Propagation of whistler-mode waves in the magnetic duct caused by the compressional component of ULF wave oscillation

Whistler-mode waves play crucial roles in radiation belt dynamics, facilitating the acceleration of electrons from kiloelectron volts to megaelectron volts energy range and the loss of radiation belt electrons via wave-particle interaction. Recent studies suggest the important role of the duct propagation of whistler-mode waves for the radiation belt dynamics because the resonant energy increases to the relativistic energy in the high latitude region where ducting whistler-mode waves can reach. While the density duct caused by electron density structure has been studied for decades, it is evident from the dispersion relation that the refractive index is affected not only by the cold electron density but also by the magnetic field. We study the propagation of whistler-mode waves in ULF wave-derived magnetic ducts by two-dimensional ray-tracing simulations in the dipole coordinate system. We assume a magnetic duct structure at L=6 by considering the dipole field and a waveform of ULF wave oscillation with compressional and poloidal components. The refractive index fluctuations of the duct are calculated from the background field fluctuations caused by modeled compressible amplitudes associated with poloidal oscillations in the fundamental mode. The duct's shape is determined using a Gaussian function, and the rate of change of the magnetic field and the duct width are given parametrically. The refractive index structure is modeled every eighth of a ULF wave period, and the propagation of upper/lower-band frequency whistler-mode waves is simulated. Depending on the wave phase of the modeled ULF wave, the background magnetic field increases or decreases with each ULF phase, generating a depletion or enhancement duct. The simulation results show duct propagations, while the frequency where ducting of whistler-mode waves observed switches because the duct structure shifts with each phase of the modeled ULF wave. The duct width corresponds to the spatial scale of high-m ULF waves. A larger spatial scale can be expected if the ULF-induced plasma density variations are included. Furthermore, the duct propagation in other harmonics is also confirmed. This study reveals the characteristics of whistler-mode wave propagation by magnetic ducts due to ULF waves.