The collective Thomson scattering (CTS) diagnostic proposed for ITER is designed to measure projected 1D fast-ion velocity distribution functions at several spatial locations simultaneously. The frequency shift of scattered radiation and the scattering geometry place fast ions that caused the collective scattering in well-defined regions in velocity space, here dubbed interrogation regions. Since the CTS instrument measures entire spectra of scattered radiation, many different interrogation regions are probed simultaneously. We here give analytic expressions for weight functions describing the interrogation regions, and we show typical interrogation regions of the proposed ITER CTS system. The backscattering system with receivers on the low-field side is sensitive to fast ions with pitch |p| = |v∥/v| < 0.5–0.9 depending on the ion energy and the frequency shift of the scattered radiation. A forward scattering system with receivers on the high-field side would be sensitive to co- and counter-passing fast ions in narrow interrogation regions with pitch |p| > 0.6–0.8. Additionally, we use weight functions to reconstruct 2D fast-ion distribution functions, given two projected 1D velocity distribution functions from simulated simultaneous measurements with the back- and forward scattering systems.

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We compute tomographies of 2D fast-ion velocity distribution functions from synthetic collective Thomson scattering (CTS) and fast-ion D α (FIDA) 1D measurements using a new reconstruction prescription. Contradicting conventional wisdom we demonstrate that one single 1D CTS or FIDA view suffices to compute accurate tomographies of arbitrary 2D functions under idealized conditions. Under simulated experimental conditions, single-view tomographies do not resemble the original fast-ion velocity distribution functions but nevertheless show their coarsest features. For CTS or FIDA systems with many simultaneous views on the same measurement volume, the resemblance improves with the number of available views, even if the resolution in each view is varied inversely proportional to the number of views, so that the total number of measurements in all views is the same. With a realistic four-view system, tomographies of a beam ion velocity distribution function at ASDEX Upgrade reproduce the general shape of the function and the location of the maxima at full and half injection energy of the beam ions. By applying our method to real many-view CTS or FIDA measurements, one could determine tomographies of 2D fast-ion velocity distribution functions experimentally.

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