-scale processes. Also, it might be useful to explicitly\nshow the (expected) similarity of the EMIC wave observations on the 4 spacecraft in a\nSupplementary Figure and to mention it very briefly in the main text.\nNow, Supplementary Fig. 2d shows the GSE-x components of the magnetic field measured by the\nfour MMS spacecraft. It illustrates the similarity of the EMIC wave observations across the four\nspacecraft. We have mentioned this point in lines 112-113 of the main manuscript:\nGiven the similarity of the EMIC wave fields across the four MMS spacecraft\n(Supplementary Fig. 2d)…\nWe also show the suggested correlation analysis of the lower-hybrid electrostatic waves in\nSupplementary Fig. 3d. The left sub-panel shows the correlation coefficients of the electrostatic\npower observed by different MMS pairs, as a function of the perpendicular distances between the\ncorresponding spacecraft. The results show a clear decreasing trend with increasing distances for\nboth the lower and higher-frequency band waves, aligning with our expectations. The right sub-\npanel shows the correlation coefficients as a function of parallel distances. No clear trend is\nidentified, but this may be due to the fact that the separations of the MMS spacecraft in the\nparallel direction (0-15 km) are not large in this event (for comparison, the perpendicular\nseparations vary from 20 to 60 km).\n2. Adding the results of the SVD analysis to the Supplementary material certainly was a\nreasonable answer to a comment of another reviewer but it generated a minor referencing\ninaccuracy. Ellipticity in doi:10.1029/2000RS002523 is always positive. A reference for the signed\nSVD ellipticity, which is used in Supplementary Figure 2c might rather be\ndoi:10.1029/2001JA000146.\nThanks for pointing out this issue. We have corrected ref. 44 accordingly."}]

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