Electric field imaging using polarized neutrons
Yuan-Yu Jau, Daniel S. Hussey, Thomas R. Gentile, Wangchun Chen
aa r X i v : . [ phy s i c s . i n s - d e t ] J u l Electric field imaging using polarized neutrons
Yuan-Yu Jau ∗ Sandia National Laboratories, Albuquerque, NM 87123, USA
Daniel S. Hussey, Thomas R. Gentile, and Wangchun Chen
National Institute of Standards and Technology (NIST), Gaithersburg, MD 20899, USA (Dated: July 10, 2020)We experimentally demonstrate that electrically neutral particles, neutrons, can be used to di-rectly visualize the electrostatic field inside a target volume that can be isolated or occupied.Electric-field images were obtained using a polychromatic, spin-polarized neutron beam with asensitive polarimetry scheme. This work may enable new diagnostic power of the structure of elec-tric potential, electric polarization, charge distribution, and dielectric constant by imaging spatiallydependent electric fields in objects that cannot be accessed by other conventional probes.
Non-destructive but penetrative imaging technologiesare powerful diagnostic tools, because they can revealstructure inside diagnosed objects or subjects that cannotbe easily observed or measured externally. These kindsof visualization technology have been broadly utilized inmedicine, science, non-destructive testing and evaluation,security applications, etc. and it will be highly beneficialto continuously develop new imaging diagnostic technolo-gies. One of the advantageous imaging capabilities thathas been long pursued but is very challenging is the vi-sualization of the distribution of the static electric field( E ), especially when it is physically isolated and can-not be reached by physical probes. With or withoutthe externally applied electric field, the E informationfrom the diagnosed target can be used to reveal spatiallydependent electrostatic characteristics, such as electricpotential, electric polarization, charge distribution, anddielectric constant, which are highly valuable for studiesof material properties and physical structure, examina-tions of electronic components and enclosed electronics,and security screening applications.To date, the previously demonstrated and proposedapproaches of static E imaging use physical sensors ofelectric potential or sensors of electric field based on fieldeffect transistors [1, 2], electro-optic effect [3], Kerr effect[4], and Rydberg atoms [5]. Therefore the electric fieldcan be mapped out over the sensor locations. Althoughdetermining the electric field away from the sensor lo-cations may be feasible in some cases, inverse problemsof electric field are mostly ill-posed [6]. Therefore the E imaging based on physical sensors is restricted to the freespace around the sensor locations and the imaging reso-lution is limited by the distance from the imaging targetto the sensors [1, 2, 7]. However, this approach doesnot work for the occupied or physically isolated space.Hence, the previously demonstrated images are mainly E surveys near the surface of the diagnosed objects. Inaddition, owing to the technical difficulty of making ahigh-density, two-dimensional (2D) array of E sensors, ascanning scheme with a single sensor or a 1D sensor arrayis usually used to obtain a full image [2, 8, 9]. To overcome the natural limitation of sensor-based E imaging, a novel approach is to send a probe to directlyinteract with the electric field, and carry the E infor-mation to strike the detector. From this perspective, aneutron beam would be a good candidate E probe, sinceneutrons have good penetration capability through manymaterials, especially metals, and the neutron spins inter-act with an electric field due to their motion [10, 11]. Inthis paper, we show images of an electrostatic field forthe first time using polarized neutrons. Our work mayinitiate a new avenue in imaging diagnostic technology.The underlying physics of neutron-based E imagingis based on the neutron spin precession when neutronsare moving through a region of electric field. A neutroncarries a non-zero magnetic moment that is aligned an-tiparallel to its spin orientation. The dynamics of spinprecession are described by ddt h I i = γ n h I i × B eff , (1)where h I i is the ensemble average of the neutron spinvector, γ n = − . × rad s − T − is the gyromag-netic ratio of the neutron, and the effective magnetic field( B eff ) vector seen by a moving neutron is B eff = B lab − v × E c , for | v | ≪ c. (2)Here, B lab and E are the spatially dependent B lab and E vectors in the laboratory frame, v is the velocity vectorof the moving neutron, and c is the speed of light. UsingEq. (1) and Eq. (2), we find a net change in the anglevector of a neutron spin due to field-induced precessionfrom its trajectory l to be θ = Z l d h I i|h I i| = Z l γ n (cid:20) e I × B lab | v | − e I × ( e v × E ) c (cid:21) dl, (3)where e I = h I i / |h I i| is the unit vector of neutron spin,and e v = v / | v | denotes the unit vector along the ve-locity direction. In practice, we can polarize neutronsto have most of their spins aligned to the same direc-tion, and the polarization vector is P = 2 h I i . The B lab SMs PolarizerBeam exit with a slit Low-field chamber He NSF analyzer I m a g i n g s c r ee n V (Not drawn to scale) Guiding magnetic field l d
FIG. 1. A schematic of the E imaging experiments with polarized neutrons. The blue arrow represents the polarization of theneutron beam before arriving at the E region (small gray arrows), which exists in between the two parallel electrodes drivenby a voltage source. The gray big arrow denotes the analyzing direction of neutron spins at the analyzer. and/or E information then can be determined by mea-suring the rotation angle of the polarized neutron spins, θ = ∆P / | P | through a neutron polarimetry method. InEq. (3), we see that the E effect on the spin rotation isindependent of neutron velocity, but the B lab effect is ve-locity dependent. Hence, unlike the B lab measurement,the E measurement is not affected by the velocity spreadof neutrons when using a polychromatic beam. Mathe-matically, different neutron velocities, different probingtrajectories, different polarization orientations, and dif-ferent analyzing directions can be employed to retrievefull vector information of both the magnetic field andelectric field in the laboratory. The experiments reportedhere employed cold neutrons, but if the electric field is theonly interesting quantity in the measurement, in principlehigher energy neutrons could be employed to minimizethe effect from the magnetic field. B lab imaging based on neutron spin rotation sig-nals [12–14] has been demonstrated. The effects of lab-oratory electric fields on the neutron phase have beenstudied in interferometry-based Aharonov-Casher exper-iments [15, 16] and the strong spontaneous electric field( > V/m) inside a large noncentrosymmetric crystalhas been measured by neutrons [17]. However, to ourknowledge neither E imaging nor measurement of spinrotation with applied E has been demonstrated. Onemajor challenge of detecting electric fields with polarizedneutrons is the small magnitude of the induced spin ro-tation angle θ E , which is generally much less than 1 raddue to the very small factor 1 /c in Eq. (3). On the otherhand, the magnitude of the B lab induced rotation angle θ B can easily be greater than 1 rad in many experimen-tal conditions. Thus, in order to detect E signals andproduce E images, a neutron polarimetry method withhigh sensitivity of spin rotation angle is desired. In our E imaging experiments, we incorporated our previously de-veloped transverse neutron polarization analysis schemewith an angular resolution ≪ − rad) [18] intoa neutron imaging setup to visualize the electrostatic fieldproduced inside experimental samples.We conducted experiments of E imaging using theNeutron Guide 6 end station (NG6e) [19] beamline at the U.S. National Institute of Standards and Technology(NIST) Center for Neutron Research (NCNR). An exper-imental diagram is sketched in Fig 1. Unpolarized poly-chromatic neutrons, primarily wavelengths from 0.2 nmto 0.6 nm, that left the beam exit and passed a slit werepolarized by two sequential supermirror benders (SMs)to facilitate alignment. The polarized neutrons were thenadiabatically transferred into a longitudinal (beam direc-tion) guiding field of about 1 mT (10 G)). The polarizedneutrons maintained their polarization and entered a lowmagnetic field chamber made of mu-metal with internallongitudinal B lab strength less than 10 µ T (0.1 G) andtransverse B lab strength less than 1 µ T (10 mG). In-side the low-field chamber, there was a capacitor-like E sample with two parallel electrodes connected to a low-current, high-voltage (HV) source via HV cables. Theelectric field was produced in the region between the twoparallel electrodes. Using Eq. (3), we find the total spinprecession angle through the E region to be θ E = − γ n κEl/c , (4)where l is the length of the electrodes, and κ is the cor-rection factor that is slightly greater than one due to thefringe E caused by the finite length l . Here the electricfield amplitude E = V /d is defined by the driving volt-age V across the parallel electrodes and the spacing d between the electrodes. The primary reason for placingthe E sample inside a low-field chamber was to minimizethe spin precession due to the background B lab , giventhe slow neutron velocity of ≈ He [18] as shownin Fig. 1 to provide spin-angle-dependent neutron inten-sity I ( θ ) ∝ N (1 + P n A sin θ ) [18] on a 300 µ m thick,LiF:ZnS imaging screen. Here, θ is the projection of θ on the analyzing direction, N is the detected neutronnumber within a given area on the screen, P n A ≤ P n andthe analyzing power A for different neutron wavelengthsin a polychromatic beam, and θ = θ E + θ B . In this exper-iment, θ B ≪ E state. For θ ≪
1, we find the E Dielectric layer (a)(b)
35 kV, 16 Ave. -
35 kV, 1172 Ave. (c)
35 kV, Modeling-35 kV, Modeling
FIG. 2. (a) Normal neutron image of the short-version E sample. (b) Electric field images from the dashed-line se-lected area in (a) with two different statistics and two drivingvoltages of 35 kV and -35 kV on the E sample. (c) Modelingresults of the E images for the same field of view. Note: for(b) and (c), the color scales and the zero-field color are dif-ferent for the 35 kV and -35 kV images for the best imagingpresentation. For (b), the apparent texture in the electroderegion is due to higher noise produced by the strongly attenu-ating electrodes. The statistics for the -35 kV image are muchbetter than for the 35 kV image due to much longer averagingtime. signal contrast I ( θ E + θ B ) − I ( θ B ) I ( θ B ) = P n Aθ E . (5)The LiF:ZnS screen generates scintillation photons thatare proportional to the neutron intensity for optical imag-ing. In the E imaging experiments, we set the slit widthto be 11 mm at the beam exit. The distances from the E sample to the beam exit and to the imaging screen wereabout 7 m and 55 cm, respectively. The vertical imagingresolution was then about 1 mm. More detailed infor-mation regarding the NG6e beamline, the experimentalapparatus, and the transverse polarimetry scheme usedin this work can be found in Ref. [18].In this proof-of-concept experiment, we imaged two E samples (long and short versions). The body of the E samples are made of perfluoroalkoxy (PFA), which has high dielectric strength, and relatively high neutrontransmission with low scattering. The rectangular, bo-rated aluminum electrodes are enclosed in a PFA bodyseparated by a PFA membrane as the dielectric layer. Inthe long-version sample, the electrodes are 5 cm wide and6.35 mm thick, l = 11 . d = (400 ± µ m. In the short-version sample, the elec-trodes are 5 cm wide and 6.35 mm thick, l = 5 . d = (500 ± µ m. In Fig. 2,we compare some experimental images and the model-ing results. Figure 2(a) is a normal neutron image of theshort-version E sample. The two rectangular, black areasat the center are the two electrodes. The PFA dielectriclayer in between the electrodes can be clearly seen. Fromthis image, we can also see some nylon screws and thetwo HV cables. The usable imaging area is defined bythe two straight-line boundaries on the sides and curvedboundaries on the top and bottom due to the openingwindow on the He NSF analyzer and the opening of thelow-field chamber [18]. For E imaging, we sequentiallytake images with the HV source alternating between theON and OFF states. Each image is the result of the me-dian combination of 3 frames, with a frame exposure timeof 45 s. Since the PFA material and the plastic screws inthe E sample produced scattered neutrons that can im-pact the quality of the E image, we use a borated maskplaced right before the low-field chamber to minimize thevolume of the sample that is exposed to the neutron beamfor reducing the scattered neutrons. The mask has a rect-angular opening, and the field of view is defined by thearea selected by the dashed line in Fig. 2(a). To producethe E image, we generate a contrast image by performing(IM(ON) − IM(OFF))/IM(OFF) from each image pair asindicated in Eq. (5). Here, IM(ON) and IM(OFF) de-note the images with the HV source ON and OFF. Weaverage all the contrast images to obtain better statistics.Figure 2(b) presents two E images of the short-version E sample at 35 kV supplied voltage with 16 averages andat -35 kV supplied voltage with 1172 averages. Since re-versing the driving voltage changes the sign of the electricfield and therefore the sign of θ E , we then see the brightand dark responses on the images. Figure 2(c) illustratesthe modeling results of the same conditions and field ofview with an assumption of uniform neutron fluence. Wecan see qualitative agreements between the experimentaland the modeling images.To verify the signal contrasts observed for applied elec-tric fields, we measured the signal contrasts from thedielectric area on the images with several driving volt-ages from −
35 kV to 35 kV on the short-version sam-ple; 36kV on the long-version sample; and 35kV on theshort-version sample with an iron shim (neutron depo-larizer) in front of the sample. In Fig. 3 we show themeasured signal contrasts versus the values calculatedusing Eqs. (4) and (5). From finite element modeling(FEM), we found κ ≈ .
032 for the short-version sample -0.010 -0.005 0.000 0.005 0.010 0.015 0.020 0.025-0.010-0.0050.0000.0050.0100.0150.0200.025 M ea s u r e d s i gn a l c on t r a s t Calculated signal contrast
Short, 64 Ave. Short, 16 Ave. Short, 1172 Ave. Long, 64 Ave. Linear fit Shimmed, 16 Ave.
Slope = 1.01 0.02
FIG. 3. E signal contrasts vs the contrasts calculated usingEqs. (4) and (5). “Short” and “Long” represent the datapoints from the short-version and long-version E samples.“Shimmed” represents the data point using depolarized neu-trons. The horizontal error bars are set by the machininguncertainty on the PFA membrane thickness, which is ± µ m, and the vertical error bars are limited by the imagingstatistics. Also shown is a linear fit to the data, which yieldsa slope of 1 . ± . and κ ≈ .
014 for the long-version sample. The experi-ments were carried out over the course of a week usingtwo different He analyzer cells that were each operatedfor a few days due to their exponential relaxation timesof ≈
200 h. Corrections were applied for the weak de-cay of the analyzing power for each cell. Based on eachcell’s properties and the polarizing efficiency of the super-mirror pair, the range of P n A was between ≈ .
96 and ≈ .
85 over the course of the experiment, which was con-sistent with a direct measurement performed as discussedin Ref. [18]. The slope of a linear fit to the data yields1 . ± .
02, hence the results are consistent with expec-tations. We see zero signal contrast with the shimmedcase as a proof of the need for polarized neutrons for E imaging. The neutron transmission is about 10.5 %through the short-version sample and 1.6 % through thelong-version sample. With the short-version sample, thedetected neutron fluence rate on the imaging screen wasabout 10 cm − s − in the dielectric area based on thegray-value readings from the image. In the experiments,the E image with the best statistics is the −
35 kV driv-ing voltage on the short-version sample with 1172 aver-ages of the contrast images. Using the entire E signalarea (about 5 cm by 1 mm, defined by the dielectriclayer), we find the relative standard uncertainty in themeasured θ E is about 1.5 %. The shot-noise-limit angu-lar resolution δθ of the neutron spin precession can becalculated by ( P n AN ) − / [18, 20]. We find N = (neu-tron fluence rate) × (area) × (frame number) × (exposuretime) × (image number)= 10 cm − s − × . × ×
45 s × . × . Hence, δθ = 0 .
12 mrad. The θ E from -35 kV on the short-version sample is − . δθ/ | θ E | = 1 . cm − in a day. For thislevel, we find that the minimally detectable E strengthfor 1 cm resolution to be about 5 × V/m (equiv-alent to 500 V across 1 cm distance) and 1 mm reso-lution to be about 5 × V/m (equivalent to 5000 Vacross 1 mm distance). As we can see, trading sensitiv-ity for higher volumetric resolution is inevitable. We be-lieve this kind of E sensitivity is sufficient for several im-age diagnostics applications for targets like: high-voltageelectronics, which usually contain capacitors with inter-nal E strengths > V/m; dielectric materials withexternally applied very high E ; and ferroelectric materi-als, which usually have spontaneous electric polarizationwith equivalent E strength > V/m.We have demonstrated direct images of an electrostaticfield in parallel plate capacitors using a polarized, poly-chromatic neutron beam. In the future, we can imple-ment the capability of spin flipping the polarized neu-tron beam or flipping the analyzing direction of the NSFanalyzer. This will enable E imaging without the needof changing the E state in the sample and will also en-hance the signal contrast by a factor of 2 with the sameexperimental time. Before this work, visualizing electricfield within an occupied diagnostic space was not feasible.In addition, owing to the great penetration capability ofneutrons through metals, this neutron-based E imagingtechnology can also measure the electric field that is in-side a shielded space, which cannot be achieved by anyother existing technology. Our work may enable newdiagnostic power of the structure of electric potential,electric polarization, charge distribution, and dielectricconstant inside an investigated target by visualizing spa-tially dependent electric field from a distance.This work was supported by the Laboratory DirectedResearch and Development program at Sandia NationalLaboratories. Sandia is a multimission laboratory man-aged and operated by National Technology and Engineer-ing Solutions of Sandia (NTESS), LLC, a wholly ownedsubsidiary of Honeywell International Inc., for the U.S.Department of Energy National Nuclear Security Admin-istration under contract de-na0003525. We acknowledgethe support of the National Institute of Standards andTechnology, US Department of Commerce, in providingthe neutron facilities used in this work. The NIST ef-fort was partially supported by the U.S. Dept. of En-ergy, Office of Nuclear Physics, under Interagency Agree-ment 89243019SSC000025. 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