Introduction

Neutrons with no net electric charge mainly interact with the nucleus of an atom; hence, neutrons penetrate deep into thick samples with adequate contrast. Moreover, neutrons are sensitive to light elements (such as H and Li) in many condensed matter samples and can distinguish adjacent elements in the Periodic Table and isotopes (such as ¹H, ²H, and ³H). Consequently, similar to X-ray imaging, neutrons serve as ideal probes for the nondestructive detection of internal structural defects in objects at the macroscopic level. Distinct from X-rays and electrons, their unique properties have made neutron radiography and tomography, primarily in transmission mode, a valuable complement to X-ray imaging techniques for material analysis. Since its first report in 1935, this method has been extensively developed over the past few decades using a white beam. Conventional neutron-imaging techniques rely on measuring the intensity attenuation of a transmitted neutron beam as it passes through a sample [1-5].

In recent years, advances in neutron-imaging techniques and data processing across various neutron sources have significantly expanded their applications [6-10]. These developments, including both direct and indirect methods [11-14], have been particularly important in many scientific research fields such as materials science [15, 16], renewable energy [17, 18], lithium-ion battery technology [19-23], civil engineering [24-27], and the preservation of cultural heritage [28, 29]. Moreover, to satisfy the various nondestructive requirements in several targeted scientific fields, several specific neutron-imaging methods have been exploited. For example, energy-selective neutron imaging and neutron Bragg-edge imaging are currently used to investigate crystal-engineered materials. In addition, a neutron phase-contrast imaging method employing a grating interferometer has been introduced [9, 30-33]. In addition to conventional imaging by thermal and cold neutrons, fast neutrons with relatively high energies have also been exploited, which can be used for imaging applications such as isotope analysis [34].

However, visualizing the magnetic distribution and flux generated by a magnet using conventional neutron-imaging techniques is a significant challenge. Neutrons possess another unique property in the form of a nonzero intrinsic magnetic moment that lies antiparallel to their internal angular momentum. This allows neutrons to interact with the magnetic field deep inside the solid matter, which is not possible with traditional field probes. Therefore, the distribution of magnetic induction inside a solid magnetic material and in free space can be nondestructively visualized (in terms of the magnetic interaction with spin-polarized neutrons) through imaging with polarized neutrons (only one spin state). The polarized-neutron imaging (PNI) technique was first realized by the CONRAD instrument at the Helmholtz Centre, Berlin, enabling clear observation and quantitative analysis of the trapped three-dimensional magnetic flux distribution within a polycrystalline lead cylinder below the critical temperature [35]. Subsequently, various PNI facilities have been designed and constructed using various neutron sources [36-39]. Established PNI is employed to investigate the spatial magnetic fields inside and outside matter, magnetic domains and magnetic phase transitions, inhomogeneous ferromagnets, Meissner effect, and flux pinning, where conventional neutron imaging is not suitable [40-45]. For example, the skin effect in a bulk aluminum conductor has been observed and theoretically calculated, indicating an inhomogeneous distribution of the electric current and resulting magnetic field [45]. Owing to the severe polarization loss of polarized neutrons passing through a ferromagnetic material, PNI has also been used to investigate the phase transition process from the ferromagnetic to the paramagnetic state [1].

Polarized neutron

Neutrons are subatomic particles with a spin of quantum number and an angular momentum of . The neutron spin is, therefore, easily influenced by a magnetic field owing to its intrinsic magnetic moment (μ = −9.66 × 10⁻²⁷ J T⁻¹), which is usually aligned antiparallel to the neutron spin. When neutrons pass through an applied external magnetic field (), their interaction with the magnetic field can change their motion behavior. According to the Schrödinger wave equation, the time-dependent motion of spin vector () of neutrons can be expressed as follows [46, 47]:(1)where γ represents the gyromagnetic ratio of the neutrons (-1.832×10⁸ rad s^-1T^-1). The change in the neutron spin in an external magnetic field is known as Larmor precession, which always occurs at a specific frequency , where B is the scalar magnitude of the magnetic field (). When neutrons with a wavelength of λ travel through a magnetic field with a velocity () adiabatically, the wavelength-dependent precession angle () can be described by a path (s) integral [35, 42, 47]:(2)where t represents the time required for neutrons to pass through the magnetic field (t=s/v), m represents the remaining mass of a neutron (1.675×10^-27 kg), and h represents Plank’s constant (h=6.626×10^-34 J s). Therefore, the precession angle is related to the wavelength (λ) and is proportional to the magnetic field strength (B), according to Eq. (2), indicating the strong impact of the applied magnetic field strength on Larmor precession. As neutrons propagate through an applied magnetic field caused by either an external current source or localized magnetization, the Larmor precession of neutron polarization is closely dependent on the magnetic field distribution along neutron’s motion trajectory. Therefore, as defined in Eqs. (1) and (2), the magnetic field distribution can be deduced by analyzing the accumulated shift in the neutron polarization.

The PNI technique, which combines neutron polarization analysis and neutron-imaging techniques, can be used to visualize magnetic flux by measuring the variations in neutron polarization. In comparison with conventional attenuation-based neutron imaging, the intensity of the transmitted neutrons is further modulated by neutron polarization (P) [40, 48, 49]. Polarization P can be obtained through polarization analysis owing to only two possible neutron spin orientations, including the spin-up and spin-down states caused by Zeeman splitting in a magnetic field,(3)where I_up and are the neutron intensities recorded in spin-up and spin-down states, respectively. The polarization analysis process introduced during the imaging tests first generated polarized neutrons before the sample and then examined the polarization change along a certain direction after passing through the studied sample. When performing polarization analysis, the neutron polarization information is converted into an additional intensity with respect to the conventional transmission attenuation contrast . According to Eq. (3), the contrast variation introduced by Larmor precession of the polarization vector in front of the polarization analyzer within a magnetic field can be described as [35, 50]:(4)(5)(6)where and are the recorded intensities after the polarization analyzer and the intensity of the incident beam, respectively. Σ is the linear attenuation coefficient of the studied sample caused by conventional neutron imaging and is the corresponding coordinate in the detector plane of the imaging detector system. Note that the polarization vector can be viewed as the average of all the spin states for a neutron beam. Using this method, variations in the polarization orientation for a given path are indicative of the magnetic field distribution when polarized neutrons traverse the magnetic field.

Design of the PNI

Developing neutron-imaging techniques requires a high-quality source, as high-flux neutron sources can reduce measurement time for dynamic processes [10, 11, 17]. The China Advanced Research Reactor (CARR), a high-flux research neutron source, focuses on neutron-imaging capability. Two neutron-imaging instruments have been established at the China Institute of Atomic Energy (CIAE). Cold neutron-imaging instrument at the CNGC beamline provides a maximum neutron flux of 1.87×10⁸ n cm^-2s^-1 at 30 MW of CARR. The aperture system enables L/D values from 160 to 3200, suitable for energy-selective and high-resolution imaging. L/D is the ratio of distance (L) between aperture system and sample to diameter (D) of applied aperture. Various PNI facilities have been constructed at different neutron sources using optical devices such as neutron polarizers and spin flipper, since the first report by CONRAD instrument at Helmholtz Centre Berlin [36-39]. To enhance the neutron-imaging capability, developing PNI technique on the cold neutron-imaging instrument at CARR is urgent, considering future research of magnetic domains, phase transitions and Meissner effect in superconductors.

The PNI setup consists of a double-crystal graphite monochromator after an aperture system, a supermirror polarizer with three V-shape cavities coupled with RF-flipper, a guide magnetic field, electromagnetic coils, and a polarized ³He neutron spin filter (NSF) using a spin-exchange optical pumping (SEOP) ³He cell as analyzer, followed by an imaging detector system [35, 36, 48]. An aperture system of 7 holes with varying sizes in the upstream tunes the incident beam profile. A pinhole with different radii behind the supermirror polarizer tunes spatial resolution, L/D (D is the pinhole diameter) and neutron flux, as shown in Fig. 1. The beam generates coverage of 100 mm diameter at the sample position and field-of-view (FOV) of 110 mm×110 mm at the camera, illuminating the neutron camera scintillator. To reduce background noise and activation, the monochromator, polarizer, pinhole, guide field and NSF system are covered by ¹⁰B-doped rubber shielding.

Fig. 1Full-screen View

(Color online) (a) Schematic illustration of PNI setup at the beamline CNGC at the CARR. (b) The physical picture of the designed PNI setup

3.1

Double-crystal graphite monochromator

Because neutron polarization precession is wavelength-dependent in an external magnetic field according to Eq. (2), a polarized monochromatic neutron beam is required. White beam with various neutron wavelengths leads to reduced measured polarization through dephasing. Therefore, monochromating the white beam from the reactor is critical for the PNI setup. This can be achieved via time-of-flight method at pulsed neutron sources, or through a monochromatization device. Devices like mechanical neutron velocity selector and double-crystal monochromator can select neutrons with desired wavelength from white beam at continuous reactor sources like CARR [33, 51]. The mechanical neutron velocity selector’s key component is a rotating drum with helical lamellae coated with neutron absorption material. It allows neutrons with certain velocity to pass through, selecting wavelengths by drum rotation speed. The neutron wavelength (λ) depends on rotation speed: , where h and m are Plank’s constant and neutron rest mass, L is rotor length, Φ is lamella helical angle, and ω is rotor angular velocity. The main factors influencing wavelength resolution (Δλ/λ) of a velocity selector include distance (d) between adjacent lamellae, radius of rotor (R) and helical angle (Φ), as described by . A desired wavelength from an incident white beam can be selected through a double-crystal monochromator, based on Bragg’s law by a crystal material: , where d, θ and n are the lattice distance, diffraction angle and order of diffraction. The neutrons are reflected parallel to the incident beam by a second crystal, creating a monochromatic beam. Higher order reflection generates secondary neutrons, decreasing the final wavelength resolution. Wavelength resolution and neutron flux are key parameters for evaluating monochromatization devices. The selection of a device should be guided by experimental requirements. A double-crystal monochromator offers high wavelength resolution with lower neutron flux, while a neutron velocity selector provides lower resolution but higher flux [33, 51]. High wavelength resolution suits energy-selective imaging and scattering experiments, but requires longer measuring time.

A double-crystal graphite monochromator is installed at the cold neutron-imaging beamline, composed of pyrolytic graphite single crystals with a mosaicity of 0.8° and size of 70 mm × 70 mm, as shown in Fig. 2. Through double reflection by the two crystals, neutrons with a required wavelength can be defined from the incident white beam without changing beam direction in Fig. 2. Previous experiment demonstrated a wavelength resolution (Δλ/λ) of 2.6% for neutrons with 4 Å wavelength and beam size of 100 mm × 150 mm through time-of-flight measurement [52]. The beam center height is lowered by 90 mm after selecting the desired neutron wavelength compared to the incident beam.

Fig. 2Full-screen View

(Color online) Double-crystal graphite monochromator for the PNI experiment

3.2

Polarizer coupled with a RF-flipper

To develop polarized-neutron techniques and perform polarized-neutron experiments, including scattering and imaging, the production of polarized neutron beams (only spin-up or spin-down) is a prerequisite at the beamline [53]. Currently, three main methods exist for generating polarized-neutron beams, each with its unique advantages. The first is the use of polarizing crystals such as Co₉₂Fe₈ and Heusler alloys (Cu₂MnAl), which can polarize monochronmatic neutrons through preferential Bragg diffraction. Cu₂MnAl has a high reflectivity and relatively low absorption in contrast to Co₉₂Fe₈ [54]. The second is the use of polarizing supermirror mainly including cavity and bender types, which are highly efficient and suitable for a wide neutron wavelength range. However, polarizing supermirror is very difficult to polarize neutrons with short wavelengths (below 2.0 Å) and neutron beams with large divergence using polarizing supermirrors. In addition, the polarizing S-bender (generally in reflection mode) has a small device size and relatively high polarization, but can increase the beam divergence and decrease the resolution function; therefore, a collimator is always required for imaging applications [35]. A polarizing V-cavity supermirror (generally in transmission mode) can maintain the beam direction by transmitting neutrons with only one spin state (spin-up or spin-down). However, it generates a low polarization and increases the total device length, which takes up more precious space at the beamline relative to the S-bender [55, 56]. In contrast, the polarized ³He NSF has been rapidly developed and used to polarize neutron beams in recent years owing to the high polarization of beams with large divergence and neutrons with a broad energy band [57-61]. Polarized ³He NSF operates on the principle of preferential absorption by polarized ³He nuclei, selectively transmitting neutrons with a spin parallel to ³He and absorbing neutrons with a spin antiparallel to ³He. In contrast, the polarized ³He NSF can not only polarize neutrons with various wavelengths, but also a neutron beam with a large divergence. One of the major disadvantages of polarized ³He NSF is the polarization loss with an increase in operation time, which occurs because of several factors, such as collision with the glass cell wall and stray magnetic fields around the device [57-61].

A V-shape transmission cavity is adopted as a neutron supermirror polarizer, instead of a bender polarizer, to produce polarized neutrons and maintain beam divergence [55, 56]. Various V-shape cavity configurations with different m values were analyzed in the 2–8 Å wavelength range (in Fig. 3) using McStas software [35, 38]. Considering available space and cost, a supermirror polarizer with three parallel V-shape cavities (Parallel 3Vs) in the horizontal direction was selected, as shown in Fig. 3. Si-wafers coated with Fe-Si polarizing supermirror (m = 3.3) transmit spin-up neutrons and absorb spin-down neutrons. The neutron beam divergence is preserved through the polarizer along the neutron flight path (y-axis), as shown in Fig. 1. The polarization is parallel to the z-direction. An adiabatic π radio-frequency flipper (RF-flipper), comprising static vertical and radio-frequency longitudinal magnetic fields, is coupled with the polarizer to tune polarized-neutron spin direction for polarization testing [62].

Fig. 3Full-screen View

(Color online) Different configurations of V-shape cavity and the corresponding physical picture of the designed supermirror polarizer with parallel “3V”-shape cavities (Parallel 3Vs, beam direction is from right to left in the physical picture)

3.3

Guide field and electromagnetic coils

A guide field along the polarized-neutron flight path is required to preserve neutron polarization, as neutrons would depolarize through interaction with earth and stray magnetic fields otherwise, unlike the white beam. A guide field is designed behind the polarizing device, as shown in Fig. 4. The total length is 6000 mm, consisting of three 2000 mm segments. The segmented design allows manageable installation and convenient switching for different instrument lengths. A series of pure iron rods with NdFeB permanent magnets at both ends is distributed along the z-direction at 100 mm intervals, sandwiched between two pole plates of pure Fe material (in the xy plane). The pole plates and iron rods form a low reluctance path for magnetic flux from the NdFeB magnets, distributing it uniformly between the polar plates. The vertical guide field strength is 4.7 mT, sufficient to maintain neutron polarization and tolerate external disturbances 10 times stronger than earth’s field. The magnetic field is directed from the lower pole plate to the upper one. Evacuated aluminum tubes with thin aluminum windows are positioned between the pole plates along the neutron flight path to reduce atmospheric scattering, as shown in Fig. 4.

Fig. 4Full-screen View

(Color online) (a) Simulated uniform distribution of magnetic field between the two pole plates and (b) physical picture of the guide field system with permanent magnets and Al flight tube at vacuum state

Owing to the polarization direction of polarized ³He spin filter and guide field along y-axis and z-axis respectively, electromagnetic coils made of pure Cu wires are installed to adiabatically rotate and maintain the polarization along y-axis in Fig. 1. The magnetic field amplitude can be modulated by changing the coil current based on experimental requirements. The coil field strength enables an adiabatic transition between vertical permanent magnet and horizontal coil-magnetized sections. Notably, owing to the trigonometric function behavior, a slight non-adiabatic transition with the final polarization vector at 15° from the z-axis causes minimal longitudinal polarization loss of 0.035; however, it maintains a significant transverse component of 0.26. Therefore, careful simulation and implementation of field direction transition are crucial. The simulated adiabatic parameter k exceeds 10 across the beam profile at shortest operating wavelength, enabling good adiabatic transition with low transverse components.

Measurements of key parameters

To evaluate the designed PNI setup, measurements and experiments will be discussed. Polarized-neutron experiments use neutrons with longer wavelength as cold neutrons are suitable. However, cold source at CARR was not operational during this experiment, with insufficient cold neutrons at the CNGC beamline. Neutrons with wavelength of 2.7 Å were used for polarization tests, balancing polarizer performance and secondary-wavelength neutron contamination, due to minimal contamination from higher order reflections of the double-crystal monochromator. This leads to lower total polarization due to limitations of the designed supermirror polarizer..

The neutron flux before the aperture system is 4×10⁷ n cm^-2 s^-1 (thermal neutron spectrum) at 30 MW. A pinhole with diameter mm after the polarizer provides L/D of 2100 ( mm, distance between pinhole and sample for PNI setup), improving spatial resolution and reducing beam divergence. Data acquisition takes 15 mins per polarization test, including high-flux spin state, low-flux spin state, and polarization state flip time. Both RF-flipper after polarizing supermirror and ³He NSF can adiabatically flip polarization state according to Eq. (3). ³He NSF is used to flip polarization state during experiments, recording images with spin-up and spin-down states. Figure 5 shows initial experiments evaluating the PNI setup.

Fig. 5Full-screen View

(Color online) (a) FOV of over 50 mm × 50 mm, (b) spatial resolution of better than 400 μm using Siemens star, and (c, d) total polarization with a homogeneous distribution at 2.7 Å. The acquired FOV in PNI mode

A Siemens star test shows spatial resolution better than 400 μm, as in Fig. 5(a-b). The effective FOV exceeds 50 mm × 50 mm, marked by a square frame in Fig. 5(a). Figure 5(c-d) demonstrates 60% uniform neutron polarization across the 80 mm ³He cell region at 2.7 Å, covering the FOV. This polarization results from the supermirror polarizer, guide field and ³He analyzer. Polarization could improve using a cold source to shift toward cold neutron, enhancing polarizing supermirror efficiency. Though polarization is moderate due to 2.7 Å neutrons, the PNI setup parameters suffice for extracting magnetic information, albeit requiring longer experimental time.

The magnetic field distribution of a solenoid has been well studied and can examine the practicability of the PNI setup [46]. A solenoid generates a controlled magnetic field for the PNI measurement, along with motors and superconductors. The solenoid is placed perpendicular to beam direction between the last guide field and in-situ ³He polarization analyzer in Fig. 6. The cylindrical solenoid (30 mm in diameter, 80 mm in height) is powered by a DC supply with 50 ppm/°C stability, generating a horizontal magnetic field orthogonal to the guide field. Two electric currents of 3 A and 5 A generate calculated magnetic fields of 24 G and 34 G at the solenoid center. Though the systematic polarization is not very high compared to other neutron sources, the magnetic field can be detected through contrast across the solenoid body in Fig. 7(a-b). With increasing current, additional precession is detected at the solenoid center due to longer neutron flight path. For understanding the phenomena, theoretical simulation has been performed. The Larmor precession caused by the solenoid magnetic field is calculated through Eq. (1) and Eq. (2) as:(9)where l denotes the neutron path length within the solenoid. Neutron polarization is related to spin precession inside the solenoid, as defined by Eq. (9) were calculated and plotted across the centerline of the solenoid in Fig. 7(c-d). The theoretical results are consistent with the experimentally acquired data, indicating the practicability of the designed PNI setup for CARR.

Fig. 6Full-screen View

(Color online) Configuration of the tested solenoid installed on the developed PNI setup

Fig. 7Full-screen View

(Color online) Configuration of the tested solenoid installed on the developed PNI setup

Discussion and summary

For several applications in typical macroscopic magnetic samples, such as electrical motors, transformers, superconductor wires, and magnetic samples, the established PNI setup with a resolution better than 400 μm and an FOV greater than 50 mm × 50 mm is sufficient to characterize the most significant magnetic behavior. Therefore, the developed PNI setup at the CARR can be applied to study magnetic transitions and detect magnetic leakage in the motor’s rotor or transformer cores. It can also be used to observe the Meissner effect in superconductors or quenching in sample environments.

In summary, a PNI facility was successfully designed and constructed for the first time, based on an established cold neutron-imaging instrument in the guide hall at CARR. It is equipped with a double-crystal graphite monochromator, a supermirror polarizer featuring three V-shaped cavities, and an in-situ polarized ³He NSF. The experimental results demonstrate that the designed PNI setup can provide relatively high polarization with 2.7 Å neutrons and good spatial resolution with a large FOV, significantly improving the neutron-imaging capability at CARR. Finally, a clear magnetic field distribution inside the solenoid was easily observed using the designed PNI setup, although the cold source was not operated during the experiments. In addition to the solenoid samples used in this study, a series of other scientific experiments, such as superconductors and motors, were also carried out simultaneously. Detailed results combined with the finite element method are currently being analyzed and will be published elsewhere. In addition, the capability of the designed PNI setup at CARR can be further enhanced in the future through optimization of the gas pressure and length of the ³He cell inside the in-situ ³He NSF, operation of a cold source at CARR, and introduction of different sample environment devices involving temperature, pressure, and/or field conditions.