ABSTRACT
This chapter discusses more aspects of reflection and resonance in a plane-stratified medium. Approximations are developed that apply over the whole range including the turning point and resonance. The mathematical properties of the approximate wave equation in such systems are studied in detail, including series solutions and WKBJ approximations. These can be smoothly joined onto numerical solutions of the more general equation. The chapter considers the case of a cylindrical structure, representing idealizations of various situations in the solar corona. These solutions allow for an azimuthal component of the background magnetic field and for small resistive losses in the plasma, which only become important near the resonance. The calculation of numerical solutions of the resonance equation is complicated by the presence of the singularities in the fields at the resonance. WKBJ or phase integral approximations are often used in discussions of problems related to resonance.
