Substorm Induced Nighttime Plasma Flow Pulsations Observed by ROCSAT‐1 at Topside Ionosphere

The Republic of China Satellite‐1 orbiting at 600 km topside ionosphere has observed the topside ionospheric plasma flow pulsations induced by the substorm onsets. These pulsation events indicated that the plasma flow pulsations mainly oscillate in the two mutually perpendicular directions with respect to the geomagnetic field lines. The field‐aligned flow as well as the ion density indicates almost no variation. This implies that the pulsation events are of Alfven wave in nature. The Hilbert‐Huang transform analysis is applied to study the dominant wave frequencies and the polarization in the two perpendicular components of plasma flows (i.e., the perturbed electric/magnetic fields). The hodograms of the polarization in the Pi1 frequency is shown to be linearly polarized, while the left‐handed polarization is seen in the Pi2 frequencies that are in harmonic relationship. These plasma flow pulsations in the nighttime topside ionosphere are caused by the field‐line‐resonance magnetic field pulsations converted from the inward propagated compressional disturbance across the nighttime magnetosphere/plasmasphere which is originated at the near‐Earth magnetotail at the substorm onset.

2 of 13 & Klimushkin, 2021; Mann et al., 1995;Mond et al., 1990;Southwood, 1974;Wright et al., 2022;Zhu & Kivelson, 1988). Direct space observations that indicate the coupling effect between the compressional modes and the transverse modes have been observed (Cahill et al., 1990;Keiling et al., 2001Keiling et al., , 2003Lin et al., 1992). These pulsation events of amplitude variation appear in the transverse standing wave modes  and the polarization reversal together with small amplitude variations Su et al., 2005). For the low latitude or low altitude observations in space, the recent AMPTE (Active Magnetospheric Particle Tracer Explorers) observations indicate that the FLR oscillation spectra have been frequently observed when AMPTE passes through the plasma trough region (Anderson et al., 1990). The C/NOFS (Communication/Navigation Outage Forecasting System) observations show the ULF fluctuations in the low-latitude ionospheric electric field during the sudden commencement on 8 March 2012 . The magnetometer onboard Swarm-A satellite observed the ULF wave activity at low altitudes on 23 June 2020 (Piersanti et al., 2022).
Similar to the ULF oscillations that occur in the magnetosphere, the plasmasphere ULF events can occur inside the plasmasphere when excitation appears at the plasmapause (Chen & Hasegawa, 1974b;Ghamry et al., 2015;Lee, 1996;Lee & Kim, 1999). During the substorm period, the excitation force can come from the plasma flow rushing in from the magnetotail (Denton et al., 2002;Kepko et al., 2001;Kepko & Kivelson, 1999;Nosé, 2010;Nosé et al., 2003). These geomagnetic pulsations observed are pre-dominantly in the radial direction as in the magnetosphere (Ghamry et al., 2015;Kim et al., 2010;Kwon et al., 2012;Sutcliffe & Luhr, 2003;Sutcliffe & Yumoto, 1991;Takahashi et al., 1995Takahashi et al., , 1999Takahashi et al., , 2003. In a series of publications by Menk et al. (2000), Waters et al. (2000), and Waters et al. (2002), the characteristics of FLR pulsation frequencies at Pc3 pulsations in the daytime plasmasphere/magnetosphere have been studied with the observational data from Australian magnetometer chain and the theoretical simulations with 1D to 3D models. The lowest latitude to observe the FLR oscillation is stated to be at L ∼ 1.30. As the ULF oscillations observed in the low latitude or low altitude region are rare, we would like to present the ROCSAT-1 (Republic of China Satellite-1) observation of the ULF pulsations in the midnight topside ionosphere in this report. ROCSAT orbits at the 600 km topside ionosphere with the Ionospheric Electrodynamics and Plasma Instruments (IPEI) can measure the ion concentration, ion plasma flow vector, ion temperature and composition . With its orbital inclination of 35°, ROCSAT can reach to the dip latitude of ∼45° (L = 2.16) at certain longitudes. The ionosphere at dip latitude of ∼45° is related to the plasma trough region. Thus the ROCSAT observations of plasma flow pulsations could be related to the regions inside the inner boundary of the plasmasphere for the possible lowest latitude limit to observe the ULF pulsations in the topside ionosphere. Such ULF pulsation events are extremely rare and valuable to study the characteristics of ULF event in the midnight topside ionosphere. We will use the Hilbert-Huang Transform analysis to study the characteristics of the pulsations at different frequency ranges. The polarization hodograms of the perturbed electric/magnetic fields derived from the plasma flow pulsations can assist us to understand the nature and the cause of ULF pulsations observed by ROCSAT-1.

ROCSAT Observations
They are only three ULF plasma pulsation events observed in the midnight sector during the 5 and half years of ROCSAT mission from March 1999 to June 2004. These events are shown in Figures 1a-1c chronically as they were observed. The ROCSAT data shown in these figures are plotted with 1-s data and are available at http:// cdaweb.gsfc.nasa.gov/index.html/. In Figures 1a-1c, three ion flow velocity components are shown in the first three panels from top to bottom in each figure. The ion flow velocities are plotted in the local right-hand Cartesian coordinate with the outward (upward) flow, ⟂ , that is perpendicular to the geomagnetic field line and lies in the meridian plane. The other flow velocity, ⟂ that is perpendicular to the field line and directed toward the zonal direction, is positive eastward. The field-aligned flow that flows along the geomagnetic field is denoted by ‖ . The last panel shows the ion density variation. In the bottom of each figure, we show the universal time (UT), local time (LT), the dip latitude (DLat), and the L-shell value.
The flow pulsations are noted to appear only in the two perpendicular flow components ⟂ and ⟂ in every figure. Also these two flow components are seen to start the pulsation out of phase. When the ⟂ starts upward (outward), the ⟂ moves westward (in Figures 1a and 1b), and vise versa (in Figure 1c). The fact of the out of phase pulsations in the two flow components appears in either the northern or southern hemisphere as noted by 3 of 13 the dip latitude location shown in each figure. There is no discernible oscillation observed in the parallel flow component. The pulsations manifest many cycles of oscillatory variation as seen in Figure 1b, but only a few cycles in Figures 1a and 1c. We indicate the onset of the pulsation with the dashed line in each figure as shown in Figures 1a-1c. The gross oscillation period of the observed pulsation events could be a Pi2 (∼100s) as by eye inspection of the pulsation cycles.
As these three events are all observed near the midnight sector, the occurrence could be related to the substorm impacts that cause the topside ionospheric plasma flow and density variations. Figures 2a-2c show the SYM-H and AU/AL variations (https://wdc.kugi.kyoto-u.ac.jp/aedir) that identify the onsets of the substorm as plotted with the dotted line in each figure. We notice that the substorm occurrence seems to be related to the magnetic storm initial phase with the SYM-H indicating an increase of ∼50-70 nT for each event. For such strong compressions of the magnetosphere indicated by the large jumps of the storm initial phase (Kataoka, 2020), the magnetospheric substorm onsets were immediately triggered as seen in Figures 2a-2c. The onset time for the substorm from the start of AL decrease to the lowest AL value is about 2 min. Because the resolution of the substorm index AL is about 1 min, while the ROCSAT data is plotted in 1-s resolution, we consider the onset of plasma flow pulsation (shown in dotted lines in Figures 1a-1c) does follow the onset of a substorm (shown in dashed lines in Figures 2a-2c) for each respective event. However, it is noted that the background ion density does not indicate any variation at the substorm onset, nor from the compression of the magnetosphere during the storm initial phase. Rather, the density variation indicates very small discernible oscillation from the background variation as seen in Figures 1a-1c.

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Finally, we would like to mention that the occurrences of plasma flow pulsations observed by ROCSAT take place inside the topside ionosphere. The ion composition measurement (though not shown here, but is available at http://cdaweb.gsfc.nasa.gov/index.html/) indicates that the O + ion is more than 75% of total ion composition at the time when the three events were observed. The observed highest dip latitude is ∼44° (L = 2.11) in the 24 November 2001 event (Figure 1b), and the lowest one is at ∼10.65° (L = 1.13) in the 29 October 2003 event ( Figure 1c). The large amount of O + observed by ROCSAT at these dip latitudes imply that the ROCSAT are all located inside the topside ionosphere and not in the protonsphere (plasmaphere) during the observations of plasma flow pulsations.

Hilbert-Huang Transform Analysis of Pulsating Plasma Flows
We now apply the Hilbert-Huang Transform (HHT) analysis (Chen et al., 2001;Huang et al., 1998;Su et al., 2005Su et al., , 2019Sun et al., 2021) to study the pulsation characteristics of the two perpendicular plasma flow components in Figures 1a-1c. The HHT analysis is a data adaptive analysis that allows the data to reveal their nature oscillation frequencies without constraining the nature signals with any a prior assumed harmonics. It is suitable to analyze a non-stationary time series like the data shown in Figures 1a-1c. The HHT analysis adopts an empirical mode decomposition (EMD) method to decompose the time series into several intrinsic mode functions (IMFs), in the time domain, with various undulation frequencies. Each IMF has a well-behaved Hilbert transform and reveals the instantaneous frequency as a function of time that clearly identifies the structure of the non-stationary data.
In the two left-hand panels of Figures 3a and 3c, we show the result of the HHT analysis for the time series of the ⟂ and ⟂ flow components in each plasma flow pulsation events in Figures 1a, 1b, and 1c, respectively, and their IMFs (∆ ⟂ and ∆ ⟂ ) from C1 to C8 in the following panels. In general, the IMF C1 contains the highest-frequency component of the original time series, while C8 the lowest. Since each IMF component from either ⟂ or ⟂ reflects its own undulation characteristics within the respective flow component, the dominant oscillation frequency and amplitude for the same IMF components in ⟂ and ⟂ need not be the same.
The two highest-frequency components C1 and C2 in either ⟂ or ⟂ flow pulsation may contain some digitization noises and small fluctuations, so they will not be discussed here in relation to the pulsation event. On the other hand, the lowest-frequency component C8 is related to the background ion flow variation along the ROCSAT orbit.
In the two right-hand panels of Figures 3a-3c, we show the HHT instantaneous frequencies for each IMF component for the respective flow pulsations in the left-hand panels. We will use the event of a large plasma pulsation on 24 November 2001 shown in Figure 3b as an example for the detailed explanation of the result of HHT analysis. The vertical axis in each IMF panel in the left-hand side of Figure 3b represents the amplitude of the oscillation in the pulsation event. The mean of each IMF is zero. As the instantaneous period varies with time, as seen in the right-hand side of Figure 3b, we have to select a certain time duration to obtain an averaged oscillation period to study the characteristics of oscillation. To obtain a meaningful oscillation period, we take averages within a chosen time period that the IMF components have significant oscillations. For the 24 November 2001 event, we choose 200-500s after 05:52:30 UT. The time duration is shown in the red-colored bar in IMF components in the left-hand side of the figure with the calculated averaged oscillation period shown in the right-hand side of the figure. For the C3 components in the ⟂ and ⟂ variations, it is noticed that the ⟂ component is much smaller than that of ⟂ . This implies that the oscillation at this frequency (∼19-25s) is linear in the east-west direction as the data implies. The next large IMF component is C4 with the oscillation period of ∼34-40s. Following that, the C5 component has an oscillation period of ∼63-65s. This seems to be a first harmonics of the C4 component. Then the second and the third harmonics are C6 (∼98-100s) and C7 (∼124-130s), respectively, with diminishing amplitudes. Thus the oscillation characteristics revealed by the HHT components indicates that there is one Pi1 (∼25s) oscillation appeared only in the ⟂ f low componet that oscillates in the east − west direction. The other oscillation components are in the Pi2 (40-150s) oscillation characteristics with the fundamental oscillation period of ∼34s and its harmonics.
As the density variations seen in the third panels of Figures 1a and 1b Figure 1c, no density variation can be noted, so that no HHT analysis has been performed. The reason for no density variation in this event could be due to the fact that this case is observed at a low dip latitude. For the illustrated example of the 24 November 2001 event in Figure 3b, we notice that the IMF components C1 through C6 seem to correspond to the flow pulsations in the same respective components. The result of density and flow pulsations for the illustrated example of the 11 November 2001 event is summarized in Table 1 for reference.

Pulsation Hodogram
One of the important features in studying the characteristics of a pulsation event is to study the pulsation polarization.
Before doing that, we should find out the relationship between the observed pulsating variables of ⟂ and ⟂ , and the perturbed magnetic field and/or electric field components in the wave. Assume that an ideal MHD fluid with a uniform magnetic field and homogenous plasma exists around the local background geomagnetic field in a Cartesian coordinate (x, y, z) as shown in Figure 5, the wave variables and wave vector are, ( , , ), The first-order MHD equations can be shown to yield the results with the wave variables varying with exp − ⋅ Here 0 and 1 are the background and perturbed plasma density, respectively. 0 is the geomagnetic field strength at point O in Figure 5, and is the compressional component of the magnetic field perturbation.
From Equations 1 and 2, we see that the wave components and vary proportionally with the observed flow variables ∆ ⟂ and . This is what has been observed in Figures 1a-1c. In addition, the density is directly proportional to the compressional perturbation. Figures 1a and 1b, and c indicate that the observed pulsation event is mainly a transverse  The hodograms for the pulsation amplitudes in the ∆ ⟂ and ∆ ⟂ obtained in the HHT analysis are constructed as shown in Figures 6a-6c. The plot of the hodogram is arranged with the background geomagnetic field pointing into the paper. The hodogram of the wave vector is drawn starting at a point indicated by a black dot and ends with a red arrow. The hodogram in Figure 6a Figure 6b shows the polarization is linear at the high frequency Pi1 oscillation. In inspection of Figure 3a, it is also noted that the C3 IMF components in the 15 July 2001 event also have a linear polarization in the oscillation at the Pi1 frequency. For all other cases in Figure 6, the wave polarizations are all left-handed circularly/elliptically polarized with respect to the background geomagnetic field line in the frequency ranges of Pi2.

Discussion
The three plasma flow pulsation events observed by ROCSAT-1 at nighttime topside ionosphere indicate that the plasma flow components are pulsating perpendicular to the field line. The HHT analysis further reveals that the pulsating frequencies have components in the Pi1 (∼25s) and Pi2 (∼36 to 130s) ranges. These pulsation events are all related to the substorm onsets because every event contains a component of Pi2 pulsation which has been used to identify the substorm onset from the ground magnetometer observations (Olson, 1999;Rostoker, 1967;Rostoker and Olson, 1979). The detailed HHT analyses for the 24 Nov 2001 event are summarized in Table 1 for quick references. The results indicate that the oscillations periods for the C4, C5, C6, and C7 IMF components in the density and flow oscillations are in a harmonic oscillation of the fundamental period of ∼36s of Pi2 pulsation.
Although it has been reported that each individual magnetic shell will have a distinctive oscillation frequency in the MHD oscillation (Poulter and Nielsen, 1982), multiple frequency oscillation could have resulted from the current pulsation event when ROCSAT moves across different dip latitudes (magnetic shells) at 600 km topside ionosphere (cf. Figures 1a-1c) during the observation. Furthermore, multifrequency pulsations have indeed been observed in the past (see, e.g., Lin et al., 1986;Anderson et al., 1989). On the other hand, the model simulation has shown that bands of frequencies in transverse oscillation can exist for the field line resonance at one single field line (Allan et al., 1986). We think the current observations of multi-frequency oscillations have occurred within a limited number of magnetic shells that were traversed by ROCSAT. This is concluded from the results of harmonic oscillations shown in Table 1 and the results of same polarization in the harmonics.
As for the sense of polarization in the flow pulsation, except for the Pi1 pulsation that is linearly polarized in the east-west zonal direction, the lower frequency pulsations in the Pi2 range are all left-hand circular/elliptical polarized with respect to the background geomagnetic field. This indicates that the pulsation events are all of Alfven wave in nature (Stix, 1992). It is further noted that the left-hand polarization in the Alfven wave will become linearly polarized when the wave frequency is much lower than the ion cyclotron frequency. At the ROCSAT altitude of current observation, the proton cyclotron frequency is about 350 Hz, that is much higher than the observed ULF pulsation frequencies in the mHz ranges. The observed oscillation at Pi1 frequency is linearly polarized as it should as seen in Figure 6b, but the Pi2 is left-hand circularly polarized (cf. Figures 6a, 6b1, and 6c). Thus, it is concluded that the ROCSAT observed plasma pulsation events are the transverse Alfven wave mode of oscillation.  The cause of these observed ROCSAT plasma pulsation events should be related to the magnetospheric substorm. The formation of the field-aligned current (FAC) system during the substorm onset period will drive a surge of auroral electrojet that will then cause the ground magnetic field Pi2 pulsations observed near the auroral zone. Such a process has been reported in many reports (Baumjohann & Glassmeier, 1984, p. 347;Rostoker, 1967;Rostoker & Olson, 1979;Samson & Rostoker, 1983;Samson, 1985). The Pi2 pulsations observed by the ground magnetometer chain in the North America also indicate that the magnetic polarization depends on the location of auroral electrojet current surge (Baumjohann & Glassmeier, 1984;Rostoker, 1967;Rostoker & Olson, 1979;Samson & Rostoker, 1983). At the latitudes lower than the auroral electrojet location, a left-hand polarization is observed. Thus when the Pi2 pulsation is caused by the current surge related to the substorm, a left-hand polarization should be observed at the midnight sector from mid to high latitudes.
However, it is noted that there is no distinctive oscillation harmonics created during auroral electrojet current surge process observed in the above mentioned reports. This is contrary to what has been observed by ROCSAT (cf . Table 1). Furthermore, the current ROCSAT-1 observed Pi1/Pi2 pulsation events that occur at low to mid latitudes. The ROCSAT observed pulsation events also indicate that compressions of magnetic field intensity have been observed. Therefore, other mechanism besides the auroral electrojet current surge could cause the current ROCSAT observations.
The other substorm related phenomenon that can cause magnetic pulsations is the direct forcing oscillation of the nighttime magnetosphere/plasmasphere by the disturbances generated during the substorm onset. As the stretched nightside tail-like geomagnetic field in the magnetosphere is napped back to become more dipolar-like at the substorm onset. The disturbance creates a compressional MHD fast wave to propagate across the magnetosphere to reach the plasmasphere. The impact at the plasmapause will produce the ULF pulsations in the poloidal mode of cavity resonance (Nosé, 2010;Takahashi et al., 1995Takahashi et al., , 1999Takahashi et al., , 2001Takahashi et al., , 2003Yeoman et al., 1991;Yeoman & Orr, 1989). In addition, bursts of plasma flow that appeared during the substorm period will move toward the Earth to generate micropulsations in the magnetosphere and plasmasphere (Kepko et al., 2001(Kepko et al., , 2004Kepko & Kivelson, 1999). It is noted that these two mechanisms will produce the compressional fast mode of ULF pulsations. To produce what has been observed in the current report, the plasmaspheric poloidal mode oscillation should be converted to an Alfven wave oscillation at a location where the fast mode oscillation frequency matches the local Alfven wave oscillation frequency as has been published in many reports in the past (Allan  , 1986Chen and Hasegawa, 1974;Kivelson & Southwood, 1985, 1986Mann et al., 1995;Mond et al., 1990;Lee and Lysak, 1989;Southwood, 1974;Zhu & Kivelson, 1988).
In the 1-D and 3-D simulations of dayside magnetospheric ULF oscillations, two distinctive oscillation frequencies have been obtained at the low latitudes that can convert the compressional plasmatrough-plasmasphere mode to the FLR mode as reported by Waters and Menk et al. (2000) and Waters et al. (2000). They are f = 28 mHz at L = 1.14 and f = 36.8 mHz at L = 1.1. The oscillation periods for these two frequencies are 35.7 and 27.2s. These are the frequencies that have been observed in the 24 November 2001 event (cf . Table 1). However, it should be noted that the dominant frequencies of the oscillations in the 24 November 2001 event are ∼19-25s and ∼63-65s for the linearly and left-hand circularly polarized component, respectively. On the other hand, there is no specific statement for the sense of polarization reported in the previous observations or model simulation presented in the reports of Menk et al. (2000), Waters et al. (2000), and in the observational result by Waters et al. (2002).
The fact of converting a compressional poloidal mode to the transverse Alfven oscillation can be noted in the ROCSAT observations as seen in the small density oscillations shown in the third panels of Figures 1a and 1b. These density oscillations can be regarded as the remnants of the poloidal mode oscillation. The HHT analysis performed on the 24 November 2001 events and summarized in Table 1 indicates that the dominant oscillation frequencies in both the density and plasma pulsations are almost identical to each other. It should be mentioned that the compressional and transversal mode of ULF oscillations have been shown to occur together theoretically (Southwood & Kivelson, 1984) and observed in the ground-based magnetometer data (Tokunaga et al., 2007). Nonetheless, the ROCSAT data indicate that the pulsations are predominantly in the transverse direction with a very small compressional component observed. Thus the current ROCSAT observed plasma pulsations in the transverse Alfven mode should originate from the compressional fast mode generated during the subtorm period in the magnetotail and propagated Earthward to be converted to the Alfven mode observed by ROCSAT.
Finally we would like to mention weather the ionospheric conductivity loading has caused the current ROCSAT observed ULF plasma pulsations any damping at low latitude regions is unclear at the moment. Nonetheless, in the Supporting Information of the current report, ground magnetometer data from Kakioka station are attached for reference of the ionospheric conductivity effect on the propagation of ULF pulsations from space to ground. Hughes (1974) and Hughes and Sothwood (1976) have mentioned the screening effect of the ionosphere conductivity on the magnetospheric ULF pulsations to the ground. In addition to the damping effect caused by the ionospheric conductivity, Hughes (1974) has also mentioned the rotation of pulsation polarizations in the ground pulsations against the space observed ones. There is other theoretical study of damping the uncoupled poloidal and toroidal modes by ionospheric conductivity reported by Newton et al. (1978). Although Newton et al. indicated that the damping of the wave mode is 10 times more severe in the nighttime than in the daytime so that there are more Pc type oscillations observed on the dayside and Pi type oscillations observed on the night side. All these reports indicate that the ionospheric conductivity could reduce the observation opportunity of ground pulsation observations. As the current report focuses on the characteristics of space observed ULF plasma pulsation events, further study of the concurrent or collocated space and ground observations described in the Supporting Information are beyond the scope of current report.

Conclusion
The three plasma flow pulsation events observed by ROCSAT-1 at 600-km topside ionosphere seem to be induced by the substorm onsets. These events indicate that the dominant plasma flow pulsations exist in the two components that are perpendicular to the geomagnetic field lines. The parallel flow component and the density do not indicate any discernible variations. The HHT analysis reveals that the plasma flow pulsations in each event indicate that the pulsations consist of the Pi1, and Pi2 and its harmonics of ULF pulsations. The wave oscillation is linearly polarized in the Pi1 component and left-hand circularly/elliptically polarized in the Pi2 component. The Pi2 pulsation frequencies are observed to be harmonics of the fundamental period of ∼34s. The cause of the pulsations is attributed to the conversion of an Earthward propagating compressional fast mode generated during the substorm to the transverse Alfven mode oscillation that is observed at the topside ionosphere.

Data Availability Statement
The ROCSAT-1 1-s data is archived at Coordinated Data Analysis Web (CDAWeb) at http://cdaweb.gsfc.nasa.gov/ index.html/. CDAWeb is physically located at Space Physics Data Facility (SPDF) of NASA Goddard Space Flight Center, USA. CDAWeb contains selected public non-solar heliophysics data from current and past heliophysics