Observations from satellites demonstrate that small-scale, localized packages of VLF waves are frequently detected inside the field-aligned density depletions (low-density ducts) and enhancements (high-density ducts) with comparable sizes. Because the conditions for the wave trapping in these inhomogeneities depend on the parameters of the wave and the duct, the information about the background media can be used to find parameters of the wave trapped in the duct. We present results from the modeling study of the propagation of VLF whistler-mode waves in the field-aligned density inhomogeneities with the perpendicular sizes comparable to (and even less than) one perpendicular wavelength of the wave inside the duct. Simulations of the electron-MHD model reproduce in good quantitative detail observations from the satellites and let us identify perpendicular and parallel wavelengths of the waves trapped in the ducts. Simulations also reveal the conditions causing trapping of the oblique VLF waves in the low-density and high-density ducts with the transverse size comparable with the perpendicular wavelength of the smallest (and most oblique) wave inside the duct.
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