THE SCATTERING PHASE-SHIFT DUE TO BRAGG RESONANCE IN ONE-DIMENSIONAL FLUCTUATION REFLECTOMETRY

An explicit integral representation is derived for the tangent of the phase shift due to one-dimensional (1D) scattering of an S-polarized, O-mode, electromagnetic field from a localized wavepacket sitting on t op of an inhomogeneous plasma. A Green function technique is used in t he derivation together with the Born approximation. The integral repre sentation is evaluated using asymptotic techniques and Bragg resonance is seen to be the dominant mechanism producing the phase shifts due t o fluctuations with wavelengths that are short compared to the Airy le ngth. By suitably normalizing the governing differential equation, we have identified the two dominant parameters that control the approxima tions in our analysis. These are <(delta n)over bar> and k(f). The fir st is the magnitude of the maximum density fluctuation multiplied by t he square of the dimensionless length scale that characterizes both th e background plasma density profile (with scalelength L) and the incom ing microwave field (with vacuum wavenumber k(0)): <(delta n)over bar> /n(0) = (delta n/n(0)) x (k(0)L)(2/3). The second is the fluctuation w avenumber normalized to k(0) and scaled by the similarly normalized Ai ry wavenumber: (k) over bar(f) = (k(f)/k(0)) x (k(0)L)(1/3). The Born approximation is expected to be valid as long as <(<deltan>)over bar>/ n(0) < 1, and the Bragg resonance picture dominates as long as (k) ove r bar(f) > 1.