Analytical study of ultra-short pulse reflectometry

The results of an analytical treatment of the time-dependent 2D fun-wave equation are presented here for the case of ultra-short pulse (USP) reflectometry. We consider several models of the plasma geometry, namely linear and nonlinear slab models, as well as a 2D plasma density profile with cylindrical symmetry. The latter model is more realistic when compared to the 1D stratified plasma models previously employed in all the analytical, and most numerical, treatments, since the plasma in 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 modelling, a signal record analysis method of profile reconstruction is proposed. The method has the advantage of using raw signal records instead of poorly localized frequency modes, which makes it robust for the profile measurements using, USP reflectometry.