Effects of thermal expansion of the crystal lattice on x-ray crystal spectrometers used for fusion research

X-ray imaging crystal spectrometers with high spectral and spatial resolution are currently being used on magnetically confined fusion devices to infer the time history profiles of ion and electron temperatures as well as plasma flow velocities. The absolute measurement of flow velocities is important for optimizing various discharge scenarios and evaluating the radial electric field in tokamak and stellarator plasmas. Recent studies indicate that the crystal temperature must be kept constant to within a fraction of a degree to avoid changes of the interplanar 2d-spacing by thermal expansion that cause changes in the Bragg angle, which could be misinterpreted as Doppler shifts. For the instrumental parameters of the x-ray crystal spectrometer on Alcator C-Mod, where those thermal effects were investigated, a change of the crystal temperature by 1 °C causes a change of the lattice spacing of the order of Δd = 1 × 10⁻⁵ Å introducing a fictitious velocity drift of the order of ∼3 km s⁻¹. This effect must be considered for x-ray imaging crystals spectrometers installed on LHD, KSTAR, EAST, J-TEXT, NSTX and, in the future, W7-X and ITER. (paper)