Principle and simulation of efficiency of ³He LPSD

Thermal neutron detection by the ³He LPSD relies on the following nuclear reaction: $\begin{array}{l}n{\text{+}}^3\text{He}\to p\text{+}T\text{+}{E}_{\text{Q}}\text{=764 keV,}\\ \sigma \text{=5315}\text{.77 barn for }{E}_{\text{n}}\text{=25}\text{.3 meV}\end{array}$ (1)

This indicates that a thermal neutron reacts with one ³He nucleus to generate two daughter products: a proton and a tritium ion. The products of this reaction move in opposite directions from the reaction point and share a 764 keV reaction energy, of which the proton takes 573 keV and the tritium ion takes 191 keV. The ³He LPSD was fabricated using thin-walled stainless steel, which acts as the detector cathode. A thin tensioning wire with uniform resistivity was installed along the length of the tube and serves as the anode of the detector. It is sensitive to its position along the anode wire. Compared with the multiwire proportional chamber (MWPC), the ³He tube is superior in terms of facilitating large-area array fabrication and easy maintenance.

The capacity of location of the scattering neutron plays a critical role in the design of neutron scattering instruments. Based on the charge division principle, the ³He LPSD can determine the location of a neutron hit along the direction of the anode wire, as shown in Figure 1. Secondary charged particles from the neutron react with ³He deposit energy, and ionize the working gas to create electron–ion pairs that are the primary signal of the detector. However, the signal was too weak to be recorded by the readout electronics. To improve the signal-to-noise ratio (SNR) of the neutron event, a gas multiplication effect was produced by creating a high electric field in the center of the LPSD tube and applying a high anode bias voltage at the anode. The neutron signal was amplified through the avalanche effect, which occurs in a region near the anode wire and produces a large charge cloud. Electrons in the charge cloud move towards the anode and quickly reach it, while ions with lower velocity travel to the cathode. This indicates that the latter makes a major contribution to the detector signal. The movement of the charge cloud creates a pulse current in the anode wire that is transmitted toward both ends of the tube. The current signals are collected and converted to voltage signals, the amplitudes of which represent the charge values of the neutron event.

Fig. 1Full-screen View

(Color online) (a) Schematic of the charge division of the ³He linear position-sensitive detector (LPSD) tube, (b) average detection efficiency of 1-inch ³He LPSDs filled with different pressures, (c) positional response of the efficiency of detection of neutrons with different wavelengths of the 1-inch ³He LPSD with a pressure of 20 atm.

A high detection efficiency is indispensable for sample experiments in neutron instruments. This not only reduces the measurement time but also improves the utilization ratio of the neutron beam. The MPI demands an operating wavelength range of 0.1–3 Å, which covers the range of energy from thermal neutrons to epithermal neutrons. To evaluate the efficiency of the ³He LPSD, Monte Carlo (MC) simulations were performed in Geant4 [22]. A detector with a 500-mm-long rectangular prism with depth of 19.95 mm (the average depth of gas in a ³He tube) was built in the Geant4 program and filled with ³He gas. Four pressure values of ³He gas were used in this case, and the sources of the neutrons with different wavelengths were set to irradiate the detector. Figure 1b shows the average distribution of ³He tubes filled with different pressures. The detector filled with ³He gas at a pressure of 20 atm yielded an average efficiency of above 25% for 0.1 Å neutrons and almost 100% for 2 Å neutrons. An increase in the pressure of the ³He gas improved the detection efficiency of the detector, and ³He gas at a higher pressure required a higher bias voltage for the anode. For safety, the ³He LPSD with a pressure of 20 atm was considered suitable for satisfying the efficiency requirements of the MPI.

Meanwhile, the incident direction and energy of the neutron significantly affect the detection efficiency. Therefore, a 1-inch, 500-mm-long tube model was constructed and filled with ³He gas at a pressure of 20 atm, and four neutron sources with four wavelengths were used to illuminate the tube along the direction vertical to its diameter. As shown in Figure 1c, “Position” represents the distance between the cross point of the diameter and the incident direction to the anode. The efficiency sharply declined near the region of the ends of the diameter owing to a decrease in the effective depth of the gas in the detector and the effects of the wall. For neutrons with wavelengths greater than 1 Å, a rectangular efficiency distribution was observed, which diminished the impact of the incident direction of the neutrons. Therefore, the 20 atm ³He LPSD was adequate for use within the operational wavelength of the MPI.

Structure of the detector

Air significantly influenced the measurement results of the neutron scattering experiments. Thus, we designed a large evacuated tank with a vacuum environment in the MPI to reduce the influence of air scattering. It had a volume of 12 m³, which was sufficient for installing devices to create an extreme environment for the sample to satisfy specific experimental demands and could be operated at a pressure ranging from 100 to 1 × 10^-6 mbar during the experiment. To facilitate operation and maintenance, the detector was designed to operate under atmospheric conditions isolated from the sample environment. As shown in Figure 2a, the detector was based on a modular design consisting of 13 banks (Bank01 to Bank13), which were symmetrical with respect to the beam path, and eight ³He LPSDs fixed on a module as a detector unit mounted on these banks. The main body of the bank was made of nonmagnetic stainless steel, which resulted in long-term stability without mechanical deformation and satisfied the special requirements of the sample environment. These banks were divided into two types: those with a single-plane support structure and those with a three-plane support structure to match the shape of the scattering chamber. An adjusting system was fixed at the bottom of each bank to provide a convenient means of altering its position during installation. Figure 2b shows a photograph of the detector array installed in the MPI scattering room. The unfilled regions in the banks were reserved for the detector modules that were built in the second phase of the MPI, and B₄C plastic plates were fixed at it to absorb the stray neutrons and reduce the level of neutron background in the scattering room during operation.

Fig. 2Full-screen View

(Color online) (a) Layout and (b) site photograph of the multi-physics instrument (MPI) detector; (c) computer model and (d) physical photograph of a 500 mm LPSD module assembled.

The complete MPI detector contains 576 ³He LPSD tubes, which are arranged into 72 modules to cover an active area of approximately 7 m² with a scattering angle ranging from 3° to 170°. For the Phase-I construction of the MPI, 240 ³He tubes were manufactured by Reuter–Stokes. Two specifications of LPSDs with active lengths of 300 and 500 mm were used to satisfy the demands of the MPI. The latter LPSDs are considered in detail in this paper. These LPSD tubes formed a large-area detector array of 30 modules covering an active area of 3 m² and scattering angles ranging from 31° to 170°. The detector modules were fixed at Bank03 to Bank12, and all modules in a bank covered a close scattering angle. Bank07 and Bank08 contained four detector modules with an active length of the ³He tube of 300 mm, and were completed during this construction. The detector modules with 500 mm active length ³He tubes were installed at the other banks. Figure 2c presents the computer model of the LPSD module with an active length of 500 mm, which shows the outer shape of the detector module. Only the detector plane, which formed the active area of the module and comprised eight ³He tubes, was exposed to capture the neutrons scattered by the sample. The ³He tubes were mounted onto three support panels shaped as semicircular grooves to support the tube. The coaxial tolerance of each set of grooves needed to be below 0.1 mm to guarantee the straightness of the ³He tube. Near every support point there was a 5-mm-wide and 0.1-mm-thick stainless steel strip to fix the tube tightly to the support. A simple frame structure made of high-strength aluminum alloy was used inside the detector module. It reduced the overall weight and facilitated cooling of the electronic system by air, while guaranteeing the reliability of the repetitive assembly. The front-end electronics boards were installed under the ³He tube to achieve good grounding performance and reduce the stray capacitance, whereas the digital electronics were located close to the front-end boards to reduce electromagnetic interference. In addition, the lateral and back plates utilized a 5-mm-thick boron–aluminum alloy that provided effective radiation shielding for the readout electronic system inside the module. At the same time, it served as an electromagnetic shield for the entire detector unit to isolate it from outer interference, thus creating an ideal condition for the stable operation of the detector module. Figure 2d shows a 500 mm LPSD module assembled in the laboratory. A customized logo can be observed in the back plate, which provides the serial number and module type of this detector module.

Position calibration

In a neutron scattering instrument, a detector with a high spatial resolution and positioning accuracy is required to record the spatial distribution of neutrons scattered by the sample. For ³He LPSDs, it is imperative to determine the relationship between the actual position of irradiation in the tube direction and the position measured by the detector. Experimentally, it is given by the formula Real_Position = Slope × Measured_Position + Intercept, where the Slope and Intercept represent the correction factors in the linear relation provided by the position calibration experiment. The peak position in the raw count distribution of each irradiated point along the tube path is the Measured_Position item, whereas the Real_Position item represents the actual position of each site. Figure 4a shows a schematic of the module calibration. A 3-mm-thick mask with seven slits, each with a width of 1 mm, made of boron-aluminum alloy, was mounted close in front of the detector module. A polyethylene brick was placed at the beam exit, which scattered the neutron beam to cover the active detection area of the module. Thus, the eight ³He LPSDs in the module can be calibrated simultaneously. Figure 4b shows a site photograph of the position calibration. The center of the detector module was aligned to the neutron beam by a laser aligner (as seen in the inset), and two boron-aluminum alloy plates were placed separately at the bottom and top of the module to offer adequate shielding for the marginal ³He tubes on the module. Ideally, the module should be illuminated by a uniform neutron beam. In this example, polyethylene bricks with different thicknesses were tested, and the 30-mm-thick one was the optimal solution. The actual positions of the slits in the mask used here were 25.6, 100.6, 175.6, 250.6, 325.6, 400.6, and 475.6 mm, respectively. This constituted an array of seven numbers representing the real positions of the slits for the following calibration.

Fig. 4Full-screen View

(Color online) (a) Schematic drawing and (b) site photograph of ³He LPSD’s position-calibration, (c) calibration curve of a single ³He LPSD in a module, (d) corrected distribution of module counts, (e) slope values, and (f) Intercept value in a module

The calibration experiment was performed at HV = 2200 V. The raw positions measured by each ³He LPSD were extracted from the Gaussian function fitting to every peak in the raw count distribution along the tube path, which formed a one-dimensional array with seven numbers. The linear function mentioned above was then used to fit the two arrays to obtain the correction coefficients. Figure 4c shows the calibration curve fitted by the linear function for a ³He LPSD in the module, and the results of the fitting are provided in the legend. It reveals that the correction coefficients Slope = 1.415 and Intercept = −102.1 are used for the position reconstruction of this ³He tube, while the “Prob” is almost equal to one, which signifies a good position correlation for this calibration curve. After completing the position calibration for every ³He LPSD in the detector module, the actual count distribution of each tube was reconstructed. As shown in Figure 4d, there are seven straight slits in the 2D count distribution of the module, where the positions of these slits are consistent with their actual positions. However, slight distortions appear in the image of the two slits near the tube’s ends, which result from the decline of the position resolution of the ³He tube at those sites, which will be discussed in the next section. The distributions of the calibration coefficients for the eight ³He tubes in a module are displayed in Figure 4e and 4f, which clearly show that the calibration factors of the tubes in this module exhibit good consistency. The values of slope are all nearly equal to 1.41 while those of intercept are equal to −102. The excellent consistency of the calibration coefficients also reflects the good performance of the ³He LPSD tubes in the detector module.

Position resolution

Neutron scattering experiments using the PDF method require high-precision measurements for momentum transfer (Q). Thus, the detector must not only have a high spatial resolution but also ensure sufficiently high positional accuracy. A spatial resolution of 10 mm is stipulated in the MPI design and is defined as the full width at half maximum (FWHM) of the position distribution along the tube path. The experimental setup was similar to that shown in Figure 4b, except that the mask was replaced with a single slit, and a lead brick with thickness of 10 cm was placed at the exit of the beam to reduce the neutron flux. The tests for the position resolution were carried out through the irradiation of different sites of the detector by neutrons, and the hit positions of neutrons along the tube direction were corrected by the factors considered in Section 4.1. Figure 5a presents the count distribution of a single ³He LPSD and the results of the fitting using the Gaussian function (working HV = 2200 V). The spatial resolution was calculated using the formula FWHM = 2.355 × sigma. The best resolution (6.4 mm) was located at the center site along the tube length. As depicted in Figure 5b, there was excellent position linearity in the ³He LPSD. This indicates that a deviation of less than 2 mm between the real and measured positions is attainable. To find a suitable working HV for instrument operation in the future, three HV values were used in this test. Figure 5c shows the distribution of the FWHM of the ³He tube in the module at different working HVs. It indicates that an HV value greater than 2150 V is adequate for the implementation of a position resolution below 10 mm, and a better resolution can be realized using a higher working HV. Further, it is noteworthy that there is a concave shape that the FWHM gradually decreases along directions to both ends of the ³He tube, and the best one is situated in the center point. This is mainly derived from the charge-equalization effect [24], which is caused by the front-end board in the readout electronics system. The charge-equalization effect arises from the difference between the input impedance and the ideal impedance (as depicted in Figure 1a), which yields additional noise to the front-end board, leading to inaccurate position measurement. Figure 5d depicts the spatial resolution distribution of ³He LPSDs in the detector module at the 250 mm position, and it shows good agreement in terms of the position resolutions of the module. The fluctuation in the FWHM in the module stems from the difference in the ³He tube, and the average of the minimal resolutions in the module can reach less than 9 mm. Considering the application requests of MPI and the safe operation of the detector array, a value of 2150 V for the HV will be applied in the experiments on the sample under normal operation.

Fig. 5Full-screen View

(Color online) (a) Count distribution of a ³He tube in the module and its full width at half maximum (FWHM) fitted by the Gaussian function, (b) position-linearity of a ³He tube in the module, (c) variations in the FWHM of the irradiated sites at three HV values, (d) FWHMs in a module for the three HV values.

Timing resolution

The maximum counting rate of the ³He LPSD is primarily confined to the timing resolution, which is defined as the minimum interval at which the detector can distinguish events generated by two successive incoming neutrons. It depends on the signal width created in the detector and the intrinsic time resolution of the readout electronics. To measure the timing resolution of the ³He LPSD, the direct neutron beam was used to irradiate the detector and the electronic system recorded the TOF distribution of the incident neutrons. As shown in Figure 6a, a serious deformation in the TOF spectrum occurs because of the accumulation of signals in the readout electronics. A 4.2 μs timing resolution of this detector can be obtained from Figure 6b, which verifies the good timing resolution of the MPI detector array.

Fig. 6Full-screen View

(Color online) (a) Time-of-flight (TOF) spectra of neutron recorded by the ³He LPSD, and (b) time-interval distribution of the two neutron events.

Counting rate capacity

Counting rate capacity is an important representation for the evaluation of neutron diffraction instruments. Specifically, it primarily influences the positioning accuracy under a high-flux situation and the count loss under a high scattering intensity status.

To investigate the influence of the counting rate on the position resolution, an experiment was conducted at beamline-20 of the CSNS, in the same way as reported in Section 4.2. However, the slit was aligned at the 250 mm position of the ³He tube. Moreover, there was a non-uniform distribution of the neutron beam during the period of the pulse; therefore, a simple method was used to obtain the count distributions at different counting rates by extracting positional information at different intervals in the TOF. To avoid severe saturation of the ³He tube, a lead block with a thickness of 5 cm was used and set at the beam exit. The measurement results are presented in Figure 7a. A spatial resolution of less than 10 mm can be attained at an instantaneous counting rate of less than 10 kHz. A high instantaneous counting rate, especially over 10 kHz, leads to a deterioration of the spatial resolution. This decline caused by the high-flux beam mainly stems from two aspects: the space-charge effect [25] in the detector and pile-up of the pulse signal in the readout electronics. The main contribution of the movement of the charged ions, whose velocity limits the width of the signals in time, to signals in the ³He tube easily leads to pulse pile-up in the front-end electronics. When irradiating a site along the tube path with a high-flux neutron, ions with a slow drift speed form an access electric field to weaken the original electric field intensity in the region near the anode. This directly degrades the detector gain. However, the signal pile-up will give rise to an inaccurate measurement of the magnitude of charge, which in turn deteriorates the accuracy of positioning. Figure 7b shows a simple schematic of the signal pile-up on the front-end board. It is clear that the amplitude of the pile-up signal is not normal and leads to inaccurate position calculations, as shown in Figure 1a. In some serious cases, a large signal with an amplitude over the normal working range of the readout electronics is formed, which leads to non-linear saturation of the electronic system and increases the dead-time of the entire detector system.

Fig. 7Full-screen View

(Color online) (a) Variations in FWHM with the counting rate, the schematic drawing of signal pile-up, (c)the instantaneous counting rate distributions and (d) their normalized TOF spectra.

The experimental efficiency was determined by the counting rate capacity in neutron scattering measurements. In an instrument the detector system of which is composed of a large-area detector array, the counting rate capacity is basically dependent on the detector system. In this study, a novel method was adopted to determine the influence of the counting-rate capacity of the detector. This experiment was conducted at the MPI beamline, and water samples of different masses were used to change the level of neutron flux irradiating the detector modules. Figure 7c displays the distributions of the instantaneous counting rates of the five water samples, and Figure 7d shows the TOF spectra normalized by their total counts. The shapes of the TOF distributions of the different samples are essentially in agreement with one another. The peaks of the first four samples are located at 10.2 ms, whereas that of the last one is at 9.8 ms. The ratio of the instantaneous counting rate to the average one in the ³He tube here is approximately equal to 3.6 and originates from the wavelength's maldistribution of the neutron beam in the MPI beamline. Additionally, the nonlinear saturation of the detector occurs in the TOF range from 9 to 13 ms for the 1.5 g water sample. The maximum average counting rate without the saturation effect of the ³He tube is approximately 8 kHz, and the normalized value decreases with increasing sample mass. The minimum average count rate was 10 kHz when the detector was saturated. It is inevitable that event loss will exist in high-level counting rate experiments owing to the space charge effect in the detector and the pulse signal pile-up in the electronics. As discussed above, the signal pile-up causes count loss of the detector, which leads to a decline in the detection efficiency and distortion of the count distribution. In more severe cases (as discussed in Section 4.3), the TOF distribution is badly distorted, and the position resolution degenerates. This has a negative impact on the instrument operation and experimental results. Hence, the maximum average counting rate of up to 80 kHz is realizable and acceptable for the detector module of the MPI, whereas the total counting rate capacity of the entire detector array built in Phase I of the MPI is 2.4 MHz. From the above discussion of the spatial resolution, it can be concluded that the count loss in this measurement mainly occurred owing to the contribution of the pulse pile-up because of the high event rate distributed along the entire ³He tube, and not just at one position. Therefore, the position resolution remained at a normal value and remained almost unaffected.