Beam model of Doppler backscattering

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