The performance of neutron diffractometers at long and short pulse spallation sources: Comparison between ESS and J-PARC

Abstract

The general performance of diffractometers at the first long pulse spallation source ESS, is compared with their counterparts at J-PARC, a short pulse spallation source. The difference in the inherent pulse structure of these neutron sources presents opportunities for new concepts for instrumentation, where performance does not scale simply with source power. The article describes advantages and disadvantages of those diffractometers, adapting to the very different source characteristics. We find that the two sources offer comparable performance in flux and resolution when operating in high-resolution mode. ESS offers significant advantages in tunability and flexibility, notably in the ability to relax resolution in order to increase flux for a given experiment. The slow repetition rate of ESS favors long instruments. On the other hand, J-PARC instruments perform very well in spite of the lower source power and allow better access to epithermal neutrons, of particular interest for PDF analysis of diffraction data.

Keywords

ESS J-PARC source diffractometer instrument performance

1. Introduction

The European Spallation Source (ESS), currently under construction in Lund, Sweden, will be the first long pulse spallation source capable of an unprecedented 5 MW of power with a pulse width of 2.857 ms at a repetition rate of 14 Hz. Pulsed spallation sources, so far, have been using a short proton pulse of sub-1 μs duration to produce sharp neutron pulses, suitable for analyzing their energy by the time-of-flight (TOF) method. The TOF requirements at a long pulse source are similar and the approach here is to use mechanical choppers to cut out appropriately shaped and timed shorter pulses from the long pulse. This is achieved by a pulse shaping chopper (PSC), producing a favorably symmetric pulse shape in time, and potentially associated with a significant penalty in the flux delivered to the instrument.

In the present paper, we continue our analysis of the performance of neutron scattering instruments at ESS in comparison to similar instruments at J-PARC to extend our analysis of the ESS spectrometers [4].

We compare the performance of the diffractometers DREAM and BEER at ESS at a beam power of 5 MW at 14 Hz with corresponding short-pulse instruments, SHRPD, iMATERIA and TAKUMI at J-PARC, which are under operation at a power of 1 MW at 25 Hz. Those instruments have clear target requirements in resolution. Performance comparisons between instruments of the same type can thus provide a good platform for a better understanding of the advantages and disadvantages of long and short pulsed spallation sources for diffractometers. There are other measures for performance of diffractometers such as Q-range, signal-to-background ratio, available sample size and versatility. These, however, depend highly on the details of the detector arrangements, guide design, shielding and the scientific aims of the instrument. Therefore, those specific aspects have not been considered in this analysis, but are crucial factors for the realistic performance of instrument.

The J-PARC instruments were designed more than 20 years ago and have been operated since 2008, while the ESS instruments are still under construction and are planned to be operated from 2025. During this time period, instruments technologies and software have made significant progress. To ensure a fair comparison, we therefore do not aim to compare the detailed performance of instruments but to understand the essential features of advantage/disadvantage of short/long pulse sources under the general assumption of equivalent secondary spectrometers and perfect brilliance transfer from moderator to sample. We aim that this article will be helpful for the consideration of future developments, such as accelerator driven compact neutron sources, whose pulse length is controllable even during operation responding to instrument-driven requirements.

2. The source performance

2.1. Time averaged brightness

As was discussed in [4], due to the character of the Para hydrogen neutron cross-section [13], ESS has adopted a flat moderator of 3 cm in height [2] in combination with an ambient water moderator, providing an expected gain factor of ca. 2.5 in the cold neutron energy region, compared to the traditional volume moderators at J-PARC. The ESS’s hybrid moderator system provides a dual spectrum to instruments which can choose to employ bi-spectral extraction, as described in Refs. [2, 21]. Together with the high proton power of 5 MW, this advanced moderator design is expected to provide a source performance which is generally higher by a factor 10 with a remarkable gain of 60 in the thermal neutron region [4] in comparison with the coupled moderator of J-PARC [6].

Fig. 1.

Time-averaged brightness of ESS (5 MW) moderators, which are advanced coupled moderator. J-PARC (1 MW) has three types of moderators; coupled (CM), decoupled (DM), and decoupled poisoned moderators (DPM) (the last one with two distinct moderation characteristics), all of them Para-Hydrogen moderators at 20 K. The brightness here is defined as that at the surface of moderators [6]. In the figure instruments viewing each moderator are depicted.

Since the pulse time-width can be adjusted by the decoupling technique [20], there are three types of moderators at J-PARC (one of them is split into two characteristics). Those are the coupled moderator (CM), decoupled moderator (DM), and decoupled poisoned moderator (DPM, asymmetrically poisoned to provide a poisoning plate depth of 2.5 cm on one side and 3.5 cm the other). Here, we focus on the decoupled poisoned moderators which are viewed by high-resolution diffractometer, SHRPD (viewing the 2.5 cm side) and the high throughput diffractometer iMATERIA and engineering diffractometer TAKUMI (both viewing the 3.5 cm side). Figure 1 shows the time averaged brightness of J-PARC moderators at the moderator surface in comparison to that of ESS as a function of wavelength [1 Å = 0.1 nm]. As we can see in Fig. 1, the time averaged brightness of ESS significantly exceeds that of J-PARC. The available brightness of DPM at 1 Å is lower by about a factor of 200 and 600 at 3 Å. Moderator design at short pulse sources is strongly coupled with instrument design. Therefore, requirements from instrumental resolution sometimes results in significantly sacrificing brightness as we will explain in more detail in the next section. Conversely, moderator performance, particularly its time structure, has a less strong connection to instrument design at a long pulse source, in which a PSC can produce an optimized time-width. As far as the time averaged brightness is concerned, it is obvious that the potential performance of ESS could far exceed that of J-PARC. However, as we will discuss in the following sections, we need to estimate “practical” brightness, which is operationally defined according to the required resolution of each instrument, and we will see the very large difference in the time averaged brightness become modest when comparing the practical brightness for a set of particular use cases, while seeing great benefits for ESS instruments in another aspect.

2.2. Time-width and pulse shaping

The resolution of TOF diffractometers is described as [3]; $\begin{array}{l} (1) & {(\frac{Δ Q}{Q})}^{2} = {(\frac{Δ d}{d})}^{2} = {(cot (θ) \cdot Δ θ)}^{2} + {(\frac{Δ t}{t})}^{2} + {(\frac{Δ L}{L})}^{2}, \\ where Q = 4 π \cdot sin θ / λ \\ (2) & Δ θ = SQRT ({(Δ θ_{s})}^{2} + {(Δ θ_{d})}^{2}) \\ (3) & t [μ s] = \frac{L}{v} = \frac{m \cdot λ \cdot L}{h} = \frac{λ [Å] \cdot L [cm]}{0.3956}, \end{array}$ where Q is the momentum transfer, d is the crystal lattice spacing, $2 θ$ is the scattering angle, t is the flight time of neutron, and $Δ t$ is the time uncertainty, which can be simplified as the pulse time-width at the moderator. λ is wavelength, L is the flight distance, $Δ L$ is the uncertainty in the flight distance, m is the neutron mass, and h is Plank’s constant. Angular uncertainty is composed of incident beam divergence and angular divergence defined by sample size and detector element size. The diffraction geometry and the relevant parameters are illustrated in Fig. 2. Following Eq. (1), a classic high-resolution diffractometer design would ideally feature a long flight path with a sharp pulse time-width and neutron detection placed at a back-scattering angle.

Fig. 2.

Illustration of a typical diffractometer. Neutron starts from the source on the left, propagates through a guide, is scattered at the sample to a scattering angle at $2 θ$ , and is detected at a detector. In case for a sharp pulse source, a chopper defines a wave length band and does not shape a pulse structure. On the other hand, for a long pulse source, a pulse shaping chopper (PSC) cuts out short pulse from the original long pulse at the source.

Traditionally at a short-pulsed source, powder diffractometers use a limited detector extent with a constant angular resolution with $Δ t / t$ = constant configuration in order to produce as constant $Δ d / d$ as possible in 1-D histogram (see Eq. (1)) so as to resolve the higher density of diffraction peaks in the high Q region as much as possible. A constant time resolution $Δ t / t$ can be achieved by the decoupling technique of moderators at short pulse sources [20]. In the epithermal region because of the dominating decay process in the moderator, $Δ t / t$ = constant is naturally achieved regardless of the moderator, giving an opportunity for observation up to very high Q and providing the high r-resolution, see Fig. 3. Those are the key reasons why high-resolution powder diffractometry and PDF analysis are very successfully used at short-pulse sources so far [5].

On the other hand, at long-pulse sources, fast counter-rotating pair of choppers can produce symmetric short pulse, down to a wavelength of ∼0.5 Å and with a pulse time as low as ∼10 μs. The mechanically generated short pulses offer new perspectives for high-resolution backscattering particularly with a fully coupled cold source at ESS.

Fig. 3.

Pulse time-width as a function of wavelength [Å]. Plots are for three J-PARC’s moderators, $Δ t = 7 λ$ , the Pulse Shaping time-width of $t ⩾ 10 μ s$ for DREAM and that of a blind chopper with a distance of 15 cm for BEER. Only the practically available wavelength ranges are depicted for BEER (1 Å–3.6 Å) and DREAM (0.5 Å–15 Å). The shaded area is the extent of the available time-width of DREAM and of BEER by adjusting PSCs.

Figure 3 shows the pulse-peak time-width $Δ t$ as a function of wavelength for the coupled, decoupled and decoupled poisoned moderators (with 3.5 cm depth (viewed by iMATERIA and TAKUMI) and 2.5 cm depth (viewed by SHRPD)) of J-PARC. A straight slope in the figure corresponds to “ $Δ t / t$ = constant” [14], almost extending in the entire region, which is roughly approximated for DPM (3.5 cm) as $\begin{matrix} (4) & Δ t [μ s] \sim 7 \cdot λ [Å], \end{matrix}$ resulting from the scattering decay process of neutrons in the moderator [9]. The practically available wavelength band for each instrument is listed in Table 1. Figure 3 also illustrates the high-resolution setting (dotted line) of DREAM with a 10 μs pulse width and of BEER with $d_{ch} = 15 cm$ as described below. The shaded areas indicate the tunable time-width by adjusting PSCs; it consists of quasi-discrete steps for DREAM because of the counter rotating chopper pair system.

An alternative pulse shaping technique to a fixed-time window chopper opening, is the blind chopper setup, which provides a pulse train with $Δ t / t$ = constant and independent of λ as illustrated in Fig. 3 for BEER. The instrument is designed to cover a wavelength range of 1 Å–3.6 Å [15]. Figure 4 illustrates further the blind chopper concept. Here, a time resolution specified in Eq. (5) is given by the ratio between the distance “ $d_{ch}$ ” between a pair of choppers and the distance “ $L_{1}$ ” from the center of the two choppers to the sample. $\begin{matrix} (5) & Δ t / t = 0.68 \cdot d_{c h} / L_{1} \end{matrix}$ A conversion factor of 0.68 between a half width (Δ) and full width (X), $Δ = {(1.5 \cdot ln 2)}^{1 / 2} \cdot X = 0.68 X$ , is taken [18]. The concept imitates a short pulse source characteristic, and is important to keep a constant resolution at a specific detector angle, allowing stress analysis to be done at near ±90° on an engineering diffractometer.

Fig. 4.

Blind chopper concept. A pair of choppers create a virtual source, which behaves as a sharp pulse source with $Δ t$ proportional to λ.

2.3. Peak brightness

Peak brightness of a pulsed neutron source is a helpful indicator of the expected performance of a neutron diffractometer because it directly contributes to a Bragg peak intensity. Figure 5 shows the peak brightness per second in wavelength for various J-PARC moderators and ESS. The peak brightness can also be shown on a per pulse basis, as is done in Fig. 4 and 5 of Ref. [4]. However, since an actual measurement accumulates statistics by measuring over many pulses, the presentation in Fig. 5 is more practical to foresee the diffraction signal within a given measurement time. It can be approximated by the time averaged brightness in Fig. 1 divided by the time-width in Fig. 3 for the J-PARC moderators or divided by 2.857 ms for ESS moderator, and the peak brightness per pulse can be obtained by further dividing by the source frequency of 14 Hz for ESS and 25 Hz for J-PARC. In Fig. 5 we see how the J-PARC moderators have high peak brightness even with their much lower power of the accelerator compared to ESS. Enhancing the peak brightness is a key objective in the design of short pulse sources, especially below 1 Å in the epithermal region, which significantly exceeds that of ESS.

Fig. 5.

Peak brightness per second for the moderators, $B_{P} (λ)$ [n/cm²/s²/str/Å], which are produced as the time averaged brightness in Fig. 1 divided by the time-width in Fig. 3 for the J-PARC moderators and by 2,857 ms for the ESS moderator.

2.4. Brightness and diffracted Bragg peak intensity

In order to clearly see how the brightness is reflected in the diffraction peak intensity, we developed an analytical formula for the diffraction pattern as in the Appendix. According to the Appendix, the diffraction pattern is described as; $\begin{array}{l} I_{h k l} (i) = & T_{expt} \cdot H_{PS} (t) \otimes H_{ANG} (λ) \cdot w (i) \cdot B_{P} (λ) \cdot Δ t_{PS} \cdot Δ λ_{ANG} \cdot {(Δ θ_{s})}^{2} \cdot ϵ (λ) \\ (A.5) & \times f_{DS} \cdot N_{s} \frac{λ^{4}}{4 π v_{u s} {sin}^{2} θ} K_{h k l} \cdot | F_{h k l} |^{2} \end{array}$ where $I_{h k l} (i)$ is the observable integrated intensity in an i’th TOF bin, and $B_{P} (λ)$ is the peak brightness per second (n cm⁻² sr⁻¹ s⁻¹Å⁻¹ s⁻¹). Details of the other functions are described in the Appendix. An important point of Eq. (A.5) is that the diffraction peak-shape is specified from the two components $H_{PS} (t)$ and $H_{ANG} (λ)$ ; $H_{PS} (t)$ is specified with the time uncertainty at source or pulse shaped time-width, and $H_{ANG} (λ)$ is attributed to the angular uncertainty of the diffracted neutrons. Although we neglect a cross term between the two terms by taking a Gaussian peak shape approximation, the formula is sufficient to understand the intrinsic character of the diffraction pattern. The actual peak shape function at a short-pulse source has a complex peak structure caused by the moderation process of neutrons and is analyzed in Ref. [19]. The formulation of Eq. (A.5) is especially useful to consider a diffraction pattern at a long pulse source, where the time-width, $Δ t_{PS}$ , can be freely chosen according to the requirements of each specific measurement by PSC. Under a given geometrical set-up of the guide system, sample size, detector element size etc., the parameters such as incident angular divergence $Δ θ_{S}$ , wavelength uncertainty $Δ λ_{ANG}$ attributed to the angular uncertainty of diffracted neutrons, and other components are prescribed, which are decoupled from the effect on a choice of $Δ t_{PS}$ .

In order to clearly show the effect in the diffraction peak shape on a choice of a pulse shaping time-width $Δ t_{PS}$ , we calculated a diffraction pattern of diamond at a near backward direction, where the angular term can be neglected and the intensity related with the components sensitive to the choice of time-width in Eq. (A.5) is described as follows; $\begin{matrix} (6) & Intensity (λ) \propto \sum_{h k l} H_{PS} (λ - λ_{h k l}) \cdot B_{P} (λ) \cdot Δ t_{PS} \cdot M_{h k l} \cdot | F_{h k l} |^{2} \end{matrix}$ here, the reflection multiplicity $M_{h k l}$ is included in order to characterize the reflections.

Fig. 6.

Diffraction pattern of Diamond at near backscattering at a flight distance at 70 m estimated from Eq. (6) for $Δ t_{PS}$ of 10 μs, 200 μs and one of blind chopper with $d_{ch} = 75 cm$ , which was chosen to clearly show the development of the width in the d-spacing. The insets to the figure more clearly show it.

Figure 6 shows Bragg reflections of diamond at a near backward scattering angle at a flight distance of 70 m, corresponding to that of DREAM, calculated by Eq. (6). Figure 6 shows three cases with $Δ t_{PS}$ of 10 μs, 200 μs and one of a blind chopper pair with $d_{ch} = 75 cm$ in order to illustrate the change of the width with wavelength. The insets to the figure show that a tiny difference of $Δ d = 0.005 Å$ between the reflections $(5 5 1)$ , $(7 1 1)$ and $(7 1 0)$ can be easily resolved with $Δ t_{PS} = 10 μ s$ , and the width of the blind chopper becomes wider than $Δ t_{PS}$ of 200 μs at $(3 1 1)$ . In the calculation, the brightness is assumed to be a constant independent of λ for simplicity.

As we see in Fig. 6, the peak intensity does not change on changing the time-width, as expected from Eq. (6).

An angular component defined as $Δ λ_{ANG}$ gives another contribution at a finite scattering angles as studied in Ref. [11, 12], in which a significant reduction of peak height was observed on increasing of the uncertainties in the angular and wavelength components. This mainly arises from the angular resolution, $cot θ \cdot Δ θ$ , the Lorentz factor, $\propto \frac{λ^{4}}{{sin}^{2} θ}$ , as well as an effect arising from the fraction of the Debye–Scherrer cone, $f_{DS}$ in Eq. (A.5), that intersects the pixel of detector. However, since these effects are independent of the source character, we do not discuss them in detail in this article.

Note that in terms of actually observable intensity, the peak shape is a convolution of two peak functions $H_{PS} (t)$ and $H_{ANG} (λ)$ in Eqs (A.6) and (A.7), and that the full intensity of the diffraction peak, integrated over its width is meaningful for structural analysis. The pulse shaping time-width directly gives a cut-out portion, $Δ t_{PS}$ , out of the long pulse and the wavelength width, $Δ λ_{ANG}$ , delivers a fraction of the brightness. The flux delivered to the sample is described by $B_{P} (λ) \cdot Δ t_{PS} \cdot Δ λ_{ANG} \cdot {(Δ θ_{S})}^{2}$ in Eq. (A.5). This situation is intuitively illustrated in Fig. 7. The volume specified by the shaded area, $B_{P} (λ) \cdot Δ t_{PS} \cdot Δ λ_{ANG}$ , is directly relevant to the integrated intensity of a Bragg peak. Therefore, for an optimized measurement, it is important to match the contributions to the resolution from $Δ t_{PS}$ and $Δ λ_{ANG}$ to have an optimization between the resolution and flux at sample. As we will come back this point later, only an instrument at long pulse source can intentionally tune both widths and optimize the experimental condition.

Fig. 7.

Intuitive illustration of a contribution to the flux, which is the shaded volume area, $B_{P} (λ) Δ t_{PS} Δ λ_{ANG}$ . The volume of the shaded area multiplied by ${(Δ θ_{S})}^{2}$ gives the flux at the sample.

3. Comparison of diffractometers: DREAM vs SHPRD, iMATERIA and BEER vs TAKUMI

Here in a general fashion, we compare the performance of two diffractometers under construction at ESS with their counterpart operational instruments at J-PARC. Those are BEER [1, 15] and DREAM [1, 16] at ESS, and TAKUMI [7], iMATERIA [10] and SHRPD [17] at J-PARC. The relevant instrumental parameters of these diffractometers are summarized in Table 1.

Table 1 reports, the primary flight path length “ $L_{1}$ ”, the secondary one “ $L_{2}$ ”, which depends on the detector angle, beam divergence at sample, sample size, detector element size, pulse time-width (for highest resolution and most relaxed resolution), which is varies with wavelength for the J-PARC instruments and BEER with a blind chopper pair system, wavelength band, wavelength range for a typical single frame, which can be shifted on demand, available wavelength range over several frames, d-range for given detector angles, over-all Q-range over detector coverage, and the resolution $Δ d / d$ of the high-resolution option.

Table 1
Key parameters of diffractometers. BEER, DREAM, SHRPD, TAKUMI and iMATERIA. BEER, SHRPD, iMATERIA have several detector banks, while DREAM has continuous detector coverage. The secondary flight path $L_{2}$ and the d-range are specified for each bank. Since for BEER and the J-PARC instruments, the time-width continuously varies with the wavelength, only the time-width at 2 Å is specified in the table. BEER uses a blind chopper pair and DREAM uses fixed-time window opening. The distance $d_{ch}$ between the pair of blind choppers is given for BEER. The Q-range specifies the overall range covered by all detector banks. The element size of the helium tube detectors of SHRPD and iMATERIA is renormalized by taking the geometrical average. All the d-ranges and Q-ranges specified, except for TAKUMI, are the theoretical values estimated from the detector angles and wavelength range for single frame measurement, except for the 5-frame mode of SHRPD. The $Δ d / d$ at the specified angle is the benchmark parameter to be discussed in the text

The practical Q-range does not significantly differ between the ESS and J-PARC counterpart pairs. In this regard, the two sources seem to provide a similar Q-range for conventional diffraction measurement. The exception is iMATERIA, which has a small-angle detector bank for SANS and intentionally uses epithermal neutrons by having a short $L_{1}$ and a straight guide.

In this analysis, we compare the performance in the high-resolution option as listed in Table 1 between the two diffractometers SHRPD ( $L_{1} = 94 m$ ) and DREAM ( $L_{1} = 70 m$ ), and between the two engineering diffractometers BEER ( $L_{1} = 150 m$ ) and TAKUMI ( $L_{1} = 40 m$ ). iMATERIA is a versatile high throughput diffractometer at J-PARC, and we will compare its performance with the relaxed resolution option of DREAM. In the comparison, we assume the secondary spectrometer is equivalent between the pairs of instruments being compared, unless clearly stated otherwise. This includes the scattering angle, sample size, detector size, and secondary flight path length. We therefore assume the angular components, $Δ λ_{ANG} \cdot {(Δ θ_{S})}^{2}$ , are equivalent to each other, and the practically available brightness which depends on the choice of time-width, $B_{P} (λ) \cdot Δ t_{PS}$ , gives a direct measure of the performance of the instruments.

3.1. DREAM vs SHRPD and iMATERIA

Both DREAM and SHRPD aim to provide high-resolution powder diffraction capabilities in particular at near-backscattering angles. The highest scattering angle is 178° and 175° respectively for each instrument, where a resolution higher than $Δ d / d \sim 0.04 %$ can be achieved. However, we set this value as a benchmark at which we evaluate the intrinsic characteristics due to the difference in the source nature. With higher scattering angles, better spatial detector resolution and tighter collimation, DREAM will aim at setting a new resolution limit.

Fig. 8.

Layout of DREAM [16] and SHRPD [17], showing the difference in the design concept. DREAM extracts both cold and thermal neutrons by bi-spectral switcher, stacked multi-mirrors, in the monolith beam port followed by a pin hole at 6 m. The guide system has an elliptical shape, along a straight guide axis. Pulse shaping chopper (PSC), band definition choppers (BD), high energy neutron suppression chopper (T0) tailor the time structure of neutron pulse. Detector system has a continuous coverage from small to high angle. On the other hand, SHRPD equips a curved guide with the curvature radius of $R = 9 km$ starting just outside the monolith shield at 8 m and switches to a straight guide at 40 m out of line of sight. There are three band definition choppers. The detectors are arranged into a low angle bank, a 90° bank and a high angle bank.

Figure 8 illustrates the conceptual design of DREAM and SHRPD, which clearly shows the difference in the design concept. DREAM extracts both cold and thermal neutrons by a bi-spectral switcher in the monolith beam port by taking a great advantage of ESS moderator, which has a very high brightness at both the cold and thermal region. A pulse shaping chopper (PSC) is set at 6 m right outside the monolith shield and $L_{1}$ is 70 m between the PSC and the sample. The concept of bi-spectral extraction has never applied in any sharp pulsed source, because the different moderation process in two moderators makes a pulse peak structure complicated to be analyze, and it was intentionally avoided by setting a decouplor [20]. But it does not matter at long pulse source, where PSC makes the pulse structure clean and simple. The guide system is an elliptical straight guide viewing a pin hole at PCS and making a focal point at the sample position. Fast neutrons are eliminated by a T0 chopper. The detector arrangement is continuous from small to high angle.

On the other hand, SHRPD does not have optical components in the monolith beam port in order to reduce the angular divergence of the incident beam at sample. The curved guide section starts at 8 m just outside the monolith shield (7 m) with a curvature radius of 9 km to eliminate high energy neutrons, and switches to a straight guide section at 40 m at the point at which direct line-of-sight to the source is lost. Three band-definition choppers control the bandwidth and frames. The detector system is composed of three separated banks from low angle, medium angle to high angle. In order to achieve the highest resolution, SHRPD reduces the sample size to 3 mm from the nominal size of 1 cm, which is otherwise chosen to match the detector diameter of 1.25 cm (renormalized size is 0.98 cm using the geometrical average of the helium tube detector width).

In order to realize the high resolution, SHRPD views a decoupled poisoned moderator with a Cd plate installed at 2.5 cm in depth in the moderator. It significantly sacrifices brightness as shown in Fig. 1 in comparison with the CM, but it achieves an extremely sharp pulse width [17]. On the other-hand the high-resolution option of DREAM uses a pulse shaping chopper (PSC) with a fixed-time window opening of $Δ t_{PS} = 10 μ s$ , which traces out the horizontal line in Fig. 3. The resolution limit at larger wavelength is limited by a length uncertainty of $Δ L / L = 1.3 \times 10^{- 4}$ [1] as a result of the design of the guide system and other elements, such as sample size, and detection depth of the detector system.

Fig. 9.

$Δ t / t$ as a function of wavelength. The high-resolution options of DREAM ( $Δ t_{PS} = 10 μ s$ ) and BEER ( $d_{ch} = 15 cm$ ) and that of DREAM with $Δ t_{PS} = 40 μ s$ matching with iMATERIA’s resolution are depicted. Each wavelength range corresponds to the single time frame shown in Table 1, except for SHRPD, which uses 5 frame mode. The shaded band indicates the conventional wavelength band for standard diffraction experiments from 1 Å to 3 Å. The dotted line at 0.013% is the limit from $Δ L / L$ of DREAM.

To show this arrangement more clearly, the time resolution is illustrated as a function of the wavelength in Fig. 9 for the wavelength band (WB) of running in single-frame mode (1-FM), with the exception of SHRPD, which mostly uses a five-frame mode (5-FM) by suppressing 4 out of 5 neutron pulses. DREAM has $WB = 3.6 Å$ . SHRPD has a wider $WB = 8.0 Å$ for 5-FM, but it is 1.6 Å for 1-FM. The time resolution is almost flat for instruments at J-PARC because of the nature of intrinsic time-width at the moderator as shown in Fig. 3 and expressed by Eq. (4). On the other hand, on DREAM the time resolution gradually increases as the wavelength is reduced. When comparing of the two instruments, the different time characteristics show a possible better resolution at SHRPD for wavelength smaller than 2 Å, while DREAM does better at larger wavelength. The Figure also shows the limit imposed by the $Δ L / L = 0.013 %$ of DREAM and shows the case of $Δ t = 40 μ s$ , giving a similar resolution at 2 Å as iMATERIA.

We have shown the time averaged brightness in Fig. 1 and the peak brightness in Fig. 5. However, as we discussed in Section 2.4, a good metric for the measured height of the diffraction peaks for a given angular factor of $Δ λ_{ANG}$ and $Δ θ$ is $B_{P} (λ) \cdot Δ t$ , which depends on the choice of $Δ t$ . Therefore, here, we define “Practical Brightness”, “ $B_{P} (λ) \cdot Δ t$ “as shown in Fig. 10, where, $Δ t$ is either the pulse shaping time-width, $Δ t_{PS}$ , for the ESS instruments or the intrinsic time-width of moderator for J-PARC instruments.

Fig. 10.

Practical brightness, $B_{P} \cdot Δ t$ , for a single frame of BEER, DREAM, TAKUMI, iMATERIA and for 1-FM and 5-FM of SHRPD. iMATERIA has the same brightness as TAKUMI but with an extended wavelength up to 5.6 Å. The shaded areas for BEER and DREAM show the tunable brightness ranges given by the time-widths listed in Table 1. The dashed line in DREAM’s shaded area is the brightness for $Δ t_{PS} = 40 μ s$ matching with the equivalent time resolution of iMATERIA at 2 Å. The shaded column band indicates the conventional wavelength band for standard diffraction experiments from 1 Å to 3 Å.

On the other hand, the flux at sample is described as $B_{P} (λ) \cdot Δ t \cdot Δ λ_{ANG} \cdot {(Δ θ_{S})}^{2}$ , and we estimate that DREAM’s flux in the wavelength band of 0.5 to 4.1 Å with $Δ t = 10 μ s$ in a single frame is about $1.8 \times 10^{7} n / {cm}^{2} / s$ with an incident beam divergence of ±0.25° assuming perfect guide transport. This is consistent with Ref. [16]. High resolution can in fact be achieved at a lower cost in flux by reducing the incident beam divergence and DREAM is able to adjust the divergence in this way. However, here, we take the same incident angular divergence of ±0.25° at sample for both instruments, so that the flux at sample can be estimated from the given brightness in a straight forward comparable way.

As shown in Fig. 10, the expected practical brightness of DREAM is about 5 times higher than that of SHRPD in 5-FM. However, 1-FM gives SHRPD almost comparable brightness to DREAM. Therefore, if a measurement focuses only on an important wavelength band between 1 Å and 2.6 Å, the two instruments perform comparably in high-resolution mode. Another ESS diffractometer, HEIMDAL [1] to be installed at 160 m source distance has a shorter and comparable wavelength band width of 1.7 Å to SHRPD, and can thus have twice the flux at sample of DREAM for a given resolution.

For the high-resolution mode, DREAM utilizes only $1 / 300$ (= 10 μs/2857 μs) of available neutrons at any wavelength. However, the flexibility of the chopper window opening time gives a great tunability for DREAM as shown in the shaded area in Fig. 10, though it should be noted that the tunability has quasi-continuous steps because the chopper speed must remain an integer multiple of the source frequency. DREAM’s brightness at the equivalent time resolution with iMATERIA at 2 Å with the opening time of $Δ t_{PS} = 40 μ s$ is plotted with a dashed line in Fig. 10. We can see how the performance of the relaxed mode of DREAM exceeds the high throughput diffractometer iMATERIA. Giving that most experiments are performed at a relaxed resolution, DREAM has a great advantage over SHRPD and even iMATERIA. This well demonstrates that one instrument at ESS can cover a variety of purposes and scientific cases, which are necessary to be covered by several instruments at a short pulse source.

DREAM is unique to existing diffractometers at short pulse spallation sources with its flexibility in choosing time resolution via mechanical choppers. Emphasis is given to the high-resolution option, which outperforms SHRPD for wavelengths larger than 2 Å. A medium resolution setting (∼100 μs) seems particularly favourable, simultaneously matching needs for PDF, standard crystallography and high resolution at high (10–25 Å⁻¹), medium (2–12 Å⁻¹) and low Q (<3 Å⁻¹), respectively. The detector covers seamlessly the entire scattering angle without a particular constraint. The data assembled into a single histogram benefit from symmetric peak shapes. However, in order to best exploit the variation of angular resolution, a new 2-D Rietveld refinement method [11] has been proposed and tested [12].

3.2. BEER vs TAKUMI

BEER [1, 15] and Takumi [7] are engineering diffractometers, and are illustrated in Fig. 11. Those instruments are aimed at a similar resolution of $Δ d / d = 0.2 %$ at a scattering angle of ±90° so as to observe lateral and longitudinal stresses in each detector at the same time by applying a loading force along 45° from the beam direction as described in the inset to Fig. 11. The target resolution can well resolve strains applied to steel at a stress level of 30 MPa. TAKUMI views the decoupled poisoned moderator with a poisoning depth of 3.5 cm and uses a straight guide to utilize epithermal neutrons with a T0 chopper for high energy neutron suppression. BEER, on the other hand, views bi-spectral from two moderators as the same reason discussed for DREAM, and eliminates fast neutrons by having a sophisticated curved guide system. She also uniquely adopts a blind chopper concept [18] to realize a constant resolution. Since the diffraction on engineering materials is performed at a very limited range of detector angles around ±90°, keeping the constant resolution, $Δ t / t$ = constant, is of key importance for this type of diffractometer. The time resolution, $Δ t / t$ , produced by the blind chopper with $d_{ch} = 15 cm$ is almost equivalent to the TAKUMI resolution, as shown in Fig. 9 in the conventional wavelength band between 1 Å and 3 Å.

Fig. 11.

Layout of BEER [15] and TAKUMI [7], showing the difference in the design concept. BEER extracts bi-spectral beam by a multi-mirror in the monolith. Several sets of blind choppers can select different separations. There are also band definition choppers (BD) and a multiple repetition chopper (MC). The guide system has double curved sections to reject high energy neutrons as well as epithermal neutrons. The main detector system is set at ±90°. On the other hand, TAKUMI has a straight guide to accept epithermal neutrons. High energy neutrons are eliminated by a T0 background suppression chopper. Currently detector banks are deployed only at ±90° to analyze lateral and longitudinal stress simultaneously. The inset also shows how the stress along lateral and longitudinal direction can be observed by applying a loading force along 45° to the incident beam.

The actual chopper opening time of BEER is, however, much wider than the corresponding pulse time-width of TAKUMI because of the much longer flight path of 150 m; they are 15 μs for TAKUMI and 52 μs for BEER at 2 Å, as shown in Table 1. Thanks to the slower repetition rate of 14 Hz at ESS, a sufficiently wide wavelength band from 1 Å to 3 Å is maintained, as shown in Fig. 9. As a consequence, the available brightness at the sample position of BEER, is much higher than TAKUMI as is observed in Fig. 10, although the brightness of BEER drops down in the short wavelength range below about 1 Å and into the epithermal region.

Another benefit from the long ESS pulse is pulse multiplication as planned for BEER by pulse modulation [1]. This technique creates many pulses from the long pulse and is used to observe a specific Bragg peak diffraction, which is well separated in time-of-flight from other indexed Bragg peaks, and is especially effective to improve statistics for a time-resolved in-situ measurement of Engineering materials.

Therefore, in general, it can be said that the design of BEER is well adapted and optimized to the source characteristics of ESS with its long pulse and low repetition rate. Although the brightness of BEER is higher than that of TAKUMI in the conventional wavelength range, Takumi can utilize neutrons up to the epithermal region. In the analysis we found that the time resolution of both instruments seems to be far better than the required performance for stress analysis unless performing high-resolution diffraction at back scattering. The time resolution is about 25% of the angular resolution at 90°. BEER can, however, mitigate this mismatch of the time resolution by adjusting the distance, $d_{ch}$ , of the blind chopper system. The shaded region in Fig. 10 for BEER corresponds to $d_{ch}$ ranging from 15 cm to 120 cm, which enables a tunability of time resolution to optimize the brightness in a continuous fashion.

4. Discussion

The long pulse source ESS will give great opportunities to tailor neutron pulses with pulse shaping chopper systems by trading brightness (equivalently flux) versus time resolution. In addition, there is the benefit of a symmetric clean pulse shape, giving reliable structure refinement analysis. We did not illustrate this effect here. However, it is clearly advantageous compared to the asymmetric pulse shape obtained at short-pulse sources, created by the moderation process [19]. The slower repetition rate of 14 Hz at ESS also favours long instruments by taking a longer pulse shaping time-width while keeping a sufficiently wide wavelength band. As a consequence, ESS’s diffractometers benefit from an enhancement in the practical brightness as shown in Fig. 10 and their practical performance is significantly better than what would be expected simply from inspection of the peak brightness, shown in Fig. 5.

The flexible performance of ESS instruments due to the tunability of the chopper opening time-width is summarized in Table 1; $Δ t_{PS}$ of DREAM ranges from 10 μs to ∼1000 μs and the blind chopper distance “ $d_{ch}$ ” extends from 15 cm to 120 cm for BEER. Increasing the opening time or distance between the pair of choppers proportionally increases the practical brightness. Therefore, instruments can choose the most suitable time resolution and optimize brightness for specific experiments. This tunability is only available at a long pulse source and will give a great flexibility and advantage to instruments. As shown in the shaded area for DREAM and BEER in Fig. 10, which shows the highest resolution at the bottom and extends upward for more relaxed resolution, the available brightness can be increased by more than one order of magnitude from the high-resolution mode to the most relaxed resolution mode, in which DREAM’s brightness largely exceeds the high throughput instrument iMATERIA at a comparable resolution. In consequence, one instrument can cover multiple use cases from high resolution to high throughput at ESS. When the optimization also includes tuning of the angular contribution, $Δ λ_{ANG}$ , by widening slit openings for instance, the enhancement of flux at sample is further boosted as illustrated in Fig. 7. We further note that the brightness of SHRPD for 1-FM is comparable to that of DREAM in the wavelength range of 1–2.6 Å; the reduction in frame number makes SHRPD more competitive to DREAM, although the size of the Q-range should also be considered. In this regard HEIMDAL may be the better comparison, which has $L_{1} = 160$ and a λ-band of 1.7 Å, and can double the time-width compared to DREAM for the same resolution. On the other hand, SHRPD utilizes the traditional data collection method of using a fairly limited detector range at high angles for the best resolution; and adoption of 2-D Rietveld Refinement would benefit SHRPD, which is under planning and development for DREAM team.

While a short-pulse spallation source does not offer the flexibility of mechanical pulse tuning, the optimization of the moderators is crucial for specific instruments. In this analysis, we have found that the peak time-width at J-PARC seems to be much narrower than required especially for TAKUMI, and it could be a good idea to retune the poisoning depth of the decoupled poisoned moderator on the occasion of its replacement in the future. Since those instruments have been already applied for a lot of various experiments, the practical experiences will give a very good guide for the improvement of the moderator system.

The comparisons shown here were done under the assumption of the perfect brilliance transfer of the guide system to see an intrinsic merit/demerit attributed to the difference of the source character. However, in reality a long guide is more sensitive to cumulative misalignments and other optical imperfections. The long ESS instruments may thus be more likely to experience loss of some performance from these effects. The degradation of transfer depends strongly on the engineering design of the guide system and details of the beam extraction system from the moderator. We expect that Fig. 10 gives a good intuitive representation of the expected performance comparison, but ultimately only operational experience at ESS will determine the true comparison.

Also, in this analysis we did not assess the detector layout, detector efficiency, background etc. But the realistic performance of instruments strongly depends on those factors but not only on the source performance. Here, we remark the point, which is out of scope of this report.

5. Conclusion

We have provided an overview of five planned and existing diffractometers at ESS and J-PARC. There is a perception today that a sharp neutron source pulse structure is needed for diffraction measurements, which drives the intrinsic choice of decoupled and poisoned moderators at short-pulse sources. However, as we have seen in this analysis, that is not always the case, and by adopting an appropriate pulse shaping chopper system, instruments at long pulse source perform very well, and with an unprecedented tunability. This unique character will give a great benefit for diffractometers at ESS by balancing resolution and brightness to optimize the instrument configuration. On the other hand, it is clear that the instruments at J-PARC perform well compared to those at ESS despite the much lower source power. In addition to this, instruments at short-pulse source can naturally utilize epithermal neutrons, which provides a unique opportunity for PDF analysis at high momentum transfer and also gives less recoiling effect for light elements [3], as well as better application to highly absorbing material and very thick engineering substances. The two types of sources thus provide very distinctive and complementary roles. The real test of the instruments at a long pulse source will be evaluated with actual scientific experiments and discovering how to take best advantage of the tunable capabilities of ESS diffractometers for scientific discovery, once the facility is up and running.

Footnotes

Appendix

Here, we describe a formula specifying intensity to be observed at a detector based on Eq. (10) of Ref. [8].

For long pulse source, a choice of pulse shaping time-width is independent from other resolution components such as the angular resolution. Equation (A.1) can conveniently be described by two components. One is attributed to pulse shaping time-width and another to other resolution components, mainly the angular component. $\begin{matrix} (A.1) & {(\frac{Δ d}{d})}^{2} = {(\frac{Δ d_{ANG}}{d})}^{2} + {(\frac{Δ t_{PS}}{t})}^{2}, \end{matrix}$ where $Δ t_{PS}$ is the pulse shaping time-width and $\begin{matrix} (A.2) & {(\frac{Δ d_{ANG}}{d})}^{2} = {(cot (θ) \cdot Δ θ)}^{2} + {(\frac{Δ L}{L})}^{2} \end{matrix}$

Here, we neglect the $(\frac{Δ L}{L})$ term because of its very small contribution in genera case and explicitly specify the angular contribution; $\begin{matrix} (A.3) & {(\frac{Δ d_{ANG}}{d})}^{2} = {(cot (θ) \cdot Δ θ_{ANG})}^{2} = {(\frac{2 d \cdot cos θ \cdot Δ θ_{ANG}}{2 d \cdot sin θ})}^{2} = {(\frac{Δ λ_{ANG}}{λ})}^{2} \end{matrix}$

Therefore, Eq. (A.1) can be described by components of time and wavelength. $\begin{matrix} (A.4) & {(\frac{Δ d}{d})}^{2} = {(\frac{Δ λ_{ANG}}{λ})}^{2} + {(\frac{Δ t_{PS}}{t})}^{2} \end{matrix}$

Figure A.1 illustrates the situation in the time-of-flight diagram to show the effects of the two terms in Eq. (A.4).

Therefore, the peak shape function in Eq. (10) of Ref. [8] is described by two functions by using the peak brightness per second; $\begin{array}{l} I_{h k l} (i) = & T_{expt} \cdot H_{PS} (t) \otimes H_{ANG} (λ) \cdot w (i) \cdot B_{P} (λ) \cdot Δ t_{PS} \cdot Δ λ_{ANG} \cdot {(Δ θ_{s})}^{2} \cdot ϵ (λ) \\ (A.5) & \times f_{DS} \cdot N_{s} \frac{λ^{4}}{4 π \cdot v_{u s} \cdot {sin}^{2} θ} K_{h k l} \cdot | F_{h k l} |^{2}, \end{array}$ where $I_{h k l} (i)$ is the number of neutron counts collected in the i-th time bin for reflection (hkl), $T_{expt}$ is the duration of the experiment (time), $H_{PS} (t)$ and $H_{ANG} (λ)$ are the peak-shape functions as described in details below, $H_{PS} (t) \otimes H_{ANG}$ is convolution of two peak shape functions, $w (i)$ is the width of the i-th time bin (μs), $B_{P} (λ)$ is the peak brightness per second at the sample (n cm⁻² str⁻¹ s⁻¹Å⁻¹ s⁻¹), $Δ t_{PS}$ and $Δ λ_{ANG}$ are defined in Eq. (A.4), $ε (λ)$ is the detector efficiency, $f_{DS}$ is the fraction of the Debye–Scherrer cone that intersects the pixel, $N_{S}$ is the number of unit cells in the sample, λ is the wavelength (Å), $2 θ$ is the Bragg angle for the pixel, $Δ θ_{S}$ is the incident beam divergence at the sample, $v_{u c}$ is the unit-cell volume (Å³), $F_{h k l}$ is the structure factor with the Debye–Waller factor included (cm) and $K_{h k l} = E_{h k l} (λ) [extinction] \times A_{h k l} (λ) [attenuation] \times O_{h k l} [preferred orientation] \times M_{h k l} [reflection multiplicity]$ .

As we described above, a choice of pulse shaping time-width is independent from other resolution components. For a simplicity, the two peak shape function, $H_{PS} (t)$ , attributed to the pulse shaping, and $H_{ANG} (λ)$ , attributed to the angular resolution components, are assumed to be described by Gaussian function. Those are; $\begin{matrix} (A.6) & H_{PS} (t) = \frac{1}{σ_{PS} \sqrt{2 π}} exp - \frac{{(t)}^{2}}{2 \cdot σ_{PS}^{2}}, \end{matrix}$ and $\begin{matrix} (A.7) & H_{ANG} (λ) = \frac{1}{σ_{ANG} \sqrt{2 π}} exp - \frac{{(λ - λ_{h k l})}^{2}}{2 \cdot σ_{ANG}^{2}} \end{matrix}$

Therefore, $\begin{matrix} (A.8) & H_{PS} (t) \otimes H_{ANG} = \frac{1}{\sqrt{2 π (σ_{ANG}^{2} + σ_{PS}^{2})}} exp - \frac{{(t - t_{h k l})}^{2}}{2 (σ_{ANG}^{2} + σ_{PS}^{2})}, \end{matrix}$ where $t_{h k l}$ and $λ_{h k l}$ are the time and the wavelength when/where the (hkl) reflection occurs at the given scattering angle $2 θ$ . $Δ t_{PS}$ is the pulse shaping time-width and $Δ λ_{ANG}$ is the wavelength width attributed to the angular resolution components as described in Eq. (A.4). The conversion from the width to the Gaussian standard deviation is as; $\begin{matrix} (A.9) & Δ t_{PS} = 2 σ_{PS} \sqrt{2 ln 2} and Δ λ_{ANG} = 2 σ_{ANG} \sqrt{2 ln 2} . \end{matrix}$

And conversion from wavelength domain “λ” to time-of-flight domain “t” is made by Eq. (3).

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