Lower hybrid waves observed at the dayside polar region: SS-520-2 rocket experiment



[1] The SS-520-2 rocket experiment was carried out over Ny-alesund, Svalbard, Norway, in the dayside polar region. The onboard Plasma Wave Analyzer (PWA) succeeded in observing waveform data in the 10 Hz to 15 kHz frequency range and high frequency spectrum data up to 3 MHz. These data showed impulsive packet-like waveforms with frequencies around 3 kHz to 4 kHz as well as auroral hiss emissions. The packet-like waveforms appeared for the duration of 100–500 ms, and the frequencies of their spectral peaks were well below the lower cutoff frequency of the auroral hiss emissions. Their polarizations, which were identified on the rocket spin plane perpendicular to the ambient magnetic field, were almost linear. The most plausible wave mode is the lower hybrid wave. The PWA has the capability to identify the wave propagation direction and to estimate the corresponding phase velocity using the onboard interferometry system. From the cross correlation in the interferometry system, we estimated the phase velocity of the packet-like waves to be about 60 km/s. To examine the generation mechanism of the observed lower hybrid waves, we conducted linear dispersion analyses using realistic parameters. Since there was poor correlation between the plasma measurements and the lower hybrid waves, we expect the rocket traversed out of the generation region. As the generation mechanism, we propose the lower hybrid waves excited by electron beams. We calculate the linear dispersion with the existence of electron beams and show the lower hybrid waves are destabilized by electron beams. Under the assumption of an electron beam in the generation region, we found that waves in the frequency range around 3 kHz to 4 kHz were excited with the maximum growth rate just below the lower hybrid resonance frequency. Their frequency was in good agreement with the packet-like waves.

1. Introduction

[2] In this paper we discuss the VLF waveform data which were obtained at about 1000 km altitude in the polar region by the Plasma Wave Analyzer (PWA) onbord the SS-520-2 rocket experiment. The experiment was conducted with the Institute of Space and Astronautical Science (ISAS) in Japan in an attempt to investigate the acceleration and heating mechanism of heavy ions in the cusp region. The rocket was launched at 09:16 UT on December 4, 2000, in Ny-Alesund, Svalbard, Norway (78.55°N, 11.55°W).

[3] The maximum altitude reached was 1108 km and the observation time period was 1150 seconds. From the trajectory of the rocket and from data from another satellite, it was determined that the rocket passed to the north of the cusp region. Thus we obtained data from the dayside polar auroral region.

[4] Over the past three decades several satellite and rocket experiments have studied plasma wave emissions above and below auroral hiss [e.g., Mosier and Gurnett, 1969]. The lower cutoff of the VLF auroral hiss usually shows a sharp lower cutoff at the local lower hybrid frequency fLHR. Along with the VLF auroral hiss, the lower hybrid emissions have also been observed and studied. The lower hybrid waves as the monochromatic spikelets were first identified in the topside auroral ionosphere by LaBelle et al. [1986]. They report that the “spikelets”, which were observed by MARIE sounding rockets, were detected in about 35 events with an average timescale of 5 ms and an average amplitude of 100 to 150 mV/m. Their frequency varied between 7 and 18 kHz. By simulating a nonlinear three-dimensional fluid model, Seyler [1994] studied about the “spikelet” wave as the lower hybrid wave. The plasma density depletion is associated with the lower hybrid resonance and a density cavity concentrates lower hybrid wave energy.

[5] Pincon et al. [1997] argued that the lower hybrid waves produced by auroral electrons can collapse spatially owing to a modulational instability and that very intense and localized lower hybrid waves with short wavelengths are generated, which interact with the cold ionospheric ions to produce transversely accelerated ions(TAI). They showed that the Lower Hybrid Solitary Structures (LHSS), which were observed by the AMICIST sounding rocket, are electrostatic wave modes which rotate in a right-handed sense about the magnetic field above fLHR. They also suggested that the LHSS is probably the result of the linear mode conversion or resonant scattering of the background VLF auroral hiss to linear eigenmodes of the preexisting density cavities. The LHSS events typically last 20 ms and the amplitudes of LHSS varied around 10 to 50 mV/m. Bonnell et al. [1998] also studied narrowband features below fLHR as an electric field eigenmode within a density depletion. They studied the rotation of the electric field in the frequency around fLHR observed by the PHAZE2 rocket. They measured the electric field in the plasma at two spatially separated points which allowed them to estimate the spatial structure of that electric field interferometrically. The actual LHSS events lasted 20 ms and they suggest that the LHSS are composed of right-handed (left-handed) rotating electric fields above (below) fLHR. For finding out the generation mechanism, Kintner [1980] also suggests that TAI could directly produce a similar looking electrostatic emission if the ions form a ring in velocity space. On the contrary, several reports show that these emissions are destabilized by auroral electron beams. Ashour-Abdalla et al. [1988] show that the addition of heavy ions with an electron beam excites the lower hybrid waves and the hydrogen cyclotron harmonics in the auroral region. In the high-altitude auroral zone, sounding rockets show that ion cyclotron harmonics damping has occurred in the VLF auroral hiss spectrum [Kintner et al., 1991]. Kintner et al. [1991] suggest that the electrostatic VLF waves, existing with structure at the H+ gyrofrequency, occur in the presence of precipitating auroral electrons, though there is not a strong one-to-one correlation with electron fluxes.

[6] In the present paper, after a brief introduction of the PWA system onboard SS-520-2 rocket, we discuss the packet-like emissions observed in the frequency range between 3 kHz and 4 kHz by examining the VLF waveform data and spectra data. The timescale of the packet-like emissions is about 100 ms, and the average amplitude is about 1–2 mV/m. We have very few electron and ion particle data correlated with plasma wave data and very rough estimation about the ion components. From our estimation about the local fLHR, the waveforms which we are focusing on are lower hybrid waves. From the interferometry mode in our receiver, we can determine the direction of the phase velocity of the waves. We show that the specific packet-like waves do not rotate in phase space and the direction of the waves is from the same direction as the cusp region.

2. Plasma Wave Analyzer (PWA)

[7] Figure 1 shows the configuration of the PWA sensors. For the electric field measurement, we used two-sets of 10 m tip-to-tip orthogonal wire antennas, and for the magnetic field measurement, a loop antenna was installed. Since the rocket spin axis relative to the earth's geomagnetic field line was less than 12 degrees throughout the flight, the wire antennas observed the electric field components almost perpendicular to the ambient magnetic field.

Figure 1.

PWA antennas. For the electric field, a 10 m tip-to-tip X-axis dipole antenna and two 5 m Y-axis monopole antennas were installed. For the magnetic field, a trapezoidal loop antenna (longer side is 55 cm) was installed.

[8] The PWA system consists of five sets of receivers as shown in Table 1. The waveform capture receivers are able to observe one component of the electric field waveforms up to 15 kHz (VLF Direct E, VLF Memory E) and one component of the magnetic field waveforms up to 1 kHz (VLF Direct B), simultaneously. While the VLF Direct E receiver uses one pair of orthogonal antennas as a dipole antenna, the VLF Memory E receiver uses the other pair of antennas as two monopole antennas. This allows us to examine the phase difference of waveforms observed by the individual monopole antennas in the interferometry mode. Because of the restriction of the telemetry capacity, we had to compress the observed electric field waveform data to a total amount that was less than 25% of the real time base. Iwai [2001] proposed the application of the subband coding method for the waveform data compression in space missions. Since this technique offered a high performance way to compress the waveform data, we adopted this method for the real time data compression process of the PWA. However, even with the use of this method, the amount of the two axis electric field component data was beyond the capability of the telemetry. To overcome this, we used the onboard Synchronous Dynamic Random Access Memory (SDRAM) to store one axis electric waveform data (VLF Memory E) for 360 seconds. At 410 seconds from the launch, VLF Memory E automatically began to store the observed waveform data in the interferometry mode to the onboard SDRAM. At 770 seconds from the launch, VLF Direct E and VLF Memory E ceased their observations and the data playback sequence of the stored VLF Memory E data began. We determined these time points from the expected apex time (590 seconds from launch). The actual apex time was 601 seconds.

Table 1. PWA Onboard Receiversa
ReceiverFrequency RangeDataS/H RateRemarks
  • a

    Except for the HF receiver, all of the receivers are waveform receivers. Data from the VLF electric field receivers are compressed by the subband coding method. The VLF Memory E receiver used two monopole antennas for its sensors.

VLF Direct E10 Hz–15 kHzwaveform45 kHzSubband coding, dipole (X axis)
HF10 kHz–3 MHzspectrum9 MHzDigital Sweep receiver, dipole (X axis)
EFD0 Hz–50 Hzwaveform150 Hzdipole (X, Y axis)
VLF Memory E10 Hz–15 kHzwaveform45 kHzSubband coding, monopole (Y axis x 2)
VLF Direct B10 Hz–1 kHzwaveform3 kHzμ-CODEC, Loop antenna

[9] The high frequency spectrum analyzer (HF) covered the frequency range from 10 kHz to 3 MHz. In the past, the conventional spectral receiver was the hetherodyne type sweep frequency receiver. For the HF receiver on the PWA, we developed a new digital sweep frequency receiver using a Programmable Down Conversion (PDC) chip. Since the PDC has the capability to perform a frequency conversion digitally, a very light weight frequency receiver was able to be developed. This HF receiver has successfully provided high time and frequency resolution data [Ueda et al., 2001; Iwai, 2001; Hashimoto et al., 2003].

3. Observation Results

[10] In this section, we discuss the electric field waveform data observed by the VLF Direct E and VLF Memory E receivers. The upper panel of Figure 2 shows the frequency-time spectrogram obtained from the VLF Direct E data by performing FFT calculations. The FFT was calculated using 4500 data points and no overlapping. The time period shown is from 460 seconds to 465 seconds in the flight time and the altitude of the rocket is almost 1100 km during this period. The time and frequency resolutions in this plot are 100 ms and 10 Hz, respectively. In the lower panel, we show the waveform data plotted in 250 ms segments. The waveform data was frequency filtered between 3 kHz and 4 kHz. Two kinds of spectral features are evident in Figure 2. One is auroral hiss with bursty amplitude structure. The auroral hiss is continuously observed in the frequency range above 5 kHz during the whole period. However the hiss intensities are not continuous. They are abruptly intensified. The other spectral feature is the short timescale intensity phenomena (identified by the circle) below the lower cutoff frequency of the hiss spectra. The frequency range is almost 3–4 kHz and the observed time begins around 461 seconds after launch. We see that these packet-like waves continued for nearly a second.

Figure 2.

VLF Direct E spectra data at 460–465 seconds from launch and 250 ms segments waveform data from 461–462 seconds. Magnetic Local time was about 12.9 h. Invariant latitude was about 76.7 degrees. Altitude was almost 1100 km. The dotted circle highlights the bursty emissions observed below the auroral hiss spectra around 461–462 seconds. The frequency range is almost 3 kHz to 4 kHz (Figure 3).

[11] To investigate in detail these emissions observed below the lower cutoff frequency of the hiss spectra, we focus on the VLF Direct E waveform data observed in the period of 461.525–461.6 seconds after launch as shown in Figure 3. The first panel shows the frequency spectra in the period of 461–462 seconds obtained by FFT calculations with 45000 samples and no overlapping. The other three panels show a series of the snapshots of the electric field waveforms plotted in 25 ms segments. The displayed waveforms are the result of filtering the observed waveforms in the frequency range of 3 kHz to 4 kHz. The filtered waveform data (3–4 kHz) show the packet-like waveform features prominent during the period of 461.525 seconds to 461.6 seconds. Since the lower cutoff of the auroral hiss spectra is located around the fLHR, one of the plausible wave mode of the observed packet-like waves is the lower hybrid wave. The TSA (Thermal and Suprathermal ion Analyzer) onboard the SS-520-2 rocket observed mostly oxygen ions during the flight (private communication with A. Yau). Unfortunately, the density ratio of oxygens and protons is unclear. However, we can roughly estimate the fLHR by making an assumption on the density ratio of protons and oxygens.

Figure 3.

VLF waveform data and corresponding spectra. The first panel shows the VLF spectra data observed at 461–462 sec after launch. The other three panels show the corresponding filtered (3–4 kHz) electric field waveform data with 25 ms segments.

[12] Usually, the approximate fLHR is calculated as

equation image

where fce, fci and fpe indicates the electron cyclotron frequency, ion cyclotron frequency, and the electron plasma frequency, respectively. If we assume that there are several component of the ions, The lower hybrid resonance frequency fLHR is calculated as

equation image

where α means the number of the ion components and Aα means the density ratio of ions. We show the local fLHR, with the assumption of H+ and O+ ions, calculated from equation (2) as green dashed arrows in the first panel as the proton to oxygen ion ratio varies between 5% and 10%.

[13] For reference, we plot the proton cyclotron harmonic frequencies as blue vertical dashed lines in the first panel. The proton cyclotron frequency was determined by the ambient magnetic field observed by MGF (MaGnetic Field instrument) onboard the SS-520-2 rocket. We see that the peak of the spectra almost corresponds to the 6th harmonic of the proton cyclotron frequency (N = 6) (indicated by a red arrow).

[14] To investigate the assumed lower hybrid waves at 3–4 kHz in detail, we focus on two events centered near 461.4 seconds and 461.5 seconds. For each event, the peak frequency of lower hybrid waves is determined to be 3.18 kHz (461.4s) and 3.49 kHz (461.5s) from the FFT calculations. For these two events, we examine the polarization on the electric field antenna plane using the two components of the observed waveforms.

[15] The two panels in Figure 4 show the polarization on the electric field sensor plane for the two different time periods. Since the rocket spin axis relative to the ambient magnetic field was less than 12 degrees throughout the flight (mentioned in section 2), these polarizations are almost equivalent to those on the plane perpendicular to the ambient magnetic field. In order to examine the polarization in the fixed plane, the horizontal axis is defined in the direction along the ambient magnetic field projected onto the electric field antenna plane. In both panels, the directions of the X-axis WANT connected to VLF Direct E receiver and of Y-axis WANT connected to VLF Memory E receiver on the E1E2 plane are displayed by the dashed and dotted lines, respectively. Since both panels show the lower hybrid waves to be almost linearly polarized, we can assume the lower hybrid waves are quasi-electrostatic.

Figure 4.

Polarization at 461.4s and 461.5s. The gray arrows show the absolute wave normal direction projection onto the the electric field antenna plane.

[16] By calculating the cross correlation of the waveforms detected by the two monopole antennas which comprise the Y-axis WANT, we can estimate the phase velocity of the lower hybrid waves. We calculated the cross correlation for the same events at 461.4 seconds and 461.5 seconds. Since the time lag of the maximum correlation values was 8.89 × 10−5 seconds for both cases, we can estimate that the phase velocity projected onto the Y-axis is 56.25 km/s. From the wave normal direction projection onto the electric field antenna plane, plotted as a gray arrow in each polarization plot, we can convert the phase velocity onto the sensor plane. Each phase velocity was converted as 63 km/s and 62.04 km/s, respectively. The wave normal direction in each panel was almost the same. On a similar rocket experiment in the dusk side auroral region, Ergun et al. [1991] determined that the phase velocity near the LHR frequency (almost 3 kHz) was about 35 km/s.

[17] After determining the wave normal directions on the electric field antenna plane, we plot them together with the trajectory of the rocket in Figure 5. In Figure 4, the horizontal axis is defined in the direction along the ambient magnetic field projected onto the electric field antenna plane, which is almost perpendicular to the ambient magnetic field. We can roughly estimate the absolute wave-normal directions in geographical coordinates by referring to the IGRF model.

Figure 5.

Rocket trajectory and wave propagation directions. From the observation results, we recognize that the rocket passed by the cusp (large black circle). The directions of the wave normal were almost identical.

[18] We roughly estimate the cusp location based on the plasma measurements to be as shown in Figure 5 (Y. Saito and H. Tanaka, private communication). The dashed line in Figure 5 shows the coordinates of the terrestrial magnetism. The small circles on the rocket trajectory show the observation points of the lower hybrid waves below the auroral hiss. The wave normal directions of the observed lower hybrid waves at 461 seconds from launch are almost identical.

4. Discussion and Conclusions

[19] Seyler [1994], by using three-dimensional fluid simulations, shows that density depletions modify the homogeneous linear properties of lower hybrid waves and account for many of the observed features of lower hybrid spikelets. Pincon et al. [1997] and Bonnell et al. [1998] investigated the LHSS with the acceleration of the TAI and density depletions. They suggested that the LHSS are composed of the rotating electric fields around the fLHR. An average duration time of the LHSS is abount 20 ms and an amplitude is about 10–50 mV/m. Though the density depletion and TAI in the observation region may be one of the mechanisms to enhance the lower hybird emissions we are reporting, we did not find any correlation between observed lower hybrid waves and the plasma data. This poor correlation suggests that the rocket did not pass through the generation region of the lower hybrid waves. Thus, we can conclude that the observed waves are not LHSS. Further, we do not find the electric field rotation. The timescale of the packet-like waves is more than 100 ms, and the average amplitude is much less than that of LHSS. As shown in Figure 4, the direction of the phase velocity is determined specifically.

[20] From our observation results, we point out that the most plausible mode of the observed waves are LH waves, since the frequency range is below the auroral hiss and polarization is almost linear on the antenna plane, which is almost perpendicular to the ambient magnetic field. By the computer simulations, Ashour-Abdalla et al. [1988] demonstrate that the existence of heavy ions and the electron beam can excite the LH waves and the hydrogen cyclotron harmonics. However, we did not find any correlation between observed LH waves and plasma data. This poor correlation suggests that the rocket did not pass through the generation region of the LH waves.

[21] In order to examine the generation mechanism of the observed LH waves, we apply the generation model proposed by Ashour-Abdalla et al. [1988] to the results of our rocket experiment. We conducted the linear dispersion analyses using the realistic parameters displayed in Table 2.

Table 2. Parametersa
  • a

    The upper panel (Ωe, equation image, and ωe) shows the observed parameters obtained by the flux gate magnetometer and the impedance probe. The lower panel shows the inferred parameters based on Kintner et al. [1991].

Observed Parameters
Electron cyclotron frequency Ωe1.0146 MHz
Proton cyclotron frequency equation image557.106 Hz
Electron plasma frequency ωe1.1660 MHz
Inferred Parameters
Ion ratio(proton & oxygen)nH is 5% of nO
Electron thermal energy Te0.5eV
Proton thermal energy Th10eV
Oxygen thermal energy TO2eV
Electron beam velocity1.0274 × 107m
Electron beam ratio10% of background electron
fLHR4.2085 kHz
Wave normal angle89.69 degree

[22] The parameters calculated from the observations results are the electron cyclotron frequency, the proton cyclotron frequency, and the electron plasma frequency, which are listed in the upper panel. They can be obtained by the data from the flux gate magnetometers and the impedance probe. On the other hand, since we do not have enough data of plasma measurements correlating with observed LH waves, we make use of the plasma parameters observed by another rocket experiment at almost the same altitude of the polar region [Kintner et al., 1991], which are listed in the lower panel of Table 2.

[23] Figure 6 shows the model of the velocity distribution functions in our linear analyses. According to the model by Ashour-Abdalla et al. [1988], we define the background plasmas consist of electrons, protons and oxygen ions as well as electron beams with the drift energy, which is much larger than the thermal velocities of background plasmas. Figure 7 is the ω − k diagram in the case of the wave normal direction of 89.7 degree. The upper and lower panels show the real part and imaginary part solutions of the linear dispersion, respectively. Note that LH+ means the Larmor radius of proton.

Figure 6.

The model of the velocity distribution.

Figure 7.

Linear dispersion relation. The positive growth rate existed below the local LHR frequency (horizontal black dashed line in the upper panel). The frequency value in vertical axis is normalized by proton gyrofrequency equation image, and the wave normal value in the transverse axis is normalized by the proton larmor radius equation image. Vertical black broken line shows the maximum growth rate. Gray lines show the proton cyclotron harmonics without the positive growth rate.

[24] The dispersion curve with the positive growth rate is indicated as black line and the proton bernstein mode without positive growth rate are plotted as gray lines. Gray dashed oblique line in the upper panel mean the electron beam velocity which is projected to the wave normal direction. For this model, the LHR frequency can be calculated as 4.2 kHz (= 7.539equation image). The growth rate reaches its maximum in the frequency just below the LHR frequency. The frequency in the maximum growth rate γ is about the equal to 3.64 kHz (= 6.5420equation image), which means that the harmonic number is almost equal to 6–7. The phase velocity is about 44 km/s. These values agree with the observation results introduced in the section 3. Of course, we assume the plasma parameter listed in Table 2 because of the poor correlation of observed LH waves and plasmas. However, the model and parameters are very typical and reasonable for the analysis of phenomena taking place in the polar region. Therefore, we believe that this is one of the most plausible model for the excitation of the LH waves observed by SS-520-2 rocket experiment. In this rocket experiment, we did not find the clear correlation between the observed LH waves and plasma measurements. However the wave intensities are relatively high, the source region of the waves is not so far from the observation points. We hope to have the chance to observe the source region in order to conclude the generation mechanism of these LH waves.


[25] We greatly appreciate the efforts of the ISAS SS-520-2 rocket team members, the EISCAT Radar team and Meiwa System Co., Ltd. We thank Roger R. Anderson for his great help and useful comments. This research is supported by Japan Science and Technology Corporation (ACT-JST, 12D-1). We also thank T. Hada of Kyushu University for his help in the linear dispersion analysis.