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Geomagnetic field and plasma inhomogeneities in the outer equatorial part of the magnetosphere create a channel with low Alfvén speeds which spans from the nose to the far flanks of the magnetosphere, in both the morning and the evening sectors. This channel plays the role of a waveguide for fast magnetosonic waves. The waveguide eigenmodes and corresponding Alfvén resonance (field line resonance) regions are directly related to geomagnetic pulsations Pc3 and Pc5. U-shaped model of the waveguide allows for full analytical investigation of waveguide eigenmodes. Quantities such as mode wave numbers, group velocities, and their energy density distribution are found as functions of coordinate along the waveguide. The linkage of the waveguide magnetosonic oscillation energy to the Alfvén waves in the vicinity of the field line resonance deeper inside the magnetosphere is investigated, and corresponding energy leakage coefficient is found. Thus, the influence of longitudinal (i.e., azimuthal) waveguide inhomogeneity on wave propagation is analytically investigated. Obtained results can be used for interpretation of the observed wave power distribution in the frequency bands of geomagnetic pulsations Pc3 and Pc5, as well as for explanation of their spectral properties in the outer magnetosphere.

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The problems of large‐scale wave propagation and amplification in the outer magnetosphere are considered. Kelvin‐Helmholtz (KH) instability growth rate of the magnetospheric waveguide eigenmodes is investigated as a function of a coordinate along the magnetopause. The problem of solar wind MHD wave penetration into the waveguide is investigated for a broad range near Pc3 and Pc5 geomagnetic pulsation frequencies and realistic models of the magnetospheric waveguide. The expression for the waveguide eigenmode energy flux is obtained. This expression includes the effects of external wave penetration and mode amplification due to the KH instability, as well as losses due to dissipation in the vicinity of the Alfven resonance which are incorporated into the growth rate coefficient together with the instability.