Optimum velocity of a phase-space transformer for cold-neutron backscattering spectroscopy

Cold-neutron backscattering spectrometers are designed for inelastic neutron scattering experiments at a high energy resolution, where 0.5 µeV FWHM can routinely be achieved at the incident wavelength λ ≃ 6.3 Å. The phase-space transformation (PST) technique can be used to enhance the neutron flux at the sample position of such backscattering spectrometers at the expense of an acceptable increase of the beam divergence. Technically, the PST is achieved by a rotating disc carrying mosaic crystals on its circumference. Here a new analytical framework to describe the Bragg reflection of a divergent polychromatic beam from a moving mosaic crystal is discussed. Results obtained using this framework are compared with detailed Monte Carlo numerical simulations. The results presented here provide a deeper understanding of the PST and in particular of the optimum circumferential crystal speed of a PST device.