The High-Bandwidth Auroral Rocket (HIBAR) was launched from Poker Flat, Alaska, on 28 January 2003 at 07:50 UT towards an apogee of 382 km in the nightside aurora. The flight was unique in having three high-frequency (HF) receivers using multiple antennas parallel and perpendicular to the ambient magnetic field, as well as very low-frequency (VLF) receivers using antennas perpendicular to the magnetic field. These receivers observed five short-lived Langmuir wave bursts lasting from 0.1–0.2 s, consisting of a thin plasma line with frequencies in the range of 2470–2610 kHz that had an associated diffuse feature occurring 5–10 kHz above the plasma line. Both of these waves occurred slightly above the local plasma frequency with amplitudes between 1–100
Plasma waves generated at or near the local plasma frequency have been observed in the auroral ionosphere by satellites and rockets ever since there have been instruments capable of measuring them (review by Akbari et al., 2021). These wave amplitudes can range from a few millivolts per meter (
McAdams and LaBelle (1999) and Samara and LaBelle (2006) observed structured spectral peaks above the plasma frequency in high-frequency (HF) spectrograms. The former dubbed these bursts “chirps”, with amplitudes up to 1
Evidence for nonlinear processes has been reported, as recently reviewed by Akbari et al. (2021). In addition to these various weak turbulence phenomena discussed above, there is evidence for strong turbulence phenomena in aurora, such as Langmuir cavitons (Akbari et al., 2013), as well as for electron and ion phase space holes (Ergun et al., 1998; Schamel et al., 2020; review by Akbari et al., 2021). Stasiewicz et al. (1996), using Freja satellite data, observed evidence of both parametric decay of a Langmuir wave into a lower- hybrid (LH) wave and an oblique wave (
McFadden et al. (1986) measured both parallel and perpendicular components of the electric field, observing Langmuir waves with larger parallel components such that
The High-Bandwidth Auroral Rocket (HIBAR) was one in a series of sounding rockets equipped with the telemetry capable of measuring high-frequency waves in detail. Uniquely, it achieved these measurements in both the parallel and perpendicular direction with respect to the background magnetic field, which allows for the identity of the wave mode (e.g., parallel propagating Langmuir wave or perpendicularly propagating upper-hybrid mode) and the direction of propagation of the different waves to be determined and compared with theory. Its goal was to measure waves generated by intense beams of electron precipitating down the magnetic field at high latitudes in the F region of the ionosphere, where
HIBAR was launched from Poker Flat, Alaska, on 28 January 2003, at 07:50 UT into active pre-midnight aurora, reaching an apogee of 382 km. The geomagnetic field was strongly perturbed, exhibiting a sequence of 50–100 nT magnetic bays in the north–south component, the first of which coincided with the rocket launch, indicating that an expansion phase or pseudo breakup was in progress. Its payload included a Langmuir probe, particle detectors, and DC (direct current), very low-frequency (VLF), and HF electric field receivers. HIBAR was one in a series of rockets with a high telemetry rate to measure waves with frequencies up to 5 MHz, allowing for observations of detailed structure of high-frequency waves in the lower ionosphere, such as Langmuir and upper-hybrid (UH) waves. The rocket's spin axis was aligned to within 5
Diagram of the HIBAR rocket showing approximate antenna orientations with respect to the background magnetic field (note that the labeling of the probes has no connection to Cartesian coordinates).
The unique feature of HIBAR was the large number of HF telemetry links. Among these, two were dedicated to measurements of components of HF wave electric fields up to 5 MHz: the perpendicular electric field used probes x
Figure
The 2000–3200 kHz spectrograms of perpendicular
Figure
Frequency–power spectrogram of the HIBAR VLF wave data from 0–20 kHz and 07:54:10–07:56:10 UT (250–370 s), showing the broadband diffuse whistler-mode waves and a slightly enhanced power band at
Enhanced plots of the five Langmuir bursts indicated in Fig.
Figure
Black boxes in each spectrogram in
Fig.
The average intensity of each feature for each antenna is
determined by integrating the appropriate spectrum over the
frequency range of the feature, bounded by the vertical dashed
line in Fig.
Bottom panels of each section of
Fig.
Mean ratios of
We now use the ratios of
McFadden et al. (1986) also point out that the perpendicular component of the wave may be underestimated in the measurement by a factor
An attempt to determine the angle of the perpendicular wavevector to the antennas' orientation results in poor fits to the observed time series of
It is worth noting, however, that Langmuir waves driven in the relatively unmagnetized solar wind by electron beams with energies of order 100 keV and above can naturally have
Theory also suggests that as waves increase in frequency away from the local plasma frequency, they should become more perpendicular, decreasing the ratio of parallel to perpendicular electric field (see Fig.
Dispersion relations for the different wave modes for an over-dense (
The resulting angles
From the ratios in Table
The unique capability of the HIBAR mission to measure both the parallel and perpendicular components of the electric field means the propagation angles of waves with respect the background magnetic field can be compared to the expected values from plasma theory. Because these waves occur slightly above the plasma frequency cutoff in the over-dense plasma (
Plasma frequency cutoff (
The plasma lines and corresponding diffuse features last for identical time intervals. This raises the possibility that the diffuse features are generated by wave–wave interactions of the plasma lines with lower-frequency waves. HIBAR was equipped with a very low-frequency (VLF) receiver that measured waves from 0–20 kHz, which showed a consistent whistler-mode hiss for the times when the HF waves are observed (e.g., Fig.
To test the plausibility of the wave–wave interaction hypothesis, a dispersion solver, Wave in Homogeneous Anisotropic Multicomponent Plasma (WHAMP; Rönnmark, 1982), was employed to calculate surfaces corresponding to the normal modes in the plasma that might participate in the wave–wave interaction: the Langmuir–upper-hybrid (UH) and the whistler–lower-hybrid (LH) surfaces. WHAMP requires user-defined input parameters for the plasma environment, including the magnetic field strength, number of particle species, and their respective densities and temperatures. Table
Parameters used for computing dispersion surfaces in WHAMP associated with Langmuir bursts labeled in Figs.
Figure
WHAMP dispersion surfaces for Langmuir bursts labeled in Figs.
For each Langmuir–UH surface in Fig.
To generate the highlighted surface sections in Fig.
Assuming a nonlinear three-wave interaction is responsible for the generation of the diffuse feature, the possible third wave should be connected through the wavevector-matching condition,
These waves were produced by some form of energy exchange of particles with the plasma environment, and the electron and ion data were examined to determine the source of these waves. Similar to the analysis of growth rates in Moser et al. (2021), the electron and ion distribution functions are needed to determine growth rates on the two dispersion surfaces produced by WHAMP. The measured electron distribution for the time 07:54:19.907 UT is shown in Fig.
Measured electron distribution function from HIBAR's
electron ESA data at 07:54:19.907
Figure
Other possible sources of free energy are electrons above 20 and below 60 eV as well as the ions. Because the high- and low-energy electrons were not measured, they could not be modeled with WHAMP to find unstable features. As stated above, the instability that would be the source of the observed Langmuir waves may result from higher-energy electrons than those that were measured. The ions were measured from 80 eV to 20 keV with a time resolution of 45 ms. In a similar analysis to that described above, the observed ion ring-like distribution at 09:54:19.920 UT was modeled using the WHAMP parameters, and growth rates on the whistler/LH modes were analyzed. The resulting model produced low growth rates on the surface (
Another test of plausibility for a wave–wave interaction is to compare the electric energy density of the different waves to the thermal plasma energy density. The electric energy density,
Incidentally, Akbari et al. (2013) observed double-peaked plasma lines in incoherent scatter radar data associated with strongly turbulent Langmuir cavitons. Although there is a superficial resemblance to the double-peaked plasma frequency spectra reported here, the extremely low ratio of electric to thermal energies in this case preclude an association with cavitons.
A more quantitative analysis is to examine the ratio of wave occupation numbers for these waves. The electric energy density is related to the plasmon occupation number through
Assuming the occupation numbers are the same for each wave mode, Eq. (
The difficulty with solving this equation is determining the range of wavevectors that the modes occupy. To get a rough estimate of the ranges, the WHAMP surfaces are examined to determine possible ranges of wavenumbers for the observed waves and get an idea for the ratio of the occupation numbers. For the plasma line and diffuse feature, the broad range of wavevectors is
Following a similar derivation for the time rate of change of the occupation numbers as in Moser et al. (2021), Cairns (1988), and Melrose (1980), among others, we can show that at saturation (when the rates of change of
For each plasmon lost from the whistler/LH mode and the plasma line as the coalescence
Based on the foregoing observations and theoretical analyses it appears plausible that the diffuse band is formed by the nonlinear coalescence
The HIBAR rocket was launched into active pre-midnight aurora and observed seven short duration bursts of Langmuir waves above the local plasma frequency at altitudes from 364–377 km. Of these seven events, five consisted of a plasma line at frequencies ranging from 2470–2610 kHz with an associated diffuse feature occurring 5–15 kHz above this line. Independent measurements of both the parallel and perpendicular components of the electric field showed that the plasma lines typically have
WHAMP was used to identify the Langmuir–Z and whistler–LH surfaces where the plasma line and diffuse feature's wave modes would occur. The
This is similar to the process in Staciewicz et al. (1996), where observation of modulated Langmuir waves suggested these waves were produced through either parametric decay of the primary Langmuir wave into a LH wave and secondary Langmuir waves via the process
Data are available to the public at
JL was the PI for the HIBAR mission. JL and CM interpreted the data and experiment. CM wrote the codes and performed the data analysis. IHC contributed the theoretical analysis, and all authors contributed to the interpretation of the results. CM wrote the manuscript with contributions from all authors.
The contact author has declared that neither they nor their co-authors have any competing interests.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Thanks are expressed to the team at Wallops Flight Facility and NASA for supporting the HIBAR payload and launch, as well as engineer Hank Harjes and NASA engineer Bill Payne for instrumentation support. Authors also thank Marilia Samara, Connor Feltman, and Scott Bounds for discussions and support. Research at Dartmouth College was supported by NASA grant NNX17AF92G.
This research has been supported by the National Aeronautics and Space Administration (grant no. NNX17AF92G).
This paper was edited by Igo Paulino and reviewed by Abraham C. L. Chian and Peter Yoon.