The scattering phase shift due to Bragg resonance in one-dimensional fluctuation reflectometry

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Abstract
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 top of an inhomogeneous plasma. A Green function technique is used in the derivation together with the Born approximation. The integral representation is evaluated using asymptotic techniques and Bragg resonance is seen to be the dominant mechanism producing the phase shifts due to fluctuations with wavelengths that are short compared to the Airy length. By suitably normalizing the governing differential equation, we have identified the two dominant parameters that control the approximations in our analysis. These are delta n/n0 and kf. The first is the magnitude of the maximum density fluctuation multiplied by the square of the dimensionless length scale that characterizes both the background plasma density profile (with scalelength L) and the incoming microwave field (with vacuum wavenumber k0): delta n/n0 identical to ( delta n/n0)*(k0L)23/. The second is the fluctuation wavenumber normalized to k0 and scaled by the similarly normalized Airy wavenumber: kf identical to (kf/k0)*(k0L)13/. The Born approximation is expected to be valid as long as delta n/n01.