1 Introduction

Inner magnetospheric whistler mode waves at frequencies between about 0.5 and 4 kHz sometimes exhibit a nearly periodic time modulation of the wave intensity. The modulation period can range from tens of seconds up to a few minutes, and the respective emissions are typically called quasiperiodic (QP) emissions. Although they have been known already for a few decades (Carson et al., 1965), their origin is still not fully understood, and neither are their generation locations. Two principally different generation mechanisms have been considered. First, it has been suggested that the QP modulation may be a result of the source region being periodically modulated by a compressional ultralow frequency (ULF) wave with a period corresponding to the period of the QP modulation (Chen, 1974; Kimura, 1974; Sazhin, 1987). Second, a flow cyclotron maser mechanism able to self-consistently explain the origin of the QP modulation even without the presence of the ULF magnetic field pulsations has been proposed (Demekhov & Trakhtengerts, 1994; Pasmanik, Demekhov, et al., 2004). As for the supporting experimental evidence, some of the observed QP events appear to be more or less clearly related to the ULF pulsations (Sato & Kokubun, 1981), while for many events such pulsations are missing and the flow cyclotron maser mechanism is able to reproduce their basic characteristics and dependences (Pasmanik et al., 2019; Pasmanik, Titova, et al., 2004). It seems well possible that both mechanisms are eventually plausible, depending on the conditions and event properties. Historically, the events related to the ULF pulsations were classified as QP events type 1, while the other events were classified as QP events type 2 (Kitamura et al., 1969; Sato et al., 1974). This latter class might be related to the flow cyclotron maser mechanism. Even though such event classification seems problematic at least (Sazhin & Hayakawa, 1994; Tixier & Cornilleau-Wehrlin, 1986), Bezděková et al. (2019) demonstrated that the QP events indeed appear to form two different classes based on their properties and dependences on the solar wind parameters.

A survey of QP event observations by the Van Allen Probes spacecraft revealed that the events occur primarily, but not exclusively, inside the plasmasphere (Němec et al., 2018). Although the planarities of the wave magnetic field fluctuations (Santolík et al., 2003) are typically rather low, indicating a mixture of waves coming to the spacecraft from different directions, the waves are found to propagate mostly away from the geomagnetic equator. This suggests that the events are indeed generated in the equatorial region, which is a preferred region for wave-particle interactions in general (Trakhtengerts & Rycroft, 2008), and has been formerly suggested as a possible source location of the emissions (Morrison, 1990; Sato & Kokubun, 1980). The observed oblique wave normal angles demonstrate that the wave propagation is primarily unducted (Martinez-Calderon et al., 2016; Němec et al., 2018). The unducted propagation is believed to be responsible for the same QP modulation being observed over comparatively large regions of space (Bezděková et al., 2020; Němec, Bezděková, et al., 2016; Němec, Hospodarsky, et al., 2016; Němec, Santolík, Parrot, et al., 2013). This is supported by multipoint measurements and detailed time delay analysis, which reveals a time delay on the order of seconds between different locations (Martinez-Calderon et al., 2016; Němec et al., 2014). A plasmapause guiding (Hayosh et al., 2016) and ionospheric reflections (Hanzelka et al., 2017) may be further important for the propagation of QP emissions down to low altitudes. Ground-based measurements then, in turn, enable observations of a given event for an extensive period of time (Manninen et al., 2012). They were used to reveal variations of QP modulation periods related to substorms (Manninen, Titova, et al., 2014; Manninen et al., 2013). While both ground-based (Engebretson et al., 2004; Morrison et al., 1994; A. J. Smith et al., 1998) and low-altitude spacecraft (Hayosh et al., 2014) surveys suggested that QP emissions are primarily daytime phenomenon, satellite surveys at larger radial distances revealed the emissions essentially at all local times (Němec et al., 2018; Němec, Santolík, Pickett, et al., 2013). This apparent inconsistency can be explained by significant lightning-related background wave intensities which may obscure the events at low altitudes (Němec et al., 2020).

Quasiperiodic variations of energetic electron precipitation related to the event occurrence and related ionospheric changes were suggested as a possible explanation for concurrent magnetic field pulsations observed on the ground (Sato & Matsudo, 1986). More recently, Hayosh et al. (2013) presented a case study of energetic electron flux variations corresponding to individual QP wave elements observed by the low-altitude DEMETER spacecraft. Titova et al. (2015) used Van Allen Probes spacecraft measurements to identify energetic electron flux changes with periods corresponding to the QP modulation in the proximity of a tentative source region. Finally, Li et al. (2021) used simultaneous measurements of QP emissions by the Van Allen Probes and energetic electron precipitation by the low-altitude POES satellite to demonstrate energetic electron precipitation in association with QP emissions.

In the present study, QP electromagnetic wave events observed by the DEMETER spacecraft during its entire mission identified by Hayosh et al. (2014) are used to check for energetic electron flux variations matching the wave intensity modulations. This provides us with the information about the magnetic field lines containing tentative event source regions. A brief overview of the used data set is given in Section 2. The results obtained are presented in Section 3 and they are discussed in Section 4. Finally, Section 5 contains a brief summary of the main results.

2 Data

DEMETER was a French low-altitude satellite operating between 2004 and 2010 at an altitude of about 700 km. The spacecraft measurements were performed nearly continuously at geomagnetic latitudes below about 65°, while principally no measurements came from larger latitudes. The spacecraft orbit was nearly Sun-synchronous, resulting in the measurements being performed either close to the local noon (about 10:30 LT, “daytime”) or close to the local midnight (about 22:30 LT, “nighttime”). Out of the instruments onboard, the electric field instrument (ICE), the magnetic field instrument (IMSC), and the energetic particle detector (IDP) are used in the present study. Two different modes of the spacecraft operation were possible, called “Burst” and “Survey.” During the continuously active Survey mode, lower resolution data were measured. The Survey mode electric field measurements in the very low frequency range consisted of onboard calculated frequency spectra of a single electric field component with the frequency resolution of about 20 Hz and the time resolution of about 2 s. The Survey mode energetic particle data consisted of two different data products. First, the total energetic electron fluxes in three energy ranges (90.7–526.8, 526.8–971.8, and 971.8–2342.4 keV) were measured with a time resolution of 1 s. Second, the energetic electron spectra with 128 linearly spaced energy channels spanning between 72.9 and 2333.5 keV were measured with a time resolution of 4 s. The Burst mode was active only during specifically selected time intervals, providing some higher resolution data on top of the normal Survey mode data. During this mode, a waveform of a single electric field component sampled at 40 kHz and waveforms of all six electromagnetic field components sampled at 2.5 kHz are available. Due to a significant number of interferences in the magnetic field data at frequencies between about 1 and 8 kHz, this is the only data product of the magnetic field instrument that is used. Additionally, energetic electron spectra have better energy (256 energy channels instead of 128) and time resolution (1 s in place of 4 s). More detailed description of the ICE, IMSC, and IDP instruments is given by Berthelier et al. (2006), Parrot et al. (2006), and Sauvaud et al. (2006), respectively.

A starting point of our analysis is a list of all QP events observed during the entire duration of the DEMETER mission compiled by Hayosh et al. (2014). Altogether, the list consists of as many as 2,264 events. Out of that, 2,181 events occurred during the daytime, while only 83 events were identified during the nighttime. The list provides a beginning and ending times, as well as lowest and highest frequencies of all the events. For each event separately, these are used to plot the respective frequency-time spectrograms of power spectral densities of electric field fluctuations. Additionally, the time dependences of total energetic electron fluxes in the lowest of the three survey mode energy ranges are plotted using the same temporal scale. Individual plots are then visually investigated for the presence of energetic electron flux peaks at the times of the individual QP elements. In order to eliminate possible random coincidences, it is required that the electron flux is noticeably increased at the times of at least three consecutive QP elements. Altogether, seven events fulfilling this condition are identified, all during the daytime. Geomagnetic activity conditions during the seven events do not appear to be exceptional in any way as compared to the geomagnetic activity conditions for the entire DEMETER QP event list.

3 Results

An example of one of the identified events where a QP event is accompanied by corresponding quasiperiodic bursts in energetic electron fluxes is shown in Figure 1. The event occurred on October 24, 2006. The plotted time interval starts in the beginning of data acquisition during the given orbit. Figure 1a shows a frequency-time spectrogram of power spectral density of electric field fluctuations corresponding to the QP event. Individual QP elements with the intensity gradually decreasing toward lower geomagnetic latitudes (later times) can be seen. The white vertical bars correspond to short data gaps related to turning on/off the Burst mode measurements, that is, the Burst mode data are available in the time interval marked by the vertical white bars.

Figure 1b shows energy-time plot of measured energetic electron fluxes. Several peaks of enhanced fluxes are identifiable at the lowest energies close to the beginning of the plotted time interval. The peaks in the wave intensity and measured energetic electron fluxes are analyzed more in detail in Figure 1c, which shows the respective time dependences. The black curve shows the time dependence of the average power spectral density in the frequency range between 1,200 and 1,900 Hz, where the core of the QP event occurs. The red curve shows the time dependence of the measured energetic electron flux corresponding to the lowest energy count channel, i.e., approximately between about 90 and 525 keV. The periodic modulation of both the wave intensity and energetic electron fluxes can be clearly seen. While the wave intensity exhibits a QP modulation principally all over the plotted time interval, the QP modulation of the energetic electron fluxes is limited to the time interval shortly after the beginning of the plot. This time interval is marked by the vertical dashed lines. The individual peaks of energetic electron fluxes in this time interval occur approximately at the same times as the peaks of the wave intensity. Note that the huge increase of the electron flux seen in Figure 1c at later times (about 15:35 UT) corresponds to the slot region.A more detailed view of the time interval marked by the dashed vertical lines is shown in Figure 2 using a format analogous to the one used in Figure 1. The vertical dashed lines mark the times of five wave intensity peaks identified in Figure 2a. As demonstrated by Figure 2c, the marked times correspond well also to the peaks in measured energetic electron fluxes. Some of the energetic electron flux peaks are identifiable also in the energy spectrum plot in Figure 2b, although they are quite obscured due to the lower time resolution of the data and the used color coding representation.A similar analysis and identification of time intervals when the QP modulation is observed both in the wave intensity and energetic electron fluxes is done for all the seven events. The results obtained are shown in Figure 3, which depicts the respective extents in L-shell as a function of the event number. The black vertical lines mark the L-shell extent of individual QP events as seen in the wave data. The red vertical lines mark the L-shell extent of individual QP events as seen in the energetic electron fluxes. The QP modulation of energetic electron fluxes generally occurs in a shorter interval than the QP modulation of wave intensity, and it is located usually toward the higher L-shell edge of the QP event.Histograms of L-shells where the events are observed are shown in Figure 4a. These values show how many events span over each particular L-shell bin. The black line corresponds to the QP wave events, while the red line corresponds to the QP modulated energetic electron fluxes. The QP modulation of the wave intensity is typically observed over many L-shells, spanning to low geomagnetic latitudes and at times even all the way to the geomagnetic equator. On the other hand, the QP modulation of energetic electron fluxes is limited to L-shells between about 4 and 6. A histogram of L-shell extents of regions where the QP modulation of energetic electron fluxes is observed is shown in Figure 4b. It can be seen that the typical L-shell extents of these regions are between about 0.6 and 1.2. Additionally, while the QP modulation of the wave intensity for the seven event orbits is observed in both hemispheres, the QP modulation of energetic electron fluxes is observed in a single hemisphere for each event. This indicates that also the azimuthal extent of the QP modulation of the wave intensity is larger than the azimuthal extent of the QP modulation of energetic electron fluxes. Then, as the spacecraft orbit is generally not confined to a single magnetic meridian (Němec et al., 2010), it can get azimuthally too far from the particular meridian in the conjugate hemisphere to see the QP modulation of energetic electron fluxes. We note that the geomagnetic longitude differences between the locations of the events and the locations where the spacecraft passes through a given L-shell in the conjugate hemisphere range between about 5 and 80° with a median value of about 25°.The energy spectrum of energetic electrons responsible for the flux peaks is analyzed in Figure 5. In each energy channel, we calculate a ratio of the particle flux at the time of the peak with respect to the flux at the times of the neighboring local minima (i.e., just before and just after the peak). Altogether, 23 flux peaks sufficiently pronounced in the IDP energy spectra data are analyzed. The spectra ratios obtained for individual flux peaks vary quite considerably, among others due to comparatively low resolution of the used IDP spectral data. However, the median ratio of the energy spectra depicted in Figure 5 reveals that the measured fluxes are increased primarily at energies lower than about 250 keV. The maximum median flux increase is about 15%, at an energy of about 150 keV. Although the median flux ratio gradually decreases toward higher energies, the fluxes appear to remain slightly elevated at energies up to about 500 keV. At higher energies, the median flux ratio starts to fluctuate a lot due to low absolute flux values.

L-shells, where the QP modulation of energetic electron flux is observed, are deemed to correspond to source L-shells of QP events. We thus try to relate event properties to the respective L-shell values, although the available statistics of only seven events in total is quite a limiting factor. No significant relation between these L-shell values and QP modulation periods is found. However, there appears to be a relation between the L-shell values and QP event frequencies. The corresponding results are shown in Figure 6, which depicts the QP event frequencies as a function of the respective L-shells where the electron precipitation occurs. Each event is depicted by a color rectangle spanning between the minimum and maximum L-shells of QP modulated energetic electron flux and between the minimum and maximum frequencies of the event. The colors of the rectangles correspond to the event modulation periods, following the color scale on the right-hand side. The dashed curves at the upper right part of the figure correspond to equatorial electron cyclotron frequency and half of the equatorial electron cyclotron frequency, respectively. It can be seen that while the QP modulation period does not seem to depend on any of the variables plotted, event frequencies are systematically limited below half of the equatorial electron frequency in the tentative source regions.The example event from Figures 1 and 2 is exceptional as the spacecraft Burst mode was active for part of the event duration, for about two minutes after 15:35 UT. The measured waveform data allow us to accommodate the parameters of the spectral analysis to get a frequency-time spectrogram with significantly better time resolution than during the Survey mode. Figure 7a shows the Survey mode frequency-time spectrogram of power spectral density of electric field fluctuations, while Figure 7b shows the corresponding frequency-time spectrogram obtained using the Burst mode data. A fast Fourier transform with a length of 4,096 data points, 3,840 points overlapping, and averaging over 16 neighboring spectra is used, resulting in a time resolution of about 0.1 s and frequency resolution of about 10 Hz. Individual QP elements, in particular the three in the middle of the plotted time interval, are distinguishable in both spectrograms. However, the Burst mode spectrogram reveals an unexpected feature: the QP element intensity does not vary smoothly with time, but it exhibits a fine inner structure. Alternatively, one may describe the situation as discrete emissions with a short repetition period, whose intensity exhibits a slower QP-like modulation. Note that the intense short-lasting emissions observable in Figures 7a and 7b at higher frequencies are lightning generated whistlers, and they are not related to the topic of the present study.

This is further demonstrated in Figure 7c, which shows a time dependence of the average power spectral density in the frequency range between 1,500 and 1,750 Hz. Intensity modulation with two different periods can be identified. First, it is a slower modulation with a period of about 15 s corresponding to the QP modulation period identifiable in the Survey mode data. Second, it is the faster modulation with a period of about 3.5 s identifiable in the Burst mode data only. This shorter modulation period roughly corresponds to the wave bounce time between the hemispheres (back and forth) at L-shells where QP modulated energetic electron fluxes are observed. For this particular event (event number 5 in Figure 3), the interaction region occurs at somewhat lower L-shells than for other events. Assuming a wave frequency of 1,625 Hz, field aligned propagation at , and density dependence along a field line given by Denton et al. (2004), the bounce time is essentially a function of only the equatorial plasma density. In order to obtain bounce times corresponding to the observed modulation period of 3.5 s, one would have to assume the equatorial density of about . Assuming twice lower/larger plasma number densities would lead to wave bounce times of about 2.6 and 5.0 s, respectively. Such densities are higher than typically observed in the plasma trough (Denton et al., 2004), but they may be possibly justified by a higher density duct region required by the flow cyclotron maser mechanism (Demekhov & Trakhtengerts, 1994). A more typical equatorial plasma trough density of about would result in a wave bounce time of about 2.0 s.

Finally, multicomponent wave measurements performed at frequencies below 1.25 kHz allow us to perform a detailed wave analysis, i.e., to determine the wave polarization properties and propagation directions (Santolík, Němec, et al., 2006). Although the QP event itself does not extend to such low frequencies, we can possibly assume that the QP elements above about 1.3 kHz propagate in a similar way as the hiss emissions at not too much lower frequencies. The wave analysis (not shown) reveals that the wave magnetic field fluctuations are right-handed nearly circularly polarized. The wave normal angle is about with respect to the local field line. The wave vector azimuthal angle is close to , which means that the wave vector stays in the plane of a local magnetic meridian, being deviated from the ambient magnetic field toward lower latitudes. Considering that the event occurs in the northern hemisphere, the observed wave normal direction corresponds to a downward orientation of the wave vector. Such results are consistent with the overall QP propagation survey performed by Hayosh et al. (2016). This propagation, along with the ionospheric reflection taking place (Hanzelka et al., 2017), can account for the larger extent of the wave signatures compared to the particle precipitation. We note, however, that these waves propagating to low latitudes are eventually observable only by spacecraft, as they are generally outside the penetration cone and cannot get to the ground due to the Snell's law (Helliwell, 1965). Wave vector directions close to vertical are needed on the bottom of the ionosphere in order to allow the wave propagation to the ground. This is consistent with conjugate observations of the emissions by spacecraft and ground-based instruments, which indeed reveal the emissions to extend to lower L-shells on board the spacecraft than on the ground (Bezděková et al., 2020).

4 Discussion

Systematic analysis of propagation directions of QP emissions (Němec et al., 2018), as well as prevailing theories of their formation (Demekhov & Trakhtengerts, 1994), suggest that QP emissions are generated in the equatorial region. However, experimental determination of the source radial distance is generally complicated. As the emissions propagate primarily unducted, the L-shells where the QP modulation of the wave intensity is observed do not have to correspond to the L-shells of the source location. Specifically, while the events tend to occupy a considerable portion of the inner magnetosphere, the generation region itself is likely significantly smaller.

Considering that energetic electrons propagate—unlike unducted whistler mode waves—essentially along magnetic field lines, the analysis of energetic electron fluxes related to the event occurrence suppresses the aforementioned complications. The identification of L-shells where the QP modulation of the wave intensity is observed along with the corresponding variations of the energetic electron flux thus allows us to directly determine the L-shell of the interaction region responsible for the observed electron precipitation. However, strictly speaking, the interaction region does not necessarily mean the generation region of the emissions themselves. If the interaction and generation regions were located at different latitudes, then the unducted waves coming from the generation region would eventually reach the interaction region at slightly different L-shells. We also note that, given the low-altitude of the DEMETER spacecraft, the measured energetic electrons have very low equatorial pitch angles, being effectively inside or at the edge of the loss cone.

Although more than 2,000 QP emissions identified by Hayosh et al. (2014) are investigated in total, only seven events with simultaneous QP modulation of the wave intensity and energetic electron fluxes are identified. This can be explained in terms of the spacecraft orbit and used criteria for the event identification. At least three simultaneous peaks in QP wave intensity and electron flux are required for a successful identification. However, at the same time, the events are observed at comparatively large latitudes, where DEMETER sweeps through individual L-shells rather quickly. Considering typical modulation periods of QP events and a limited extent of the interaction region, it is thus possible that for most events DEMETER passes through the corresponding L-shells too quickly to see three subsequent wave intensity/flux peaks. More events would be possibly identified if the condition was relaxed to only two subsequent peaks (or even to a single peak). However, such a condition is deemed not stringent enough, resulting in possible false positive identifications. The aforementioned argumentation necessarily results in a significant selection bias in the identified events. In particular, events with shorter modulation periods and with interaction regions at lower latitudes and spanning over larger latitudinal intervals are more likely to result in a positive identification.

The analysis of L-shells where the QP modulation of energetic electron fluxes is observed reveals that the interaction regions are typically located at L-shells between about 4 and 5, and they span between about 0.6 and 1.2 in the radial distance. This seems to be consistent with former studies which indicated that the source region of the emissions might be located in the equatorial region at larger radial distances (Morrison, 1990; Němec et al., 2018). Considering model plasmapause locations (Moldwin et al., 2002), it seems that although the lower L-shells of the interaction regions are typically not too far from the plasmapause, there is no strict correlation between the model plasmapause locations and the interaction region L-shells. It is, nevertheless, curious that while most interaction regions appear to be located outside the plasmasphere, QP emissions themselves are observed primarily inside the plasmasphere (Němec et al., 2018). This might be possibly explained in terms of the wave propagation between the source region and the observation points, along with the wave trapping and unducted propagation within the plasmasphere similar to the one suggested for chorus-to-hiss mechanism (Bortnik et al., 2007, 2008, 2009, 2011; Chum & Santolík, 2005; Church & Thorne, 1983; Hartley et al., 2019; Santolík, Chum, et al., 2006).

A limited time resolution of the measured energy spectra (4 s) complicates a more detailed analysis of the energies of particles precipitated in relation with QP emissions. However, the results obtained indicate that mostly the particles with energies below about 250 keV are affected. This roughly corresponds to the upper energy in the simulation results (Li et al., 2021). Note that the lower part of the precipitating energetic electron spectrum is not measurable due to the experimental constraints, as the lowest energy channel of the DEMETER IDP instrument is as high as about 72.9 keV. We may try to compare these energies with the first order gyroresonance energies in the interaction regions. Assuming a typical L-shell of 4.5, plasma number density of 25 , zero pitch angles and field aligned wave vectors, one gets a resonant energy of about 30 keV for the wave frequencies of about 1,750 Hz, which is a typical frequency of the analyzed QP events. Note, however, that this is rather a lower estimate of the first order gyroresonance energy; oblique wave vectors at the equator would lead to higher resonant energies. Nevertheless, the first order gyroresonance energy stays below the observed precipitation energies unless a significantly lower equatorial plasma number density is assumed (<). Note also that we assume the North-South symmetry: the interacting waves would propagate to the opposite hemisphere than the precipitating electrons. For completeness, we remark that the Landau resonance energy is only about 5% of the first order gyroresonance energy, that is, well below the energies of the observed precipitating electrons.

The upper frequency limit on the QP emissions, corresponding to half of the equatorial electron cyclotron frequency, is in agreement with former studies based purely on wave observations, not on the particle observations (Němec et al., 2018). Considering that the half of the equatorial electron cyclotron frequency corresponds to the upper frequency limit for the wave ducting in density crest ducts (R. L. Smith, 1961), this observation can be considered as an indirect supporting evidence for the flow cyclotron maser theory of the emission formation (Demekhov & Trakhtengerts, 1994). The wave bouncing back and forth between the hemispheres, assumed by this theory, would be further in line with the fine structure of individual QP elements revealed by the high resolution Burst mode data. We note that the fine temporal structure corresponding to the whistler wave hop time is in agreement with some QP emissions observed on the ground (Manninen, Demekhov, et al., 2014). We also note that, unlike in the case of multihop whistlers, the wave elements do not become less intense or more dispersed at later times of the event. This seems consistent with the bouncing wave elements reported by Němec et al. (2009) using conjugate ground-based and satellite observations. It might be perhaps understood in terms of the wave element intensity and spectral shape not being governed simply by the propagation and dispersion, but rather by the wave-particle interactions taking place in the source region.

5 Conclusions

A set of QP emissions identified during the entire DEMETER spacecraft mission is used to check for simultaneous variations of the wave intensity and energetic electron fluxes. Only seven events out of more than 2,000 events investigated in total exhibit such simultaneous variations. This may be explained by observational restraints, as at least three simultaneous peaks of the wave intensity and flux are needed for a positive identification, requiring the region to be sufficiently extended in L-shell and the modulation period being not too large. The observed energetic electron flux modulations are found to occur primarily at energies lower than about 250 keV.

The time intervals when the QP modulation of the energetic electron flux is observed are interpreted as the spacecraft crossing the magnetic field lines going through the generation region of the emissions. Energetic particle fluxes are in this sense a better tracer of the source location, as they—unlike unducted propagating whistler mode waves—may be regarded as propagating strictly along the magnetic field lines. Despite the low number of events and the clear selection bias present, we can thus estimate the locations and radial dimensions of the anticipated generation regions. They are found to be at L-shells between about 4 and 6, with the respective source radial dimensions being about 0.6–1.2 . The event frequencies are generally confined below half of the equatorial electron gyrofrequency in these regions.

Finally, high resolution wave measurements available during the spacecraft Burst mode for one of the events revealed that the individual QP elements exhibit a fine inner structure. They are composed of faster repeating elements, with the period corresponding to the wave bouncing along the magnetic field line between the hemispheres.

Our results provide important experimental constraints for mechanisms suggested to explain the formation of QP emissions.