Modulated Upper-Hybrid Waves Coincident With Lower-Hybrid Waves in the Cusp

During the Twin Rockets to Investigate Cusp Electrodynamics (TRICE-2) High-Flyer rocket's passage through the cusp the high frequency (HF) radio wave receiver observed three intervals of banded upper-hybrid (UH) waves. The bands begin at the UH frequency (similar to 1.2-1.3 MHz), descending to as low as 1.1 MHz, with amplitudes of hundreds of mV/m. The spacing of the bands are similar to 4.5-6 kHz and the number of bands ranges from 3 to 10. Simultaneously, the very low frequency (VLF) radio wave receiver observed lower-hybrid (LH) waves with amplitudes ranging from 1 to 10 mV/m and frequencies of 4.5-6 kHz. Slight variations of the spacings of the bands in the UH waves were closely correlated with variations in the LH peak frequencies. Two possible wave-wave interactions are explored to explain this phenomenon: decay of an UH wave into a lower frequency UH wave and a LH wave, and coalescence of independent UH waves and LH waves that spawn UH waves. Using a dispersion relation calculator with electron and ion distribution functions based off those observed by the particle instruments suggests that UH waves, and to a lesser degree LH waves, can be excited by linear instabilities. Kinematic analysis of the waves dispersion relations and the wave matching conditions show that wave-wave interactions linking UH and LH modes are possible through either decay or coalescence. This analysis along with comparisons of the energy densities of the waves, and the ratio of their occupation numbers suggest that the decay process is more likely than coalescence.