One-dimensional analytical model of the phase shift due to Bragg backscattering of an ordinary wave by large amplitude density fluctuations

The phase shift due to the resonant Bragg scattering of an ordinary wave in a fluctuating plasma is numerically computed for large amplitude density fluctuations, i.e. well beyond the Born approximation. The phase response (the phase shift against the perturbation position in the density gradient) is strongly distorted with respect to the small amplitude case, and phase jumps occur. For localized quasi-monochromatic fluctuations, the results are explained by an analytical model where the Helmholtz equation is approximated by a Mathieu equation. The maximum phase shift and the phase jumps are well predicted by the model. It turns out that the theoretical predictions also apply to moderate amplitudes. For an actual phase measurement where the number of different frequencies (i.e. the number of perturbation positions) is finite, most phase jumps are missed, due to the steepness of the phase jumps, and the measured phase shift increases continuously.