A Fourier-space description of oscillations in an inhomogeneous plasma. Part 2. Discrete approach

The process of phase mixing in inhomogeneous MHD or cold plasmas is interpreted as one of energy propagation in discrete Fourier space. Three instructive scenarios are examined: (i) an isolated inhomogeneity with zero boundary conditions; (ii) a periodic inhomogeneity; and (iii) a monotonic inhomogeneity sandwiched between two semi-infinite uniform regions. In each case the coefficients of the associated wave equation in Fourier space for an appropriately chosen dependent variable are very nearly constant almost everywhere, so the propagation is like that of a free unreflected wave. An exception may arise in the coupling of the lowest modes, which can be highly reflective. It is argued that Fourier space is the simplest and most natural context in which to discuss the development of fine-scale oscillations.