ABSTRACT
This chapter discusses the properties of resonances when the pressure of the plasma can be neglected. It aims to understand idealized models analytically, so that this understanding can inform the interpretation of numerical calculations. Thus, most of the analysis is carried out in a plane-stratified medium, with some discussion of dipole geometry. The physics of the resonance process is the same but geometrical factors make a considerable difference to the amplitude of the field components. The phenomenon of field-line resonance is ubiquitous in solar–terrestrial physics. In the simplest case, field-line resonance can be understood by considering a plane-stratified geometry, with the Alfven and sound speeds increasing monotonically in a direction normal to the magnetic field. If, in the theory of any physical process, a singularity such as that at the resonance point is encountered, the implication is that the theory is inadequate in the neighbourhood of that point.
