A Fourier-Space Description of Oscillations in an Inhomogeneous Plasma. Part 1. Continuous Fourier Transformation

Oscillations in inhomogeneous cold plasmas or inhomogeneous magnetofluids are interpreted in terms of the dynamics of their spectra in wavenumber space. By Fourier transforming the basic integro-differential equation of the problem, a generalized wave equation in wavenumber space is derived, thus converting the oscillation and phase-mixing processes in the original x space into processes of dispersive propagation and scattering of the spectrum in wavenumber space. The Barston singular continuum eigenmodes correspond to stationary scattering states of a monochromatic wave in wavenumber space, whereas the damping phenomena in x space correspond to transient ‘ leaking ’ phenomena accompanying scattering and dispersive propagation of a wave packet in wavenumber space.