Wave propagation in inhomogeneous plasmas

Thus far in our discussion of wave propagation it has been assumed that the plasma is spatially uniform. While this assumption simplifies analysis, the real world is usually not so accommodating and it is plausible that spatial non-uniformity might modify wave propagation. The modification could be just a minor adjustment or it could be profound. Spatial non-uniformity might even produce entirely new kinds of waves. As will be seen, all these possibilities can occur.

To determine the effects of spatial non-uniformity, it is necessary to re-examine the original system of partial differential equations from which the wave dispersion relation was obtained. This is because the technique of substituting ik for ∇ is, in essence, a shortcut for spatial Fourier analysis, and so is mathematically valid only if the equilibrium is spatially uniform. The criteria for whether or not ∇ can be replaced by ik can be understood by considering the simple example of a high-frequency electromagnetic plasma wave propagating in an unmagnetized three-dimensional plasma having a gentle density gradient. The plasma frequency will be a function of position for this situation. To keep matters simple, the density non-uniformity is assumed to be in one direction only, which will be labeled the x direction. The plasma is thus uniform in the y and z directions, but non-uniform in the x direction.