Spatial Evolution Characteristics of Plasmapause Surface Wave During a Geomagnetic Storm on 16 July 2017

Boundary dynamics are crucial for the transport of energy, mass, and momentum in geospace. The recently discovered plasmapause surface wave (PSW) plays a key role in the inner magnetosphere dynamics. However, a comprehensive investigation of spatial variations of the PSW remains absent. In this study, we elucidate the spatial characteristics of a PSW through observations from multiple spacecrafts in the magnetosphere. Following the initiation of the PSW, quasi‐periodic injections of energetic ions, rather than electrons, are suggested to serve as energy source of the PSW. Based on the distinct wave and particle signatures, we categorize the PSW into four regions: seed region, growth region, stabilization region and decay region, spanning from nightside to afternoon plasmapause. These findings advance our understanding of universal boundary dynamics and contribute to a deeper comprehension of the pivotal roles of surface waves in the energy couplings within the magnetosphere‐plasmasphere‐ionosphere system.

A special type of auroral configuration termed giant undulations (GU) or sawtooth aurora, has been noticed on the equatorward boundary of the duskside diffuse aurora (e.g., Baishev et al., 1997;Henderson et al., 2010;Kelley, 1986;Lewis et al., 2015;Lui et al., 1982;Y. Zhang et al., 2005).These were suspected to be a visual presentation of the surface wave traveling along the inner edge of plasma sheet, mostly because of their conjugate location with the plasmapause (Lui et al., 1982).Recently, conclusive correlation between the giant undulations (GUs) and PSW was confirmed by He et al. (2020), demonstrating GUs are the optical atmospheric manifestation of the PSW.This has prompted investigations on the statistical characteristics of the PSW (Feng et al., 2023;Zhou et al., 2021Zhou et al., , 2022)).
Nevertheless, many pivotal questions remain regarding the excitation, evolution, frequency selection, space weather effects, and wave-particle interactions of the PSW.Previous research has suggested that MSE originating from the dayside magnetopause with peak frequency of 1-2 mHz can naturally transport tailward along the magnetopause surface, possibly seeding fluctuations which subsequently grow, coalesce and diffuse via the Kelvin-Helmholtz (K-H) instabilities in the flank sectors despite not occurring at the dominant growth frequency of the K-H instability (Archer et al., 2021;Hartinger et al., 2015;Hasegawa et al., 2009).On the plasmapause, however, the spatial evolution pattern of the PSW remains unsolved, neither through in-situ observation nor numerical simulation.By revisiting the PSW event on 16 July 2017, confirmed by He et al. (2020), in this letter, we aim to elucidate the spatial evolution characteristics of the PSW along the duskside plasmapause by in-situ observations from multiple satellites.
The ion velocity was calculated by V = E × B/B 2 .Note that, the electric field component along the spin axis was calculated by reasonably assuming E B = 0. ULF waves are usually analyzed in a field-aligned (FA) coordinate system (He et al., 2020;Zhou et al., 2023) and a 45-min moving-average was used to define these background fields, which were subtracted to detrend the data.Normalized power spectra of perturbations were obtained via the FFT analysis.Electron densities could not be directly measured but were derived from other measurements.
The first method relied on the upper hybrid resonance frequency obtained from electric field spectrograms (e.g., the High Frequency Analyzer (HFA) onboard ERG (Kumamoto et al., 2018) and the EMFISIS onboard VAP (Kurth et al., 2015)).The second method (McFadden, Carlson, Larson, Bonnell, et al., 2008) employed the spacecraft potential and electron thermal velocity (e.g., EFI and ESA onboard THEMIS).The auroral disk images were acquired in N2 Lyman-Birge-Hopfield (LBH) band from the SSUSI (Paxton et al., 2002) onboard DMSP satellites.1-minute resolution solar wind data was obtained from the Wind satellite (R. P. Lin et al., 1995) that has been time-shifted to Earth's bow shock nose based on the OMNI database, as shown in Figure 1a-1f.
According to the auroral images of He et al. (2020), this PSW event was possibly initiated between 11:15 and 11:45 UT and ended at ∼15:10 UT.Magnetospheric satellites trajectories and T96-projected (Tsyganenko & Stern, 1996) aurora image with GU (GUs) were presented in Figure 1g, showing an excellent coverage in the vicinity of the dusk sector plasmapause (dashed line) between 13:30 and 15:00 UT.The projected GUs appeared to be the sawtooth inner boundary near the dusk-sector plasmapause, as marked by the black solid ellipse in Figure 1g.The period marked by the gray region in Figures 1a-1f corresponded to the prolonged main phase of a medium storm with a minimum SYM-H index of 65 nT and multiple peaks of the substorm.Four satellites (THEMIS-A, THEMIS-E, VAP-A, and VAP-B) were traveling earthward toward the plasmapause, whereas ERG crossed the plasmapause as it traveled toward apogee.The MMS satellites were moving earthward from magnetotail plasmasheet to inner magnetosphere in the post-midnight sector.

Overview of the PSW's Spatial Evolution
All the satellites approaching the plasmapause observed similar quasi-periodic disturbances with frequency of 0.5-2.5 mHz in magnetic fields, ion velocities, electron densities, and energetic particles, as shown in Figure 2.During this period, the AE index showed multiple peaks, and MMS-1 observed the radial and azimuthal ions velocity perturbations (Figure 2c) and the recurrent enhancement of 0.1-10 keV energetic protons (Figure 2d and Figure S1a in Supporting Information S1), possibly suggestive of quasi-periodic injections of energetic protons.Meanwhile, the injection may disturb surrounding magnetic field components in Figure 2b.
In the post-dusk sector, ERG crossed the sharp plasmapause at ∼14:09 UT, detecting the greatly earthward intensification of detrended (Figure 2f) or raw ions velocity, which suggests that the local plasmapause surface was undergoing a huge compression possibly by substorm ring current injections.Thus, ERG temporarily pierced into the magnetosphere, encountering the conical energetic electrons distribution in advance (14:05-14:11 UT).
Prior to it, a large negative dent appeared in detrended (Figure 2e) or raw field-aligned magnetic field, also  consistent with the PP compression.Sequentially, the plasmapause recovered outward and covered ERG again, leading to an electron density peak accompanied by the lack of hot electrons during 14:11-14:13 UT.Finally, ERG entirely soared into the hot magnetosphere.The azimuthal magnetic field standing for toroidal mode fluctuated at 0.9-mHz frequency (Figure 4c) regardless of its relatively weak amplitude, which could seemingly provide seed disturbances for the excitement of the PSW by the aid of the local plasmapause compression (Hasegawa et al., 2009).Besides, ERG just crossed an initial (earliest MLT) small sawtooth of GUs at ∼14:10 UT (Figure 1g), also demonstrating the incipient location of the PSW.Accordingly, this post-dusk plasmapause is tagged as "seed region" of the PSW.
When approaching the (pre-)dusk plasmapause from 2 R E away (13:50-15:00 UT), THEMIS-E traversed multiple sawtooth of GUs in Figure 1g and THEMIS-E/A detected dominant poloidal wave (B r V r ) with period of ∼15 min and medium compressional poloidal mode (B p V r ) with a longer period in Figures 2h-2m.Correspondingly, electrons energy fluxes in Figures 2j and 2m displayed an alternative distribution of cold and hot plasmas, mostly modulated by powerful poloidal waves.These features confirm the PSW existing near the (pre-) dusk plasmapause with amplitudes scale of 1-2 R E (He et al., 2020;Zhou et al., 2022).Plasmaspheric electron density (white curves) disturbed weakly in a random phase relationship with the energy fluxes of energetic electron.This kind of weak disturbance and random phase persist when THEMIS-E/A traveled closer to the plasmapause.Thus, the effect of satellite's radial distance (<2 R E ) to the plasmapause could be neglected.Instead, this indicates that the PSW was azimuthally passing through a "growth region," not developed enough to regularly and efficiently modulate the plasmaspheric cold electron density.Further, since THEMIS-A was located at the same L-shell but earlier MLT than THEMIS-E, the PSW captured by THEMIS-A should develop better, consistent with more intense magnetic and velocity fields perturbations in Figures 2k and 2l and more distinctly oscillating electron energy flux in Figure 2m.
As the PSW propagated sunward/westward, VAP-A detected the ∼15-min periodic oscillation of magnetic and velocity fields in all directions as shown in Figures 2n and 2o, indicating that the PSW on the afternoon plasmapause manifested a coupled poloidal, toroidal, and compressional poloidal mode (Archer et al., 2019;He et al., 2020;Southwood & Hughes, 1983).Driven by this well-developed PSW, the energetic electrons as well as plasmaspheric cold electron density in Figure 2p both presented the most prominent periodic modulation with the same frequency.In contrast with "growth region," the stable in-phase relationship among velocity valley, cold electron density trough, and peak of energetic electrons by VAP-A directly demonstrated the stable undulant plasmapause oscillations.Therefore, we reasonably identify the afternoon plasmapause as "stabilization region" of the PSW mainly based on wave ingredient and phase correlation described above.
When approaching closer to the noon, VAP-B traced signals of the PSW decaying including localized magnetic (B p , B r ) and velocity fields disturbances and thus the sporadic regulation of hot electrons and cold electron density in Figures 2q-2s.Notably, during these intermittent bursts of hot electrons, such as around 13:47, 14:06, 14:13, and 14:53 UT, a similar in-phase pattern persisted locally.These observations evidence the status of rarefied plasmapause oscillations or waning PSWs in the post-noon plasmapause, which we refer to as "decay region."

Viewing the PSW's Spatial Evolution in a Particle Perspective
Figure 3 details all detectable particles species including electrons, protons, oxygen, and helium ions to better trace the PSW's spatial evolution from a particle perspective.For substorm driver of the PSW, both 0.1-10 keV energetic protons and oxygen ions observed in the near magnetotail in Figures 3b and 3c and Figure S1 in Supporting Information S1 presented concurrently intensified fluxes with period of 10-20 min, which did not appear in energetic electrons and helium ions in Figures 3a and 3d.Energetic protons and oxygen ions injections carried stronger periodical dynamic pressures and could more efficiently and recurrently affect the plasmapause, further drifting westward to oscillate the sharp plasmapause to excite the duskside PSW.Thus, periodically substorm-injected energetic ions including protons and oxygen ions rather than electrons are suggested to drive the PSW.
At "seed region" and "growth region" of the PSW (Figures 3e-3l), the plasmapause oscillation was evident in energetic electron but totally obscure in protons, oxygen, and helium ions energy spectrograms.Note there is just one oscillation for the "seed region."The detrended plasmaspheric electron densities in Figures 3i and 3k clearly presented an erratic phase relation with energetic electron energy fluxes.These particles signatures further confirm that the PSW at the two regions was not fully developed to regulate massive cold electrons and heavy energetic ions regularly and efficiently.At "stabilization region," however, the PSW was completely developed, periodically modulating energetic electrons in Figure 3m, as well as plasmaspheric cold electrons density and heavy energetic protons, oxygen and even helium ions in Figures 3n-3p.At earlier MLT, the PSW began to decay, only leaving sporadic disturbances yet still visible in all electrons and ions parameters, as shown in Figures 3q-3t.

Frequency Variability and Wave Mode Transition of the PSW
Figure 4 presents normalized power spectra mainly in the dominant PSW frequency range of 0.6-2 mHz of periodically disturbed magnetic and velocity fields at four regions of the PSW.This frequency range is just a rough estimation based on previous research (e.g., Feng et al., 2023;Hao et al., 2023;He et al., 2020;Henderson et al., 2010) and particles modulation frequency herein.For the driving frequency, periodic substorm injections

Geophysical Research Letters
10.1029/2024GL109371 disturbed surrounding magnetic field in the near magnetotail, especially in poloidal waves (B r V r ) with primary ∼0.7 mHz and secondary ∼2 mHz frequency peaks in Figure 4a.
The PSW also appeared to undergo a four-stage spatial transition in terms of wave modes along the sharp plasmapause.It began as a ∼0.9-mHz seed fluctuation of Ba (Figure 4c) accompanied by the significant compressional signature (B p V r in Figures 2e and 2f) at "seed region."Subsequently, it evolved into a dominant ∼1-1.1-mHz(B r ) poloidal wave at "growth region" (Figures 4e-4h).Here the power spectra with frequency above 0.5 mHz are reliable because the detrending process by 45-min moving-average will cause a fake power spectral peak around frequency of 0.4 mHz.Hence, compressional wave (B p ) displayed no power peak within the PSW's frequency of 0.6-2 mHz, which did not constitute an ingredient of the PSW.With propagating further sunward/westward, it stabilized as a ∼1.3-mHz wave (V r ) with mixed components, including prominent poloidal and compressional poloidal waves, and medium toroidal wave at "stabilization region" (Figures 4i and 4j).
Recalling the different particles distribution at "growth region" and "stabilization region," we may infer the powerful compressional poloidal (poloidal) wave of the PSW is crucial on periodically regulating cold electron density and all kind of ions (energetic electron) (He et al., 2020).Eventually, it decayed into a composite wave which was equally dominated by a ∼1.5-mHz (V a ) toroidal wave and an unstable poloidal wave, and also supplemented by localized compressional feature at "decay region."The frequency split (V r ) and spread (B r ) of poloidal wave in Figure 4k further show the PSW decayed to be localized and unstable.Consideration of the frequencies of dominant components concentrating on a small range but offsetting slightly within it (Figures 4e-4j), we roughly focused on the cross-phase spectra within 0.6-2 mHz in Figure S2 in Supporting Information S1.
Red and blue regions within this frequency range suggest that only the poloidal waves of the PSW at "growth" region generally established standing mode structure, while at "stabilization" region the PSW displayed standing mode signatures in all the poloidal, compressional poloidal and toroidal components.
In addition to the transition in wave modes, it is noteworthy that the PSW displays a consistently increasing frequency variation in correspondence with its spatial evolution, that is, ∼0.7 mHz (B r V r ; MMS-1), ∼0.9 mHz (B a ; ERG), ∼1 mHz (B r ; THEMIS-E), ∼1.1 mHz (B r ; THEMIS-A), ∼1.3 mHz (V r ; VAP-A), and ∼1.5 mHz (V a ; VAP-B) along the midnight-dusk-afternoon plasmapause boundary.This intriguing phenomenon likely corresponds well with the presence of waves propagating along increasingly stretched magnetic field lines from the afternoon to the midnight plasmapause region, as documented in previous studies (e.g., James et al., 2013;Samson et al., 1992;Yeoman et al., 2010).Noteworthy, other ULF waves may complicate the PSW frequency and cause frequency uncertainty to some extent in Figure 4, such as the ULF waves generated by the feedback instability driven by the electric field in the ionosphere (Streltsov & Mishin, 2020) and the spatially localized enhanced ULF waves in the plasmaspheric plume (Sandhu et al., 2021).Actually, the frequency variations discussed here just reflect a possible and plausible tendency based on the center frequencies of their individually dominant and clear components.Regardless of it, these periodic disturbances all have the dominant ∼0.5-2 mHz frequency peaks and do display varying components and frequencies along the four PSW regions.

Summary and Conclusion
In this letter, we performed the comprehensive analysis of spatial evolution characteristics of the PSW, exactly recognizing the source driving the PSW and identifying a four-stage spatial evolution of the PSW, as summarized below: 1.The periodic injection of energetic protons and oxygen ions, with energy ranging from 0.1 to 10 keV, is suggested to repeatedly affect the sharp plasmapause, leading to the excitation of the PSW.This standpoint is generally consistent with the concurrent quasi-periodic disturbances in energetic protons and oxygen ions fluxes and multiple peaks in the AE index, as well as the disturbed poloidal waves in the near magnetotail.
While previous studies have suggested the PSW likely to be excited by energetic particle injections during substorms (Hao et al., 2023;He et al., 2020;Zhou et al., 2021), we further recognized the particle species responsible for this phenomenon by simultaneously monitoring magnetotail conditions and the duskside PSW. 2. The "seed region" of the PSW is characterized by a weaker seed fluctuation of Ba component accompanied by a strong compression character on the plasmapause.This presumably is in accordance with that compressional and/or transverse magnetic fluctuations seen in the dayside low-latitude boundary layer most likely serve as seed perturbations for the excitation of the K-H waves on the flank magnetopause, albeit in the opposite propagation direction (Hasegawa et al., 2009).
3. We define the "growth region" by the dominant poloidal standing wave and the periodic modulation of energetic electron energy flux, as well as the irregular weak disturbance of cold electron density and no perturbation on heavy energetic ions.At "stabilization region", however, the fully developed PSW manifests as a mixed wave of prominent poloidal and compressional poloidal waves, and medium toroidal waves, all exhibiting the signature of standing mode.This PSW can periodically modulate energetic electrons, plasmaspheric cold electrons density and heavy energetic protons, oxygen and even helium ions.By comparison, we might obtain that the powerful compressional poloidal (poloidal) standing wave of the PSW is crucial on periodically regulating cold electron density and all kind of ions (energetic electron).4. The PSW in the "decay region" takes on the form of a composite wave equally dominated by a toroidal wave and an unstable poloidal wave, and also supplemented by localized compressional feature, only leaving sporadic disturbances on the plasmapause yet still visible in energetic electrons, cold plasmaspheric electrons and heavy energetic ions.The rarefaction of the PSW can be largely attributed to the reduced pressure of energetic ring current ions near the afternoon plasmapause (e.g., Daglis et al., 1999;Wei et al., 2019), as suggested by sporadic compressional and increasing toroidal components.
The MSE and PSW usually require multiple satellites near the boundary and are obscured by the temporal and special effect.Herein, this PSW event on 16 July 2017 is an excellent candidate given that there were five magnetosphere satellites near the dusk plasmapause during 13:30-15:00 UT and the long-lasting GUs/PSW from 11:15 UT to 15:10 UT were continuously imaged by DMSP satellites at conjugate dusk ionosphere.We focus on the PSW detected by various satellites all at 13:30-15:00 UT, during which the GUs are evident and stable, to weaken the temporal effect of the PSW and finally succeed in identifying spacial evolution signature of the PSW.More similar conjugate observations, combined with global hybrid model and theoretical numerical analysis, are required to generalize the four-region evolution pattern of the PSW and provide physical mechanism behind it.

Figure 1 .
Figure 1.Solar wind parameters and satellites' trajectories on 16 July 2017.(a-f) IMF, solar wind proton density, velocity, dynamic pressure, AE and SYM-H indices.(g) Satellites' trajectories during 13:30-15:00 UT and a southern aurora image shot by Defense Meteorological Satellite Program F17 at ∼14:37 UT are projected on the SM equator plane by using the T96 model.The closed circles in the spacecrafts trajectories indicate temporal intervals of 0.5 hr with their beginning times shown.The investigated period is highlighted by the gray shaded rectangle.Two thick dashed curves denote the empirically modeled MP(Shue et al., 1998) and PP(He et al., 2017) inputted by the averaged solar wind and geomagnetic variables during the same interval.A black solid ellipse marks the projected giant undulations region.

Figure 2 .
Figure 2. Overview of the time series data measured by six spacecrafts.(a) AE index; (b-d) magnetic field, perpendicular velocity disturbances in the FA coordinate, and energy spectrogram of protons by MMS-1; (e-g) magnetic field, perpendicular velocity disturbances, and energy spectrogram of electrons by ERG; (h-s) the same parameters as panels (e-g) but by THE, THA, VAP-A, and VAP-B probes, respectively.The thick white curves superimposed on energy spectrograms represent the plasmaspheric electron density.Subscript: p-parallel; r-radial; a-azimuthal.

Figure 3 .
Figure3.Evolution of particles signatures associated with the plasmapause surface wave around the PP surface.(a-d) Energy spectrograms of electrons, protons, oxygen ions (O + ) and helium ions (He + ) detected by MMS-1; (e-h) the similar layout as panels (a-d) except by ERG; (i-j) energy spectrograms of electrons and protons by THE; (k-l) the similar layout as panels (i-j) except by THA; (m-t) the similar layout as panels (a-d) except for VAP-A and VAP-B satellites.Except for MMS, the plasmaspheric electron density, marked by thick white curves, is superposed on the spectrograms.Note the electron density by THE and THA has been detrended by the 45-min moving average.

Figure 4 .
Figure 4. Wave signatures of magnetic and velocity field disturbances of the plasmapause surface wave (PSW).Normalized power spectra and time series perturbations of (a, b) poloidal waves (Br-Vr) by MMS-1, (c, d) Ba detected by energization and Radiation in Geospace, (e-h) poloidal and compressional poloidal (Bp-Vr) waves by THE and THA, and (i-l) poloidal, compressional poloidal, and toroidal (Ba-Va) waves by VAP-A and VAP-B.The dominant frequency range of the PSW, that is, ∼0.6-2 mHz, is highlighted by gray shaded regions in power spectra.NPS: Normalized Power Spectra.