Low-frequency hiss-like whistler-mode waves generated by nonlinear three-wave interactions outside the plasmasphere

Whistler-mode waves play an important role in the inner magnetospheric particle dynamics. The direction and efficiency of energy transfer between waves and particles strongly depend on the wave frequency distribution characteristics. Recent observations have drawn attention to the low-frequency whistler-mode chorus waves below 0.1 times the equatorial gyrofrequency $fce$ of electrons outside the plasmasphere. Here, on the basis of the analysis of the Van Allen Probes wave data, we describe a new type of low-frequency hiss-like whistler-mode wave around or below 0.1 $fce$⁠. We show that two normal chorus wave bands split by the 0.5 $fce$ gap can produce the low-frequency hiss-like whistler-mode waves through the nonlinear three-wave interaction.