Small-scale Alfvén waves localized near an extremum in the finite-amplitude perturbation of the radial plasma density profile

A study is made of electromagnetic waves localized in the region where the radial plasma density profile has an extremum between two local Alfven resonances. Analytic expressions for the eigenfrequencies and eigenmodes are obtained. It is shown that kinetic and inertial Alfven waves can propagate in the vicinity of a maximum and a minimum in the density profile, respectively. Passage to the limiting case in which the plasma density is nonuniform and has a parabolic profile is considered.