Beam model of Doppler backscattering

Valerian H. Hall-Chen, Felix I. Parra, Jon C. Hillesheim

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


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 for the DBS signal localisation and the wavenumber resolution. In determining 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 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.

Original languageEnglish (US)
Article number095002
JournalPlasma Physics and Controlled Fusion
Issue number9
StatePublished - Sep 2022
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Nuclear Energy and Engineering
  • Condensed Matter Physics


  • Doppler reflectometry
  • beam tracing
  • localisation
  • microwave diagnostics
  • mismatch angle
  • plasma turbulence
  • wavenumber resolution


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