One-dimensional modeling of the wavelength sensitivity, localization, and correlation in reflectometry measurements of plasma fluctuations

The reflection of electromagnetic waves from a plasma cutoff layer has been used to examine properties of density fluctuations in fusion plasmas. In this paper an exact one-dimensional model is used to show the relation between changes in the phase of the reflected wave and the location, magnitude, and correlation properties of density fluctuations. For long-wavelength density perturbations the reflected phase can be simply related to the amplitude of fluctuating density and the density scale length, Ln, near the cutoff layer. However, the phase response falls substantially as the fluctuation wavelength approaches the free space wavelength of the reflected wave, λ0, and the location of the maximum response moves out in front of the cutoff layer following the wave matching condition kΛ= 2k ≊ 2η(x)k0. Thus, a measurement of the reflected phase is strongly weighted to and localized for phenomena whose wavelength is longer than the characteristic scale (λ20Ln)1/3. Because of this weighting and because the region of maximum response moves away from the cutoff layer for short-wavelength fluctuations, there is also a limitation in any estimate of the density correlation length from the reflected phase. The correlation of phases between several different probe frequencies can be used to estimate a density correlation length no less than about four times the free space probe wavelength.