Modulation Analysis of Whistler Mode Sidebands in VLF‐Triggered Emissions and Implications for Conditions of Nonlinear Growth

Costabile, Jamie D.; Gołkowski, Mark; Wall, Randall E.

doi:10.1002/2017ja024501

Cited by 3 publications

(5 citation statements)

References 34 publications

(61 reference statements)

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“…Lastly, although so‐called sideband waves can grow spontaneously very close to a main (sufficiently intense) wave in an inhomogeneous magnetic field (Costabile et al., 2017 ; Nunn, 1974 , 1986 ), it is worth noting that (a) such sideband waves are not generated independently from the main wave but are instead directly generated by cyclotron resonance with particles trapped by the main wave (they are a by‐product of the nonlinear growth of this main wave), and (b) their growth rate is largest for a frequency difference with the main wave Δ ω * ≃ ω tr /(1 − v res / v g ) ≃ ω tr /(1 + Ω ce /2 ω ) (Dowden, 1982 ; Nunn, 1986 ). Accordingly, a sideband wave reaching a sufficiently high amplitude, similar to the main wave amplitude, is expected to produce wave amplitude modulations corresponding to relatively long packets with β * = ω /Δ ω * > β tr , min 2 > β tr , min , similar to the trapping‐induced modulations already considered in Section 2.1 .…”

Section: Generation Of Short Chorus Wave Packets: Theoretical Modelsmentioning

confidence: 99%

Short Chorus Wave Packets: Generation Within Chorus Elements, Statistics, and Consequences on Energetic Electron Precipitation

et al. 2022

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Short and intense lower‐band chorus wave packets are ubiquitous in the Earth's outer radiation belt. In this article, we perform various Vlasov hybrid simulations, with one or two triggering waves, to study the generation of short chorus packets/subpackets inside long rising tone elements. We show that the length of the generated short wave packets is consistent with a criterion of resonance non‐overlap for two independent superposed waves, and that these chorus packets have similar characteristics as in Van Allen Probes observations. We find that short wave packets are mainly formed near the middle/end of long rising tones for moderate linear growth rates, and everywhere for stronger linear growth rates. Finally, we analyze an event characterized by Time History of Events and Macroscale Interactions during Substorms spacecraft measurements of chorus rising tones near the equator and simultaneous measurements by low altitude ELFIN CubeSats of precipitating and trapped electron fluxes in the same sector. The measured precipitating electron fluxes are well recovered by test particle simulations performed using measured plasma and wave properties. We show that short chorus wave packets of moderate amplitudes (160–250 pT) essentially lead to a more diffusive‐like transport of 50–200 keV electrons toward the loss cone than long packets. In contrast, long chorus packets are found to produce important nonlinear effects via anomalous trapping, which significantly reduces electron precipitation below 150 keV, especially for higher wave amplitudes.

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Section: Generation Of Short Chorus Wave Packets: Theoretical Modelsmentioning

confidence: 99%

Short Chorus Wave Packets: Generation Within Chorus Elements, Statistics, and Consequences on Energetic Electron Precipitation

et al. 2022

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“…It has been previously shown that sidebands can be triggered by coupling between a VLF transmitter pulse and a natural ELF emission (Bell 1985;Sotnikov et al 1991, and references therein). Costabile et al (2017) posit that the sidebands are generated as a result of oscillation of the electron phase-space hole at the trapping frequency, creating a hybrid amplitude/frequency modulation of the injected pulse. Sidebands can also be produced by two beating waves.…”

Section: Discussionmentioning

confidence: 99%

On the use of ELF/VLF emissions triggered by HAARP to simulate PLHR and to study associated MLR events

Parrot

Němec

Cohen

et al. 2022

Earth Planets Space

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A spectrogram of Power Line Harmonic Radiation (PLHR) consists of a set of lines with frequency spacing corresponding exactly to 50 or 60 Hz. It is distinct from a spectrogram of Magnetospheric Line Radiation (MLR) where the lines are not equidistant and drift in frequency. PLHR and MLR propagate in the ionosphere and the magnetosphere and are recorded by ground experiments and satellites. If the source of PLHR is evident, the origin of the MLR is still under debate and the purpose of this paper is to understand how MLR lines are formed. The ELF waves triggered by High-frequency Active Auroral Research Program (HAARP) in the ionosphere are used to simulate lines (pulses of different lengths and different frequencies). Several receivers are utilized to survey the propagation of these pulses. The resulting waves are simultaneously recorded by ground-based experiments close to HAARP in Alaska, and by the low-altitude satellite DEMETER either above HAARP or its magnetically conjugate point. Six cases are presented which show that 2-hop echoes (pulses going back and forth in the magnetosphere) are very often observed. The pulses emitted by HAARP return in the Northern hemisphere with a time delay. A detailed spectral analysis shows that sidebands can be triggered and create elements with superposed frequency lines which drift in frequency during the propagation. These elements acting like quasi-periodic emissions are subjected to equatorial amplification and can trigger hooks and falling tones. At the end all these known physical processes lead to the formation of the observed MLR by HAARP pulses. It is shown that there is a tendency for the MLR frequencies of occurrence to be around 2 kHz although the exciting waves have been emitted at lower and higher frequencies. Graphical Abstract

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“…A concise history of Siple Station operation can be found in Chapter 2 of the thesis by Gibby (2008); a more detailed history of experiments and operations during this period has been provided by Carpenter (2016). Data from the Siple Station experiment originally recorded on magnetic tape has been digitized and is the subject of continued investigations (Li et al, 2014(Li et al, , 2015aCostabile et al, 2017)…”

Section: Siple Stationmentioning

confidence: 99%

“…Sideband amplitude is usually 10 dB or more below the carrier amplitude, but sometimes it can exceed the carrier amplitude (Park, 1981). Costabile et al (2017) performed relative phase analysis of sidebands from the Siple experiment and discuss theories of sideband generation.…”

Section: Suppression Sidebands and Entrainmentmentioning

confidence: 99%

“…Omura et al (2009) and Cully et al (2011) used such expressions along with further assumptions to estimate frequency sweep rates of chorus emissions. Costabile et al (2017) used such expressions to investigate sideband formation. Although these simplifications have been validated against simulations (Katoh and Omura, 2016) and satellite observations (Cully et al, 2011) of chorus emissions, it does not entirely describe the complex dynamics of triggered VLF emissions.…”

Section: Non-linear Theorymentioning

confidence: 99%

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Review of Controlled Excitation of Non-linear Wave-Particle Interactions in the Magnetosphere

Gołkowski

Harid

Hosseini

2019

Front. Astron. Space Sci.

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Controlled experiments involving injection of 0.5 Hz-8 kHz electromagnetic waves into the Earth's magnetosphere have played an important role in discovering and elucidating wave-particle interactions in near-Earth space. Due to the significant engineering challenges of efficiently radiating in the ELF/VLF: 300 Hz-30 kHz band, few experiments have been able to provide sustained transmissions of sufficient power to excite observable effects for scientific studies. Two noteworthy facilities that were successful in generating a large database of pioneering and repeatable observations were the Siple Station Transmitter in Antarctica and the High Frequency Active Auroral Research Program (HAARP) facility in Alaska. Both facilities were able to excite Doppler shifted cyclotron resonance interactions leading to linear and non-linear wave amplification, triggering of free running emissions, and pitch angle scattering of energetic electrons. Amplified and triggered waves were primarily observed on the ground in the geomagnetic conjugate region after traversal of the magnetosphere along geomagnetic field aligned propagation paths or in the vicinity of the transmitter following two traversals of the magnetosphere. In several cases, spacecraft observations of the amplified and triggered signals were also made. The observations show the amplifying wave particle interaction to be dynamically sensitive to specific frequency and also specific frequency-time format of the transmitted wave. Transmission of multiple coherent waves closely spaced in frequency showed that the wave particle interaction requires a minimum level of coherency to enter the non-linear regime. Theory and numerical simulations point to cyclotron resonance with counter streaming particles in the 10-100 keV range as the dominant process. A key feature of the non-linear interaction is the phase-trapping of resonant particles by the wave that is believed to drive non-linear wave amplification and the triggering of free-running emissions. Observations and modeling of controlled wave injections have important implications for naturally occurring whistler mode emissions of hiss and chorus and the broader phenomena of radiation belt dynamics. A review of observational, theoretical, and numerical results is presented and suggestions for future studies are made.

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Modulation Analysis of Whistler Mode Sidebands in VLF‐Triggered Emissions and Implications for Conditions of Nonlinear Growth

Cited by 3 publications

References 34 publications

Short Chorus Wave Packets: Generation Within Chorus Elements, Statistics, and Consequences on Energetic Electron Precipitation

Short Chorus Wave Packets: Generation Within Chorus Elements, Statistics, and Consequences on Energetic Electron Precipitation

On the use of ELF/VLF emissions triggered by HAARP to simulate PLHR and to study associated MLR events

Review of Controlled Excitation of Non-linear Wave-Particle Interactions in the Magnetosphere

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