Whistler-Mode Waves in Magnetic Ducts

Observations from the NASA MMS satellites show packages of ELF whistler-mode waves localized inside the small-scale irregularities of the magnetic field. These irregularities are formed by the narrow field-aligned channels where the magnitude of the background magnetic field inside the channel is greater or less than outside. By analogy with the classical density ducts, we introduce the high-B duct (HBD), where the magnitude of the field inside the channel is greater than the outside, and the low-B duct (LBD), where the magnitude of the field inside the channel is less than the outside. We investigate the guiding of the ELF whistler-mode waves by high-B and low-B ducts. We derive the analytical criteria for the wave ducting by these ducts and confirm them with two-dimension, time-dependent simulations of the electron-MHD model. Also, we model ELF whistler mode waves observed inside the high-B and low-B ducts by MMS satellites.