By using the drift kinetic approximation, effects of the electron motion along the magnetic field lines on axisymmetric torsional hydromagnetic oscillations in an inhomogeneous, low-β plasma are considered. The result indicates that eigen oscillations are only possible when there is an energy trapping region between the turning points. If we assume the simple spatial distribution of the Alfvén speed,
VA, which has a trough corresponding with the sudden density decrease near the plasmapause, no effective trapping of oscillations appears near the trough for the case of the cold plasma limit,
VA>>
Ve. The existence of the trapping region of oscillation is strongly dependent on the relative magnitude of
VA to the electron thermal velocity,
ve. For the case of
ve>>
VA, the resonance oscillation is possible within the trough. However, the deviation of the resulting eigen-frequency from that corresponding to the field line at the bottom of the trough is small. In general, the condition for the resonance trapping of oscillations near the trough is
ve>>
Vo (the minimum value of
VA) beyond the density knee.
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