Effect of Plasma Profile Curvature on Microwave Scattering in Reflectometry(Gases, Plasmas and Electric Discharges)

The results of analytical solution of the time-dependent 2D full wave equation in cylindrical coordinates are presented here with application to plasma fluctuation reflectometry. We consider a family of plasma density profiles with cylindrical symmetry, which allow for a full integration of the microwave scattering problem in Born approximation. The cylindrical model is more realistic as compared to the 1D stratified plasma models previously employed in all the analytical and most numerical treatments since the plasma in the fusion toroidal devices, mirror machines and plasma processing chambers can often be considered axially symmetric on the scale relevant to microwave reflectometry. Based on the results of analytical modeling, the effects of beam refraction and scattering are studied taking into account possible asymmetry in the antenna alignment. The curvature effects on the microwave reflection and scattering are visualized and compared for the cases of plasma profiles with low and high curvatures. The reflectometer sensitivity to the small radial scale fluctuations is shown to increase in the plasma with the high curvature. Obtained expressions can be applied to the other reflectometry-related issues, such as Doppler refiectometry, phase runaway effect, and the turbulence amplitude estimation.