Abstract
Theoretical studies of waves and instabilities are often performed for an infinite, homogeneous plasma, and the results are given in terms of eigenmodes (plane waves) extending over all space. Real plasmas are, however, always finite and inhomogeneous, and observations of waves in space are normally presented as frequency power spectra which depend on the time and place of observation. The purpose of this study is to reconcile these apparently disparate descriptions of plasma waves. A model describing inhomogeneous spectral densities in a homogeneous plasma is first discussed in some detail. When this model is generalized to inhomogeneous plasmas, it is found that the incompressibility of the spectral densities in k space results in a remarkably simple transfer equation. A method which allows the observable frequency power spectrum to be calculated from a space and time dependent dispersion relation and appropriate boundary conditions is also outlined.
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