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

Experimental observations of very low frequency (VLF) triggered emissions are an important resource in investigation of nonlinear wave-particle interactions between whistler mode waves and energetic electrons in the Earth's radiation belts. Magnetospherically generated whistler mode sidebands observed during the Siple Station wave injection experiment are analyzed using a mixed modulation model and the MINUIT minimization package. The observed sidebands are found to exhibit features of both amplitude and frequency modulation of the input carrier wave with frequency modulation becoming more prominent as the observed amplitudes of the carrier and sidebands increase. A nonlinear whistler mode wave growth formulation based on phase bunching of counterstreaming electrons within a well-defined phase trap is shown to reproduce the salient features of the sideband observations. Whistler mode sideband amplitude is shown to be affected by the shape and uniformity of the trap. Plain Language Summary Our planet hosts fascinating interactions between waves and matter. Like other planets, it is surrounded by the most abundant form of matter in the universe that is plasma. Interestingly, plasmas interact with electromagnetic waves, and in our study we investigate the manner in which a layer of our planet's plasmas interacts with very low frequency (VLF) radio waves. Years ago, experiments were performed in Antarctica that sent VLF radio waves into the ionosphere (a thick plasma layer of our atmosphere) and beyond which then mingled with the plasma there. The waves were subsequently recorded at a receiver in Canada (because plasmas can bend radio waves!). These recordings contain details about wave-particle interactions (mingling) that helps us understand our universe more fully and can help protect our electrical equipment in space as well as here on Earth. Our research looks deeper into the secondary waves generated by the energetic electrons in the plasma layer counterstreaming to the sent VLF waves. Particularly, we explored the amplitude and frequency modulation features we noticed contained within the recordings of the altered radio waves received in Canada. Ultimately, this work helps to provide additional color into the complex wave-particle behavior that happens constantly above our heads.