A numerical analysis of time focusing of crystal analyzer spectrometers on pulsed sources

We have carried out Monte Carlo simulations that support the linear analytical theory of time-focusing on crystal analyzer instruments and provide further interesting details on the time-of-flight signals obtained for different geometries. Important non-linear effects are revealed close to the time-focusing conditions. Calculations for realistic sizes of spectrometer elements indicate an elastic-scattering time-of-flight spread σ t / t approximately 7.9×10−5, far less than the conventional (and incorrect) Δ Θ cot Θ estimate for such type of instrument. The aim is to provide a basis for design of spectrometers of the highest possible resolution with the highest possible counting rates, meanwhile to reveal new flexibilities for the design e.g. tunable analyzer energy.