On the Index of Refraction of Spatially Periodic Plasma

A knowledge of the change produced in the index of refraction of a uniform plasma by the spontaneous generation of coagula or inhomogeneities is essential to the use of electromagnetic waves as a diagnostic tool. The general problem is a difficult one to handle, but certain non-trivial cases are mathematically tractable. One of these, which is also of some practical import, occurs when the inhomogeneities are periodically distributed throughout the plasma. Here this special case is analyzed within the framework of the theory of periodic structures. The problem is reduced by virtue of Floquet's theorem to an equivalent problem for the domain of a unit cell with periodic boundary conditions. An approximate solution is obtained by a simplified theory. As a specific application the calculation for a plasma with periodically spaced spherical inhomogeneities is worked out in detail.