“…The less studied is the wave's structure across the magnetic shells. It is well known that the Alfvén waves can form resonators across the magnetic shell due to various effects beyond the one-fluid Magnetohydrodynamics, such as electron inertia (Gulélmi & Polyakov, 1983), finite ion Larmor radius (Dai, 2009;Leonovich et al, 1983), ion gyrofrequency (Dmitrienko & Mazur, 1992;Mikhailova, 2014), and finite conductivity (Churilov, 2002). In these cases, the Alfvén wave has discrete spectrum, and its transverse structure is determined by superposition of several transverse eigenfunctions.…”