Identification of the source of quasiperiodic VLFemissions using ground-based and Van AllenProbes satellite observationsE. E. Titova1,2, B. V. Kozelov1, A. G. Demekhov1,3, J. Manninen4, O. Santolik5,6, C. A. Kletzing7,and G. Reeves8

1Polar Geophysical Institute of the Kola Science Center, RAS, Apatity, Russia, 2Space Research Institute, RAS, Moscow, Russia,3Institute of Applied Physics, RAS, Nizhny Novgorod, Russia, 4Sodankylä Geophysical Observatory, Sodankylä, Finland,5Institute of Atmospheric Physics, ASCR, Prague, Czech Republic, 6Faculty of Mathematics and Physics, Charles University,Prague, Czech Republic, 7Department of Physics and Astronomy, University of Iowa, Iowa City, Iowa, USA, 8Los AlamosNational Laboratory, Los Alamos, New Mexico, USA

Abstract We report on simultaneous spacecraft and ground-based observations of quasiperiodic VLFemissions and related energetic-electron dynamics. Quasiperiodic emissions in the frequency range 2–6kHzwere observed during a substorm on 25 January 2013 by Van Allen Probe-A and a ground-based station in theNorthern Finland. The spacecraft detected the VLF signals near the geomagnetic equator in the night sectorat L=3.0–4.2 when it was inside the plasmasphere. During the satellite motion toward higher latitudes, the timeinterval between quasiperiodic elements decreased from 6min to 3min. We find one-to-one correspondencebetween the quasiperiodic elements detected by Van Allen Probe-A and on the ground, which indicates thetemporal nature of the observed variation in the time interval between quasiperiodic elements. Multiсomponentmeasurements of the wave electric and magnetic fields by the Van Allen Probe-A show that the quasiperiodicemissions were almost circularly right-hand polarized whistler mode waves and had predominantly small(below 30°) wave vector angles with respect to the magnetic field. In the probable source region of these signals(L about 4), we observed synchronous variations of electron distribution function at energies of 10–20keV andthe quasiperiodic elements. In the pause between the quasiperiodic elements pitch angle distribution of theseelectrons had a maximum near 90°, while they become more isotropic during the development of quasiperiodicelements. The parallel energies of the electrons for which the data suggest direct evidence of the wave-particleinteractions is in a reasonable agreement with the estimated cyclotron resonance energy for the observed waves.

1. Introduction

Quasiperiodic VLF emissions are wideband electromagnetic emissions in the frequency range 1–10 kHzwhich are characterized by a periodic or quasiperiodic modulation of wave intensity with typical periodsfrom tens of seconds up to a few minutes [see, e.g., Helliwell, 1965; Sazhin and Hayakawa, 1994]. It is thecommon point of view that generation of these signals results from the cyclotron interaction of whistlermode waves with energetic electrons of the radiation belts.

Ground-based and satellite observation demonstrated a wide variety of dynamic spectra of quasiperiodicemissions [e.g., Sato and Fukunishi, 1981; Pasmanik et al., 2004a]. Sato et al. [1974] proposed to dividequasiperiodic emissions into two classes: QP1 emissions that are related to geomagnetic pulsations withthe same period and QP2 emissions that do not correlate with the geomagnetic pulsations. Recent Clustersatellite observations confirm both these possibilities [Nemec et al., 2013].

An explanation of the QP1 emissions proposed by Coronity and Kennel [1970] and Kimura [1974] is based onthe modulation of the cyclotron instability growth rate by geomagnetic field line oscillations. As for the QP2emissions, they are usually explained in terms of the relaxation oscillations of the cyclotron instability[Bespalov and Trakhtengerts, 1976; Davidson, 1979] or the auto-oscillation regime proposed by Bespalov[1981] and further developed by Davidson [1986], Trakhtengerts et al. [1986], Demekhov and Trakhtengerts[1994], and Pasmanik et al. [2004b].

Quasiperiodic emissions are believed to be closely associated with pulsating precipitation of energetic(~5–50 keV) electrons into the ionosphere which, in turn, causes a certain class of pulsating auroras

TITOVA ET AL. VLF QP WAVES: GROUND AND VAP OBSERVATION 6137

PUBLICATIONSGeophysical Research Letters

RESEARCH LETTER10.1002/2015GL064911

Key Points:• Quasiperiodic VLF emissions weresimultaneously detected by RBSP-Aand on the ground

• Synchronous variations of energeticelectron distribution function and VLFwaves were observed

• Probable source region of thesesignals was identified

Correspondence to:A. G. Demekhov,andrei@appl.sci-nnov.ru

Citation:Titova, E. E., B. V. Kozelov, A. G. Demekhov,J. Manninen, O. Santolik, C. A. Kletzing,and G. Reeves (2015), Identification of thesource of quasiperiodic VLF emissionsusing ground-based and VanAllen Probessatellite observations, Geophys. Res. Lett.,42, 6137–6145, doi:10.1002/2015GL064911.

Received 11 JUN 2015Accepted 15 JUL 2015Accepted article online 16 JUL 2015Published online 4 AUG 2015

©2015. American Geophysical Union.All Rights Reserved.

typically observed during a recovery phase of a substorm [e.g., Johnstone, 1983]. Rocket-bornemeasurements ofsynchronous modulation of energetic electron fluxes and quasiperiodic VLF wave bursts were performed byGendrin et al. [1970]. Simultaneous detection of energetic-electron precipitation and quasiperiodic emissionswas reported by Hayosh et al. [2013] on the basis of low-orbiting DEMETER (Detection of Electro-MagneticEmissions from Earthquake Regions) data, which permitted them to estimate the transverse size of theprecipitation region. Correlation between pulsating aurora and THEMIS (Time History of Events andMacroscale Interactions during Substorms) spacecraft observations of VLF quasiperiodic emissions hasrecently been found by Nishimura et al. [2011]. Synchronous pulsations of energetic electron fluxes and VLFwave amplitude on board GEOS-1 (Goddard Earth Observing System version 1) and conjugate bursts of VLFwaves detected on the ground were found by Cornilleau-Wehrlin et al. [1978]. Jaynes et al. [2013] observedsynchronous quasiperiodic modulation of energetic-electron fluxes near the equatorial loss cone on boardGOES-13 spacecraft and auroral luminosity pulsations detected on the ground.

Note that such simultaneous observations are fairly difficult due to several reasons. For ground-basedobservations, the main difficulties are related to the long-range propagation of VLF waves in the Earth-ionosphere waveguide, which causes contamination of local measurements by signals from many distantsources, as well as the sensitivity of auroral observations to weather conditions. For low-orbitingspacecraft, the small size of precipitation patches is most likely the reason why simultaneous detection ofenergetic-electron precipitation and VLF waves is difficult. Equatorial observations, along with thenecessity to get into the source region of a restricted size, can require high pitch angle resolution becauseof the small size of the loss cone near which the largest flux variations can be expected. For example,Glassmeier et al. [1988] did not observe significant variations in the energetic-electron flux during aquasiperiodic event on board GEOS-2, which they explained by being slightly away from the generationflux tube.

At the present time, new possibilities for investigating mechanisms of generation of different types of VLFwaves including quasiperiodic emissions appear thanks to the measurement capabilities and orbitparameters of the Van Allen Probes (RBSP) spacecraft. Indeed, Van Allen Probes with a perigee of ~1.1 RE,apogee of 5.8 RE, and inclination of 10° [Mauk et al., 2012] are well situated to the analyses of quasiperiodicemissions which are most probably generated near the equator and are often observed inside or near theplasmapause [Engebretson et al., 2004; Manninen et al., 2014].

In this paper, we consider conjugate ground-spacecraft observations of quasiperiodic emissions during thenight on 25 January 2013 associated with a geomagnetic substorm. We use the RBSP-A spacecraft data inthe equatorial region and ground-based VLF wave data from Kannuslehto site in Finland. Comparing thisdata allows us to demonstrate temporal nature of the quasiperiodic variation in the VLF wave amplitudeobserved by RBSP-A in a wide range of L shells from about 3.0 to about 4.2. An analysis of the propertiesof the detected VLF waves including their polarization, planarity, and wave normal direction allows us toassume that the spacecraft crossed probable source location of these emissions near the geomagneticequator. We support this conclusion by reporting on the close relationship of the observed quasiperiodicemissions with the quasiperiodic variations in the flux and pitch angle distribution of energetic electronsdetected on board RBSP-A in the region which we identify as the wave source region.

2. Measurements

The wave measurements were made by the Electric and Magnetic Field Instrument Suite and IntegratedScience (EMFISIS) that provides data on DC magnetic fields and a comprehensive set of wave electric andmagnetic fields [Kletzing et al., 2013]. In the survey mode data, which is the only type of Van Allen Probeswave data used in this paper, the EMFISIS/WAVES instrument measures the wave power spectral densities,relative phases, and coherencies of three electric and three magnetic field components from 10Hz up to12 kHz every 6 s. The high-frequency receiver (HFR) of this instrument can measure the upper hybridfrequency, from which the plasma density can be calculated.

The particle measurements were made by the HOPE (Helium-Oxygen-Proton-Electron) mass spectrometerthat measures electron fluxes for energies from 10 eV to 50 keV [Funsten et al., 2013]. The HOPE sensormeasures the full plasma electron and ion distributions on alternate ~10 s intervals. For this study we usedHOPE electron data taken within ~18° of the satellite’s spin/antispin axis directions.

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Ground-based observations of VLF signals were carried out in Northern Finland at Kannuslehto site(67.74°N, 26.27°E; L = 5.3). VLF emissions were recorded in the frequency band 0.2–39kHz by using twomutually orthogonal magnetic loop antennas oriented in the north-south and east-west directions. The loopshave the sizes 3× 3m and effective area 2300m2. The sensitivity of the receiver is about 1 fT at a frequencyof 5 kHz, which is usually below the natural noise level. More detailed description of the hardware is given inManninen [2005]. The wide dynamic range of the receiver (up to 120dB) allows us to detect both very weakand intense signals.

3. Observations3.1. Quasiperiodic Emissions Detected on 25 January 2013 by Van Allen Probe-A(or RBSP-A) and on the Ground

Satellite- and ground-based data on VLF waves recorded from 22:55 UT on 25 January 2013 to 00:00 UT on26 January 2013 are summarized in Figure 1. The spectral power density of VLF waves measured on theground (Kannuslehto) is shown in Figure 1a. The magnetic field spectrogram obtained by the EMFISISWaves instrument on Van Allen Probe-A is shown in Figure 1b. Quasiperiodic emissions were detectedfrom 23:00 to 23:40 UT. During this entire interval, Van Allen Probe-A was located on the nightside(magnetic local time (MLT) about 22:15–23.36) near the magnetic equator (dipole magnetic latitudes�5.8°–7.9°) in a range of L shells 3.2–4.0. We determined the L values by dipole rescaling the measuredmagnetic field to the equator with the use of the spacecraft magnetic latitude. For the studied interval,this estimate coincided within ΔL= 0.05–0.1 with the values given by the T89 model line tracing[Tsyganenko, 1989]. The upper hybrid line emission recorded by the EMFISIS HFR (not shown) indicatesthat satellite remained inside the plasmasphere during the observation of quasiperiodic emissions.

At about 23:45 UT, the quasiperiodic event on board RBSP-A is interrupted by another strong waveintensification related with the satellite crossing of the region with strong cold plasma density inhomogeneities.

Figure 1. Quasiperiodic emission event on 25 January 2013. (a) Magnetic field dynamic spectrum of the quasiperiodicemissions observed at the ground-based station Kannuslehto. Frequency-time plots from the Van Allen Probes EMFISISof (b) the sum of the power spectral densities of three orthogonal magnetic components, (c) the ellipticity of the magneticfield polarization with a sign corresponding to the sense of polarization, (d) the planarity of the magnetic field polarization,and (e) the angle between the wave vector and the background magnetic field. Overplotted white or black lines show onehalf of the local electron cyclotron frequency obtained from the fluxgate magnetometer measurements.

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Quasiperiodic emissions were observed inthe frequency range from 2kHz to 6 kHz.It is seen that the time interval betweenquasiperiodic elements was 5–6min inthe beginning and then decreased to3min when the Van Allen Probe-A movedto higher L shells. To understand whetherthe decreasing quasiperiod of the quasi-periodic emissions is related to the chan-ging location of the RBSP-A spacecraft oris a temporal effect, we compare the spec-tra of VLF emissions recorded in space andon the ground.

The ground-based observations of VLF sig-nals were carried out in Northern Finlandat Kannuslehto station. Relative positionsof the satellite orbit and Kannuslehto sta-tion are shown in Figure 2. The thick linerepresents the ground projection of theVan Allen Probe-A trajectory along the

magnetic field lines in the Northern Hemisphere, where the quasiperiodic emissions were detected, and the pointmarks the Kannuslehto station. It is evident that Kannuslehto is located at a considerable distance of about2000km from the projection of the area where quasiperiodic emissions were detected by Van Allen Probe-A.

Figure 1a shows the dynamic spectrum of VLF signals in the frequency range 1–7 kHz observed from 22:55 UTon 25 January 2013 to 00:00 UT on 26 January 2013 at Kannuslehto. As we see, the quasiperiodic emissionevent detected at Kannuslehto on 25 January 2013 starts at the same time of about 23:00 UT as onboardRBSP-A, but then it was observed during a longer time interval and ended around 23:55 UT. Comparisonof the dynamic spectra of VLF signals in Figures 1a and 1b shows one-to-one correspondence betweenthe quasiperiodic elements on the Probe-A satellite and on the ground. The correlation coefficient forthe integrated VLF power in the band from 2100 to 6000Hz is R=0.75 for the time interval from 23:26 to23:45 UT. This means that the decrease of quasiperiodic emission quasiperiod had a purely temporal natureand was not related with the satellite motion toward higher L shells. The nonideal correlation between thesignals observed in space and on the ground can be explained by the distortion of the wave amplitudeenvelope which could be due to the propagation in the ionosphere and Earth-ionosphere waveguide.

Figures 1c to 1e show the results of multicomponent measurements of the VLF waves by RBSP-A. Figure 1cshows the ellipticity and sense of polarization of the wave magnetic field estimated by the singular valedecomposition (SVD) method [Santolik et al., 2002]. The results demonstrate that the quasiperiodicelements are mostly right-hand polarized. Figure 1d presents the SVD planarity of electromagnetic field[Santolik et al., 2003] quantifying how close is this field to a plane wave, and Figure 1e shows the wavenormal angle with respect to the geomagnetic field, obtained again from the SVD method [Santolik et al.,2003]. One can see that the waves propagate predominantly in the quasiparallel mode with the wavenormal angles below 30°, but for the two elements observed before 23:10 UT the fraction of obliquewaves (up to 50°) seems to be higher, as well as for the element observed at about 23:33. The planaritywithin the quasiperiodic elements is lower before 23:15 UT, and then it gradually increases till 23:33 UT. Inaddition, Figure 1b shows that the maximum amplitude of quasiperiodic emissions was observed for thevery first element at 23:00, and then after 23:20 UT (at L> 3.6). Below we discuss possible significance ofthese facts for inferring the source location of the observed VLF waves.

3.2. Relationship of Quasiperiodic Emissions With Electron Measurements on Board Van Allen Probe-A

The quasi-periodic event on 25 January 2013 was observed during a substorm when Van Allen Probe-A waslocated in the night sector and remained inside the plasmasphere. Intense injection of electrons associatedwith this substorm was observed by Van Allen Probe-A. During the active phase of the substorm there wasenhanced dawn-dusk electric field in the magnetosphere; therefore, the electrons of the substorm

Van AllenProbe-A

Kannuslehto

25 January 2013

23:00 UT

23:40 UT

66

60

54

48-24 -8 0 16 24 328-16

Figure 2. The map showing the relative positions of the geomagneticprojection of the part of Van Allen Probe-A orbit at which the quasiper-iodic emissions were detected (thick line) onto the Earth’s surface, andground station Kannuslehto (point).

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injection moved toward the Earth and are able to penetrate into the lower latitude plasmasphere (see, e.g.,Turner et al. [2015] for studies of similar injection events).

Figure 3a shows the energy spectrogram of spin-averaged electron flux measured by HOPE on board Van AllenProbe-A. High fluxes of low-energy electrons <10 keV can be seen up to low L=2.5. The L shell of the low-latitude boundary increases with increasing energy as is expected for the particles drifting in the convectionelectric field. The behavior of more energetic electrons is different; i.e., the polar boundary of electrons withenergies above 10 keV decreases with decreasing energy. Such a behavior is typical for the energeticelectrons trapped by the Earth’s magnetic field. Figure 3b shows a pitch angle spectrogram of ~ 7.6–35.9 keVelectrons versus time for the considered event, in which a maximum of electron flux near 90° is clearly visible.The time interval of quasiperiodic emission observation is marked by a magenta line in Figure 3c. Thus, theelectron distribution function had a transverse anisotropy in the region where quasiperiodic emissions wereobserved, with the electron flux decreasing sharply for pitch angles below 70°–60°.

The ratio of electron fluxes at the pitch angles 90° and 54° for energies from 5 to 50keV is shown in Figure 3c. Thisratio roughly characterizes the electron anisotropy, and it reaches 2–3 in the regionwhere quasiperiodic emissionswere observed by Van Allen Probe-A. Themaximum value of this ratio was recorded in the energy range 1–50keVduring the time interval 23:00–23:20 UT corresponding to L from about 3.0 to about 3.6. Later on it decreasedslightly in the energy range 10–20keV but still remained high enough at lower and higher energies. So, basedon the rough anisotropy characteristics, we can assume the possible location of the wave source in the entireregion where RBSP-A observed the quasiperiodic emissions, i.e., from 23:00 to 23:40. To place additionalconstraints on the source location, we try to identify the region of most effective wave-particle interactions byanalyzing the temporal variations of the electron pitch angle distribution on a timescale of quasiperiodic signals.

This analysis shows that the pitch angle distributions of energetic electrons measured by RBSP-A did not exhibitnotable variations until about 23:20 UT. However, such variations were recorded by the HOPE instrument after23:20 UT. Figure 4 presents the comparison of the flux bursts of 10–20 keV electrons with pitch angle 90° (4a)and quasiperiodic elements (4b) on 25 January 2013 during the interval 23:26–23:34 UT, which correspondedto L varying from about 3.8 to about 4.05. Two increases of fluxes of electrons with energies of 10 to 22 keVare clearly seen around 23:27 UT and 23:31 UT. After each increase the characteristic electron energydecreases to 10 keV, reaching the minima at about 23:28 UT and 23:33 UT. Importantly, each flux increase of

Figure 3. (a) Energy spectrogram of spin-averaged electron flux measured by HOPE on Van Allen Probe-A. (b) The pitchangle versus time spectrogram of electrons in the energy range ~ 7.6–35.9 keV. (c) The ratio J(90°)/J(54°) of the electronfluxes at the pitch angles 90° and 54° which characterizes the anisotropy of the electron distribution. The magenta linemarks the time interval of quasiperiodic emission observation.

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20 keV 90° electrons was detected during the pause between the quasiperiodic elements, and the decreases ofthe characteristic energy in the electron spectrum were observed simultaneously with the increase of waveamplitude and frequency, i.e., during formation of the quasiperiodic element.

Figures 4c to 4f show the pitch angle distributions of the electrons outside (c, e) and during (d, f)quasiperiodic elements. It is seen that the 10–20 keV electrons had a pronounced transverse anisotropy inthe absence of the waves (Figures 4c and 4e). Quasiperiodic element development was accompanied bythe isotropization or the disappearance (Figures 4d and 4f) of 10–20 keV electrons. We think it is a verystrong indication of pitch angle diffusion caused by the recorded VLF quasiperiodic emissions.

Figure 4. Comparison of electron distribution function and quasiperiodic emissions detected by Van Allen Probe-A on25 January 2013 during the interval 23:26–23:34 UT. (a) Energy spectrogram of the electron flux with pitch angle near90° measured by HOPE. (b) Frequency-time plot of quasiperiodic elements from EMFISIS. Electron pitch angle distributionstaken (c, e) between and (d, f) during quasiperiodic elements.

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4. Discussion and Summary

Consider how the presented data set allows us to identify the probable location of the source region of theobserved quasiperiodic emissions. They were detected by Van Allen Probe-A near the geomagnetic equatorduring 40min from 23:00 UT to 23: 40 UT. During this time the spacecraft moved from L= 3.0 to L=4.2, andthe time interval between the quasiperiodic elements decreases from 6 to 3min. At the same time, thesequasiperiodic emissions were also observed at the ground-based site at Kannuslehto located in NorthernFinland (L=5.3), i.e., at higher L and about 2000 km from the field-aligned projection of the zone wherethey were detected by RBSP-A (see Figure 2). So distant detection of quasiperiodic emissions on theground was probably related due to their propagation in the Earth-ionosphere waveguide. This isconsistent with the polarization parameters of VLF signals detected on the ground (not shown for brevity)which imply their probable arrival from the south or southeast direction.

Comparison showed one-to-one correspondence between the quasiperiodic elements on board thespacecraft and on the ground and similarity of their spectrum, which proves that the variation in therepetition interval of quasiperiodic elements was not related to the spacecraft motion in space but waspurely temporal. Probably, this means that there was a single source of quasiperiodic emissions during theconsidered time interval. Moreover, since the plasma parameters measured by Van Allen Probe-A changeddrastically during the interval of quasiperiodic detection (the plasma density and magnetic field decreasedby a factor of 4–5), we think that the quasiperiodic source region was smaller than the region of theirspacecraft detection. The source probably evolved or perhaps even moved during the event, whichresulted in the gradual change in the wave frequency and the interval between the quasiperiodic elements.

The VLF measurements give some hints to restrict the probable source location, but these hints are ratherweak. Indeed, the polarization of VLF waves is close to circular in all quasiperiodic elements, and the wavenormal angle and planarity do not reveal drastic changes during the event, as well as the wave amplitude.Somewhat higher amplitudes are observed for the very first quasiperiodic element starting at 23:00, aswell as for the five elements observed from 23:20 to 23:40. One can also argue that the wave normalangles for these elements are on average smaller, which could be an indication of the closeness to thesource region. However, one of these elements (started at about 23:33) shows the largest observed wavenormal angles in its low-frequency part. Therefore, the wave normal angles being mostly less than 30° onlysuggests, in general, that the measurements had to be relatively close to the generation region but doesnot help us to determine this region more precisely.

The evolution of energetic electrons observed on board RBSP-A simultaneously with the quasiperiodicemissions seems to give stronger evidence that the emission source was located at L shells crossed byRBSP-A after 23:20. In this region, the pitch angle and energy distributions of 10–20 keV electronsdemonstrated close correlation with the quasiperiodic elements, as is shown in Figure 4. Specificfeatures of the detected variations in the electron pitch angle distribution are as follows: (i) theyoccurred repeatedly for two subsequent quasiperiodic elements and two pause intervals between them,and (ii) they generally agree with the variations expected in the region where auto-oscillations of thecyclotron instability take place. i.e., the pitch angle anisotropy increased in between the quasiperiodicelements and then decreased during the intervals of wave generation [e.g., Trakhtengerts and Rycroft,2008]. During the development of quasiperiodic elements the characteristic energies of electronsdetected by HOPE gradually decrease from 20 to 10 keV (cf. Figures 4a and 4b), and the pitch angledistributions of 5–20 keV electrons become more isotropic (Figures 4d and 4f). The isotropization wasprobably caused by the pitch angle diffusion due to the interaction with the detected VLF wavesforming quasiperiodic elements, and increasing frequency of a quasiperiodic element from 2 to about6 kHz could be related to a decrease in the electron energy.

We calculated the parallel energiesWres of electrons which are in the fundamental cyclotron resonance withthe observed VLF waves at the equator near the center of the anticipated source of the quasiperiodicemissions at L~ 4.02 which was reached by the spacecraft around 23:33 UT. At this time the local plasmadensity was estimated as Nc = 399.5 cm�3 by using the upper hybrid frequency fUH ~ 1.8 × 105 Hz from theEMFISIS HFR spectra (not shown here for brevity) and the electron cyclotron frequency fce = 14.6 kHzobtained from the fluxgate magnetometer measurements. Assuming that Nc is proportional to B andusing the equatorial electron gyrofrequency fce eq = 13.45 kHz, we obtain Wres = 3.1 keV for the frequency

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of maximum intensity f = 3 kHz and Wres = 5.8 keV for the lower frequency of quasiperiodic elementsf= 2.1 kHz. For pitch angles about 50–70° this gives total energies of about 7.5–26 keV for f = 3 kHzand 14–50 keV for f = 2.1 kHz. These estimates agree fairly well with the range 5–20 keV for which thevariations correlated with waves are seen most clearly, as well as for typical values calculated, e.g., byRycroft [1972, 1976]. Note that for the region of smaller L = 3.0–3.6 crossed by the RBSP-A from 23:00to 23:20, the parallel resonant energies are above 12 keV, which means that total energy of resonantelectrons is certainly above 25 keV. The fluxes of such electrons were rather low in the observedenergy spectra, which also makes this region unfavorable for the source of the detected quasiperiodicemissions. More detailed calculations of both the growth rates and pitch angle diffusion coefficientsfor this event are worth doing but it falls beyond the scope of this paper and will be the subject forfuture work.

Note that it is rather difficult to identify nonstationary processes of wave-particle interactions in the electrondistribution functions. Fennell et al. [2014] observed and pronounced a difference between the pitch angledistributions of 17–26 keV electrons during a sporadic burst of VLF chorus and in the absence of VLF waves,i.e., before the burst. The electrons had the butterfly pitch angle distributions during the burst, while theirdistribution was peaked at 90° before the burst. It was not clear from those data whether the distributionvariation was produced by the waves or conversely it was a cause of the wave generation. In our case, theevolution of the distribution function of energetic electrons was most probably caused by pitch anglediffusion related with the VLF wave excitation.

As we mentioned above, the quasiperiodic emissions were observed over a wide range of L shells fromabout 3.0 to about 4.3, which is much wider than the region suitable for the generation of these VLFwaves. On the other hand, the waves were almost circularly polarized in the entire observationregion, and the propagation angles were fairly small. This can mean that good conditions for guidedwave propagation and their reflection from conjugate ionospheres existed in the considered event. Inthis case, the VLF waves can repeatedly return to the near-equatorial region while remaining inalmost the same flux tube, which is important for their amplification. At the same time, the VLF waverefraction in the magnetosphere results in the predominant shift of their trajectories to lower L[e.g., Shklyar and Jiricek, 2000], and this seems important for explaining their detection at rather low Lshells in our case.

The time scales of both the wave bursts and the pauses between them exceed by far the whistler mode wavebouncing period in the magnetosphere, which indicates that the instability develops in the regime involvingwave reflections from the ionosphere. There is a question whether some plasma density irregularities, whichcould provide wave ducting, existed in the generation region. Rather large repetition interval between thequasiperiodic elements indicates a long time needed for accumulating enough anisotropic energeticparticles in the generation region, which implies the low quality of magnetospheric resonator for VLFwaves. Note that auto-oscillations of the cyclotron instability can exist exactly in the case where theresonator quality is low enough [e.g., Trakhtengerts and Rycroft, 2008].

In summary, we presented Van Allen Probe observations of correlated variations in the VLF wave spectraand energetic-electron distributions during a VLF quasiperiodic emission event on 25 January 2013. Theobserved variations were not accompanied by magnetic pulsations in the source region, i.e., thequasiperiodic event belongs to the QP2 type and, therefore, could be formed due to the auto-oscillationmechanism of the cyclotron instability. The same quasiperiodic emissions were detected at a ground-based site in Northern Finland, and the one-to-one correspondence of the wave spectra measured inspace and on the ground allowed us to prove the temporal nature of the observed slow variation in thefrequency range and frequency drift of the quasiperiodic elements. Comparing the wave properties andelectron distribution during the event allowed us to identify the region of L = 3.9–4.2 crossed by thespacecraft from 23:30 to 23:40 as the probable location of quasiperiodic emission source. In this region,the pitch angle and energy distributions of 5–25 keV electrons showed synchronous variations with thequasiperiodic elements. Such variations are consistent with the development of cyclotron instabilityauto-oscillations, i.e., an increase in the electron anisotropy and energy during the pause and a decreaseduring the flash. However, a detailed study of the formation mechanism of the detected quasiperiodicVLF signals is required and will be the subject of future work.

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AcknowledgmentsVan Allen Probe data used in this papercan be found in the EMFISIS (http://emfisis.physics.uiowa.edu/data/index)and ECT (http://www.rbsp-ect.lanl.gov/rbsp_ect.php) archives. The ground-based data for this paper are availableon request from Sodankylä GeophysicalObservatory (contact J. Manninen). E.T.,B.K., and A.D. thank the Russian ScienceFoundation for funding the work on thispaper under grant 15-12-20005 andthe Sodankylä Geophysical Observatoryfor hosting their visits during which thedata for this study were selected. O.S.acknowledges funding from grantsP209-11-2280, LH14010, and PremiumAcademiae. The work of C.K. waspartially supported by JHU/APL contract921647 under NASA Prime contractNAS5-01072. Processing and analysis ofdata from the RBSP-ECT (EnergeticParticle, Composition, and ThermalPlasma) instruments was supported byfunding under NASA Prime contractNAS5-01072.

The Editor thanks Michael Rycroft and ananonymous reviewer for their assistancein evaluating this paper.

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