The excitation of shear Alfven wave and the associated modulation of compressional wave in the inner magnetosphere

Two basic but novel equations directly describing the generation of shear Alfven and compressional waves in the inner magnetosphere filled with a cold magnetized plasma are derived. The shear Alfven wave is characterized by the field-aligned current and the compressional wave by the compressional component of the magnetic field. Such a generation arises from the effects of inhomogeneous Alfven speed and curvilinear field line. Around the magnetic equator, if the Alfven speed is inversely proportional to a power of the geocentric distance, these effects have magnitudes of the same order and their signs are identical. Considered in the present study is a situation that the earthward propagating compressional wave is launched from a large scale oscillating current wedge centered at midnight and symmetric about the magnetic equator. Then, it is found that the field-aligned current excited around the equator by the compressional wave has opposite senses in direction in the northern and southern hemispheres, in the pre- and post-midnight sectors as well as just inside the plasmapause and in its surrounding regions. As a result of the excitation of shear Alfven wave, two types of oscillations appear on a field line: One is a forced oscillation and the other is an eigenoscillation. Although a modulation of the compressional wave may be caused locally (or microscopically) around the equator by the eigenoscillation of field line, the modulation can be globally (or macroscopically) neglected. So far as the propagation along the source longitude (source-earth line) around the equator is concerned, the coupling between compressional and shear Alfven waves can be almost neglected and so one-dimensional response of the inner magnetosphere around the equator plays a significant role in the compressional oscillation.