Beam model of Doppler backscattering : theory and experiment

We use beam tracing - implemented with a newly-written code, Scotty - in combination with 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 proceed to shed light on the hitherto poorly-understood quantitative effect of the mismatch angle. Armed with this knowledge, we analyse MAST DBS data for various frequency channels and at various times, demonstrating that the beam model can indeed properly account for the mismatch attenuation. Interestingly, we show that mismatch attenuation can have a significant effect on localisation, shifting it away from the cut-off. Consequently, one can use this model to correct for the attenuation due to mismatch and its effect on localisation, 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.