Beam-tracing-based diagnostic response correction for low-frequency Doppler backscattering in the QUEST spherical tokamak

A three-channel X-/Ku-band Doppler backscattering (DBS) system has been developed and installed on Q-shu University Experiment with Steady-State Spherical tokamak (QUEST) for turbulence and electric-field measurements. In spherical tokamaks, the large magnetic-field pitch angle can increase the geometric mismatch between the probing beam wave vector and the local magnetic field, reducing the backscattering efficiency. In QUEST, the low plasma density additionally requires low-frequency probing, for which beam-propagation effects become increasingly important. To address these issues, a diagnostic response correction methodology based on the synthetic DBS code SCOTTY was established. The diagnostic response, including beam propagation and scattering geometry effects, was evaluated along ray trajectories to derive a correction factor for the backscattered power. The correction factor strongly depends on probing frequency and measurement location, demonstrating the importance of accounting for these effects when comparing measurements under different conditions. After applying the correction, the resulting quantities represent sensitivity-weighted fluctuation amplitudes over effective scattering regions rather than pointwise local amplitudes. Larger corrected values were obtained at lower frequencies corresponding to the plasma edge. However, because the frequency-dependent response of the receiving system was not calibrated and the measurements correspond to different k⊥ values, these differences cannot be directly interpreted as either physical fluctuation-amplitude differences or radial dependence at a fixed wavenumber. This work demonstrates beam-tracing-based diagnostic response correction for low-frequency X-/Ku-band DBS measurements in QUEST.