Simulations of Chopper Jitter at the LET Neutron Spectrometer at the ...

Simulations of Chopper Jitter at the LET Neutron Spectrometer at the ISIS TS2 3Figure 2. LET chopper and guide layout. Top panel shows the chopper distancesand chopper geometry. Bottom panel shows the layout of the guide, with the chopperpositions outlined.[7]• The slow Frame Overlap (FO) chopper removes long wavelength neutrons from theprevious moderator pulse.• The Pulse Removal (PR) chopper selectively removes pulses, to increase pulseseparation, by running at an integer factor slower than the resolution choppers.This is illustrated in fig. 4, where the PR is run at half the speed of the resolutionchoppers, to remove every second pulse.• The contaminant removal chopper (CR) removes fast neutrons coming from the tailof the pulse.[4]Illustrated by simulation results in figure 4, the white beam from the short pulsed(4 µs) moderator is separated into a few distinct wavelengths by the first set of fast

Simulations of Chopper Jitter at the LET Neutron Spectrometer at the ISIS TS2 4Figure 3. A picture of the actual Res 2 chopper, where the double slits are clearlyvisible.SampleRes2CRPRRes1 & FOGuide startFigure 4. Flight distance vs time in ray tracing, showing the ”white” beam fromthe moderator in the energy range 4.9-5.1 meV, being separated into a few distinctwavelengths by the first resolution choppers (Res1) at 7.83 m, with the desiredwavelength singled out by the pulse removal (PR) chopper at 11.75 mresolution choppers (Res1). The desired wavelength is singled out by the slow pulseremoval (PR) chopper, as can be seen in the energy distribution in fig. 5.Note also the novel double funnel system at the Res2 choppers, seen in fig. 2,designed to further increase the resolution of the instrument, by allowing more narrowchopper windows, without sacrificing neutron flux.[5]

Simulations of Chopper Jitter at the LET Neutron Spectrometer at the ISIS TS2 53. Chopper JitterPhysical beam choppers are never perfectly at the desired phase, but rather deviate bya random error at any given time. Whereas most neutron simulations are performedwith mathematically perfect beam choppers, here a random phase error (jitter) is addedto give more physically realistic choppers. For the purposes of this article we choose thejitter to be Gaussian, parametrized by the width of the Gaussian error[6]The size of the jitter is then defined as the width of the Gaussian error, which is usedas the jitter parameter.For every event where a neutron ray reaches a chopper, the phase θ is calculated thus:θ = θ 0 + j ∗ rand norm ∗ ω (1)Where θ 0 is the chopper position without jitter, j is the jitter parameter for the chopperwith units of time, rand norm is a normalized Gaussian random number (with σ 2 = 1)and ω is the angular velocity of the chopper.To illustrate the effect of chopper jitter, we consider the basic equation for flight time:t = α ∗ λ ∗ L (2)where λ is the neutron wavelength, L is the flight length, and the constant α isα = m n /h ≈ 252 µs/m/Å.[10]Hence, if the jitter is the only source of uncertainty, we have that the uncertainty in thewavelength is:dλ = dt(3)αLSo for a realistic jitter value, (dt), of 0.4 µs in the second resolution choppers, located at15.7 m from Res1, this contribute to the uncertainty in the wavelength (dλ) of 6*10 −5 Å,and thus a dE of 0.1 µeV for 5 meV neutrons. In comparison the resolution is at about20 µeV at 250 Hz.Since the energy of neutrons arriving in the physical detector bank is calculated bythe ToF-method, a small discrepancy in the arrival time at the sample, can, over the 3.5m from the sample to detector, translate into a much larger difference in the neutronenergy perceived by the detector. Considering again the jitter dt = 0.4 µs in the 2ndresolution choppers, this corresponds to an uncertainty in the perceived wavelength (dλ)of 510 −4 Å, and thus a dE of 1 µeV for 5 meV neutrons.Some neutron instruments compensates for jitter with a ’veto’ system, where anevent is discarded if an unacceptable discrepancy of the chopper phase is detected. Theveto scheme is not included in the present simulations.4. Simulation resultsThe instrument was built in the McStas neutron simulation package[2, 3], by addingthe physical components (moderator, guide sections, beam choppers) sequentially, with

Simulations of Chopper Jitter at the LET Neutron Spectrometer at the ISIS TS2 6monitors interspersed at suitable locations. Note that the monitors used in the simulationsdoes not emulate physical detectors, in as much as they do not alter or absorb thedetected neutron rays.The simulations used to generate the figures in this paper were typically run with 5∗10 8rays, which corresponds to approximately 20 min. CPU-time on an ordinary dual-corelaptop.Fig. 5 shows the energy distribution of the beam at various positions in the instrument,with perfect beam choppers. Notice the multiple peaks after the first resolution choppers,reduced to the single 5 meV peak by the PR chopper, as would be expected in thephysical instrument.To illustrate the performance of the spectrometer, we have performed virtualexperiments using an incoherent elastic scatterer[8]. Typical outcomes of theseexperiments are shown in fig. 6, while the deduced line width is shown in fig. 9.With highly imperfect beam choppers (large jitter), the detected energy distributioncan be seen to noticeably widen. This is illustrated in fig. 6, and clear effects are visiblefor jitter values of 10 µs. The line shape is almost perfectly Gaussian at zero jitter, thenbecomes increasingly Lorentzian with added jitter.As expected from the ToF equation (2), the effect of the jitter depends significantlyon the speed of the choppers, as can be seen in fig. 7, where the intensity drops off muchmore rapidly for increasing jitter, with the chopper set to the higher speed, as can beseen in fig. 7.Simple analytical calculations of the time resolution at the detector positionsupports the simulated resolution increase with jitter, shown in figs. 6 and 9. Weuse the ToF equation to calculate the allowed arrival times of neutrons at the detector,for different values of jitter.4.1. Side peaks in simulationsWhen building non-standard components, care and attention is needed to avoidsimulation artefacts. As the chopper slits of the Res2 double choppers in the simulationsare triangular, and the guide openings of the double funnel system are rectangular, tryingto fit them onto the rectangular guide opening of the double funnel system, resulted inthe side peaks shown in the (x,t) diagram in fig. 8. What happens is that a short timebefore and after the double chopper turns to the open alignment, small slices of the10 mm wide guide openings are not covered by the absorbing section between the dualchopper slits (see fig. 2), which is 11 mm at its widest.In the actual instrument, the chopper slits have been shaped so as to avoid this effect.See fig. 3

Simulations of Chopper Jitter at the LET Neutron Spectrometer at the ISIS TS2 7(a) After Res1 choppers(b) After PR chopper(c) After CR chopper(d) After Res2 choppers(e) Sample position(f) TOF at sample positionFigure 5. a-e: Energy distribution of the beam at the chopper and sample positions,at nominal energy E = 5 meV. f: Time of flight (TOF) distribution at sample position.The slight tail seen on the left side of panels d,e can be traced back to the long time-tailof the source pulse. Note also the very small side peaks at 2.566 and 2.570 in panel f,explained in section 4.1

Simulations of Chopper Jitter at the LET Neutron Spectrometer at the ISIS TS2 8(a) Zero jitter(b) 2 µs jitter(c) 10 µs jitter(d) 20 µs jitterFigure 6. A virtual experiment: Detector output when scattering off a vanadiumsample of radius 1 cm, with both beam choppers running at 140 Hz, and with 4different jitter settings.5. Discussion and ConclusionWe have conducted a detailed simulation of the LET spectrometer. We find that theinstrument performs in general as expected.As can be seen in fig. 9, jitter values at or below 2 µs have less than 1 % effect onthe instrument resolution, judged from virtual experiments of elastic scattering, withthe chopper speed set at 250 Hz. In comparison, the jitter when running the actualLET resolution choppers at the same speed, is at 0.4 µs. The simulated degradation ofresolution at this jitter is well below the statistical uncertainty (0.04 %) of the simulationresults.In conclusion, our simulations show that jitter will have negligible effect on theperformance of the actual LET instrument. In cases where a lorentzian tail in theresolution function is particularly detrimental, a more careful analysis is needed.Simulation of jitter effects on future designs of high resolution instruments could lead to

Simulations of Chopper Jitter at the LET Neutron Spectrometer at the ISIS TS2 9(a)Figure 7. Intensity vs. jitter at the detector position, for two different chopper speedsettings, from 0 to 10 µs jitter. At 140 Hz a drop of approximately 4 % can be seen,vs. 10 % at 250 Hz. Blue is 140 Hz, red is 250 Hz.a more detailed understanding of demands for chopper precision. In particular, it canbe investigated whether precision can be sacrificed to reduce costs.[1] ISIS Pulsed Neutron & Muon Source http://www.isis.rl.ac.uk/[2] McStas documentation is available at the homepage: http://www.mcstas.org[3] K. Lefmann and K. Nielsen, McStas, a General Software Package for Neutron Ray-tracingSimulations, Physica B 283, 426 (2000)[4] R. Bewley, Multi-rep rate on LET version 3, ISIS report (September 2005)[5] R. Bewley: Simulations of the double funnel construction for LET. Comparison with a singlefunnel, ISIS report (2005).[6] Jitter is now included in the official McStas software.[7] R. Bewley, LET specification, ISIS report (Jan. 2006)[8] K. Lefmann et al: Virtual Experiments: The Ultimate Aim of Neutron Ray Tracing, accepted forJournal of Neutron Research, 2008[9] K Lefmann, H Schober, F Mezei: Simulation of a multiple-wavelength time-of-flight neutronspectrometer for a long pulsed spallation source. Measurement Science and Technology A 589,34, 2008[10] G. L. Squires: Introduction to the Theory of Thermal Neutron Scattering, Dover Publications,

Simulations of Chopper Jitter at the LET Neutron Spectrometer at the ISIS TS2 1010^y (neutrons/s)(a)(b)Figure 8. A simulation artifact: side peaks created by trying to fit the rectangularguide openings of the double funnel system, with the triangular chopper slits of theRes2 double choppers. Top panel: Logarithmic ToF at the sample position. Bottompanel: Horizontal position vs. time at the 2. resolution choppers, centered in timewhen the main peak in graph a hits.

Simulations of Chopper Jitter at the LET Neutron Spectrometer at the ISIS TS2 11(a)Figure 9. Resolution of the instrument detector, as a function of jitter, with resolutionchoppers running at 250 Hz. Line width is found by the standard deviation of the data,and not by actual curve fitting. Note that most error-bars are eclipsed by the dots.1996.