Beam model of Doppler backscattering

TL;DR

This paper develops a beam tracing model for Doppler Backscattering diagnostics in tokamaks, accounting for magnetic geometry effects, mismatch correction, and signal localization, enhancing diagnostic accuracy without empirical tuning.

Contribution

It introduces a new beam tracing model using Scotty, incorporating magnetic shear and field line curvature effects, and provides explicit mismatch correction formulas for DBS signals.

Findings

Model accurately predicts DBS power and localization.

Magnetic shear and field line curvature are key factors.

Mismatch correction improves measurement accuracy.

Abstract

We use beam tracing -- implemented with a newly-written code, Scotty -- and the reciprocity theorem to derive a model for the linear backscattered power of the Doppler Backscattering (DBS) diagnostic. Our model works for both the O-mode and X-mode in tokamak geometry (and certain regimes of stellarators). We present the analytical derivation of our model and its implications on the DBS signal localisation and the wavenumber resolution. To determine these two quantities, we find that it is the curvature of the field lines and the magnetic shear that are important, rather than the curvature of the cut-off surface. We also provide an explicit formula for the hitherto poorly-understood quantitative effect of the mismatch angle. Consequently, one can use this model to correct for the attenuation due to mismatch, avoiding the need for empirical optimisation. This is especially important in spherical tokamaks, since the magnetic pitch angle is large and varies both spatially and temporally.