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ULF waves are MHD waves observed in the Earth's inner magnetosphere, especially oscillations with periods ranging from a few seconds to a few hundred seconds. The excitation and propagation processes of ULF waves have been extensively studied. Field line resonance (FLR) is a process in which Alfvén waves resonate with fast modes that are excited at the magnetopause and propagate toward the inner magnetosphere. This process excites ULF waves in the inner magnetosphere and explains field line oscillations associated with the Pc4-5 phenomenon (Dungey, 1954; Chen & Hasegawa, 1974; Southwood, 1974). This is one of the most important processes in the excitation of ULF waves whose energy source is outside the magnetosphere; the FLR process has been extensively studied theoretically in cartesian, cylindrical, and dipole coordinate systems (e.g., Mann et al., 1995; Allan et al., 1986; Wright & Elsden, 2016). As a result, it has become clear that the resonance between fast modes and Alfvén waves occurs in the inner magnetosphere, where the Alfvén speed varies with spatial variations in plasma mass density, strength of magnetic field, and field line length.
We have further developed this viewpoint by analyzing how the geometrical characteristics of the background magnetic field geometry, i.e., the curvature and torsion of the field lines, play a role in generating FLR in an arbitrary background magnetic field geometry. The real configuration of the inner magnetosphere is not a dipole-shaped magnetic field or a magnetic field that can be represented by a potential, and its shape changes drastically due to the solar wind and other factors. Therefore, by focusing on the geometrical shape of the magnetic field lines, rather than the shape of the magnetic field, the process of FLR formation can be clarified, and a theoretical study of the region where FLR occurs can be performed even in a realistic magnetosphere shape. We apply an analytical method of Yoshikawa (JpGU 2023). The method employs a local frame with three axes: tangential, normal, and subnormal directions with respect to the magnetic field. The local frame makes it possible to analyze the effects of geometrical properties of arbitrary background magnetic field geometries.
We derived the linearized equations of cold MHD in the local frame. We examined the impacts of the curvature and tortuosity of the magnetic field lines on the orientation of plasma fluctuation and its alteration. The findings propose that the excitation of Alfvén waves might be influenced by magnetospheric compression owing to the dynamic pressure of solar wind and torsion of the flux tube.
