Beam focusing and consequences for Doppler Backscattering measurements

TL;DR

This paper analyzes microwave beam focusing in plasma and its impact on Doppler Backscattering measurements, revealing how focusing enhances scattering signals and affects the measurement of turbulence spectra.

Contribution

It provides an analytical model linking beam focusing effects to DBS signal enhancement and spectral measurements in plasma diagnostics.

Findings

Beam focusing increases scattering contributions near the focus point.

DBS signal enhancement is due to beam focusing, not forward scattering.

The spectral exponent of turbulence can be measured via DBS, but not the spectral peak.

Abstract

The phenomenon of beam focusing of microwaves in a plasma near a turning-point caustic is discussed in the context of the analytical solution to the Gaussian beam-tracing equations in the 2D linear-layer problem. The location of maximum beam focusing and the beam width at that location are studied in terms of the beam initial conditions. The analytic solution is used to study the effect of this focusing on Doppler backscattering (DBS). We find that the filter function that characterises the scattering intensity contributions along the beam path through the plasma is inversely proportional to the beam width, predicting enhanced scattering contributions from the beam focusing region. We show that the DBS signal enhancement for small incident angles between the beam path and the density gradient is due to beam focusing and not due to forward scattering. The analytic beam model is used to predict the measurement of the $k_y$ density-fluctuation wavenumber power spectrum via DBS, showing that the spectral exponent of the turbulent, intermediate-to-high $k_y$ density-fluctuation spectrum might be quantitatively measurable via DBS, but not the spectral peak corresponding to the driving scale of the turbulent cascade.