Monte Carlo simulation of a pulsed-source time-focused crystal analyzer spectrometer

We have carried out simulations of a time-focused pulsed-source crystal analyzer (inverse geometry) spectrometer using the VITESS Monte Carlo neutron scattering instrument simulation code(1,2). The configuration of the instrument is one suggested by the recently reported general theory of this class of instrument(3,4). That theory provides the basis for design to accomplish high resolution while allowing other than backscattering geometry and more flexibility in choices of the type of analyzer crystal and the detector location. The VITESS code has all the capabilities needed to treat this type of spectrometer: three-dimensional generality, time-of-flight, off-cut mosaic crystal reflection, and high computational efficiency, all of which we exercised. We analyzed a configuration with a 50.-m incident flight path, 2.-m distance from sample to analyzer, and 1.8-m distance from analyzer to detector, assuming elements 1.-mm thick and considering reflectivity widths up to 0.5degrees. The Bragg angle at the analyzer was 80.degrees and the assumed d-spacing was 3.13 Angstrom. We report results concerning the orientations of the moderator (neutron source), the sample, the analyzer crystal, and the detector that prove out the focusing conditions resulting from the theory. Calculations for realistic sizes of elements and 90degrees scattering angle indicate an elastic-scattering time-of-flight resolution Deltat/t approximately 6. x 10(-5) (far less than a conventional estimate cot ThetaDeltaTheta) for the instrument geometry alone, absent the contributions from finite moderator emission-time width and finite-width monochromator d-spacing distribution. Simulations of a second analyzer arm at 60degrees also show the focusing effect, although we have so far been unable to carry this out for the same sample orientation as for 90degrees, as theory assures should be possible. The calculations also provide indications of the limits of the linear focusing theory.