Measured velocity spectra and neutron densities of the PF2 ultracold-neutron beam ports at the Institut Laue--Langevin
MMeasured velocity spectra and neutron densities of the PF2 ultracold-neutron beamports at the Institut Laue–Langevin
Stefan Döge,
1, 2, ∗ Jürgen Hingerl,
1, 2 and Christoph Morkel Institut Laue–Langevin, 71 avenue des Martyrs, F-38042 Grenoble Cedex 9, France Physik-Department, Technische Universität München, D-85748 Garching, Germany
Ultracold neutrons (UCNs) are a useful tool for fundamental physics experiments. Theycan be used to probe the lifetime of free neutrons, search for new CP violating processes andexotic interactions beyond the Standard Model, perform Ramsey spectroscopy, and carry outneutron-optical interference experiments. All of these experiments require high neutron count ratesfor good statistics. For optimal exploitation of experimental beam time, these experiments needto be prepared and, at times, even simulated in advance. To this end, it is crucial to know thevelocity-dependent UCN flux at each beam position. Knowing the absolute neutron flux also allowsfor an absolute calibration of previously gathered data. Using the same time-of-fight experimentalsetup, we have measured the differential neutron flux of three out of the four UCN beam ports atthe PF2 instrument at Institut Laue–Langevin, Grenoble. These beam ports are commonly usedfor UCN flux experiments and proof-of-principle tests.Published online on 11 November 2019: https://doi.org/10.1016/j.nima.2019.163112
S. Döge et al., Nuclear Instruments and Methods in Physics Research, A 953 (2020) 163112© 2020. This manuscript version is made available under the CC-BY-NC-ND 4.0 license.
PACS numbers: 29.25.Dz, 28.20.Cz, 61.05.F-, 14.20.Dh
I. INTRODUCTION
Many fundamental physics experiments use ultracoldneutrons (UCNs). These are neutrons with a kinetic en-ergy low enough to be confined in material bottles ormagnetic traps, typically (cid:46)
300 neV ( v < . II. PREVIOUS MEASUREMENTS
Steyerl et al. carried out UCN flux (also called currentdensity) and density measurements after the Turbine had ∗ Corresponding author Stefan Doege: [email protected] been installed [9, 10]. In these experiments, both fluxand density inside the Turbine vessel were determined.However, no systematic measurement has yet been takenof the UCN flux available outside the vessel at the fourPF2 beam ports (MAM, UCN, EDM, TEST), nor havethese beam ports been compared with one another.In 1999, the group led by A. V. Strelkov from JINRDubna (Russia) measured the neutron density of theEDM, UCN, and MAM beams using a spherical copperstorage vessel with a volume of 27 liters ( v Cucrit = 5 . v steelcrit = 6 . density at one neutron beam port of the Turbine (PF2-EDM).The neutron densities at the exits of other UCN con-verters, based on solid deuterium and liquid helium asconversion media, were measured using the same storagevessel and then compared with one another [12].Many experiments, especially long-term experiments,will benefit from the data of the velocity-dependent UCNfluxes at the Turbine’s beam ports [dataset] [13]. Thisdata will facilitate the simulation and preparation of ex-periments before the setup is installed at the Turbinefor its allocated beam time. The data will also serve asa retroactive calibration standard for past experimentsand as a reference for future instrument upgrades. III. THE EXPERIMENTAL SETUP
For the comparative measurement of neutron spectra,the UCN ports of the Turbine were equipped with beam a r X i v : . [ phy s i c s . i n s - d e t ] J a n tube configurations that are often used by experimenters,see Fig. 1. The beam port PF2-MAM was permanentlyoccupied by the long-term experiment “Gravitrap” [14]and thus its spectrum could not be measured.For safety reasons, the vacuum in the Turbine’s beamguides is separated from the Turbine vacuum by a 100 µ mthick AlMg3 foil. The neutron guides between the safetyfoil of the Turbine and the chopper were standard NiMo-coated electropolished stainless steel tubes of variouslengths and with outer diameters as indicated in Fig. 1.The tubes all had a wall thickness of 2 mm. Their trans-missivity was measured to be 95% per meter for the UCNspectrum of the Turbine. T u r b i n e p o r t P F - E D M T u r b i n e p o r t P F - U C N T u r b i n e p o r t P F - T E S T A l f o il g l a ss t ub e L = c h o pp e r g l a ss t ub e L = C a s c a d e d e t e c t o r s t ee l t ub e L = s t ee l t ub e L = Ø Ø Ø Ø s hu tt e r t r a n s i t i o n p i e c e A l f o il s t ee l t ub e L = f l a n g e c h o pp e r g l a ss t ub e L = C a s c a d e d e t e c t o r s t ee l t ub e L = s t ee l t ub e L = s t ee l t ub e L = Ø Ø Ø Ø Ø s hu tt e r f l a n g e A l f o il s t ee l t ub e L = f l a n g e c h o pp e r g l a ss t ub e L = C a s c a d e d e t e c t o r s t ee l t ub e L = s t ee l t ub e L = s t ee l t ub e L = Ø Ø Ø Ø Ø s hu tt e r f l a n g e FIG. 1. Beam tube configurations used for comparing theflux of the three Turbine beam ports PF2-TEST, PF2-EDM,and PF2-UCN with one another. The Turbine’s safety foil isindicated as “Al foil”. For each beam tube, the length L andouter diameter ∅ are given in millimeters. Connected to the last steel guide tube was an UCN chopper similar to the one developed by Lauer [15] butwith 1 mm thick titanium grids, a NiMo-coated glasstube of 80 mm inner and 90 mm outer diameter, anda Cascade neutron detector [16], which together consti-tuted the time-of-flight (TOF) geometry of this experi-ment. The transmissivity of the glass tubes for neutronsin the UCN range was 87% per meter, and the neutronflight path had a length of d TOF = 458 mm. As the neu-tron beam was uncollimated, the TOF method measuredthe neutrons’ velocity component along the beam axis, v z . All spectra were measured at the height of the Tur-bine exits and without any bends in the neutron guides.The absolute efficiency of the Cascade detector wasdetermined to be 34 ±
5% [17, 18] across the Turbine’sneutron spectrum. This value, together with the beamtubes’ transport efficiencies, and the chopper’s duty cy-cle of 3.94% and geometric opening of 36% allowed themeasured UCN transmission to be extrapolated back tothe position of the aluminum safety foil and the absolutedifferential neutron flux φ ( v ) at the Turbine’s beam portsto be obtained. All in all, the beamline and TOF setupreduce the usable number of UCNs to about 0.5% of theoriginal flux at the position of the safety foil.All measurements were carried out at a thermal reactorpower of 55.8 ± P F 2 - U C N P F 2 - E D M P F 2 - T E S T
Diff. neutron flux F (v), extrapolated (cm-3) N e u t r o n v e l o c i t y ( m / s )
FIG. 2. Comparison of the Turbine’s differential neutronfluxes φ ( v ) at the beam ports PF2-UCN, PF2-EDM, and PF2-TEST at the position of the respective safety foil. Of the errorbars, a systematic error of 15% is due to the uncertainty ofthe absolute Cascade detector efficiency for UCNs. The peakvelocities can be calculated using Eq. 5 and the respectivespectral temperature from Tab. I. Some error bars have beenremoved for better legibility. TABLE I. Neutron densities N , fluxes Φ, and temperatures T extracted from the Maxwell–Boltzmann (MB) fits and thereal experimental spectra of the beam ports PF2-UCN, PF2-EDM, and PF2-TEST. The uncertainty indicated for the datain column 1 is the fit error. The fit error for the temperature in column 2 is of the order of 10 − mK. All experimentaldata have a relative systematic uncertainty of ± v steelcrit = 6 . v Ni-58crit = 8 . N (cid:0) v steelcrit (cid:1) N (cid:0) v Ni-58crit (cid:1) beam port N [cm − ] temp. T [mK] flux Φ [cm − s − ] flux Φ [cm − s − ] N [cm − ] [cm − ] [cm − ]Maxwell–Boltzmann fit ExperimentalPF2-UCN 61 . ± . . ± . . ± .
01 3.0 3,060 2,928 3.37 0.69 1.62
IV. EXPERIMENTAL RESULTS ANDCALCULATIONS
The Turbine ports’ neutron spectra, which extend be-yond the UCN range into the VCN energy range, areshown in Fig. 2. They were corrected for detector effi-ciency and chopper duty cycle, and extrapolated back tothe position of the Turbine’s safety foil.The measured differential neutron flux φ ( v ) (in unitsof cm − ) from Fig. 2 can be well approximated by aMaxwell–Boltzmann (MB) distribution f MB ( v ) for theneutron density N ( v ) = N × f MB ( v ), where φ ( v ) = N ( v ) × v , and thus φ ( v ) = N π (cid:16) m n πkT (cid:17) / v × exp (cid:18) m n v kT (cid:19) . (1)In Eq. 1, N represents the total neutron density (in unitsof cm − ) over the entire spectrum, m n the neutron’smass, k the Boltzmann constant, T the temperature ofthe Maxwell–Boltzmann shaped neutron spectrum, and v the neutron velocity. f MB ( v ) is normalized to unity, inother words, Z ∞ N ( v )d v = N . (2)By integrating Eq. 2 not over the entire spectrum butrather over an arbitrary velocity range, e.g. from 0 m/sto v crit , the neutron density N ( v crit ) over that range canbe calculated. Here, v crit = r U opt m n , (3)where U opt is the neutron-optical potential of a givenmaterial [1, 2]. When calculating the neutron densityinside an UCN storage bottle, U opt is determined by thestorage bottle’s inner wall coating, to which the neutronsare exposed. Materials of choice are often steel, copper,nickel, diamond-like-carbon (DLC), or fomblin grease.The data from Fig. 2 have been fitted with the func-tion φ ( v ) = N ( v ) × v , see Eq. 1, over the velocity in-terval (6 m/s , ∞ ). From this fit, the total neutron den-sities N , temperatures T , and integral neutron fluxes Φ shown in Tab. I could be extracted. It must be noted,however, that the experimental data for v < v Alcrit = 3 . φ ( v ∗ ) in Fig. 2, while the most probable velocity of theMaxwell-Boltzmann spectrum is found at f MB (ˆ v ). Bothare related to each other by v ∗ = r
32 ˆ v, (4)which can easily be demonstrated by calculating the firstderivatives ∂/∂v of both distributions.Using the relation ˆ v = r kTm n , (5)one can convert the temperature of the neutron spectra,see Tab. I, into each spectrum’s peak velocity ˆ v , and alsorewrite Eq. 1 as φ ( v ) = N √ π × (cid:16) v ˆ v (cid:17) × exp (cid:18) − h v ˆ v i (cid:19) . (6)Calculated for the neutron flux peak φ ( v ∗ ) using therelation from Eq. 4, Eq. 6 simplifies to φ ( v ∗ ) = N √ π (3 / / × exp( − /
2) = N × . . (7)The total neutron density N of a MB distributed neu-tron spectrum is thus related to the peak of the differen-tial flux by a simple scaling factor.The integral neutron flux Φ (in units of cm − × s − ) ofthe spectrum up to a critical velocity v crit can be calcu-lated by integrating Eq. 6Φ = Z v crit N ( v ) × v d v = N R v crit f MB ( v ) × v d v R v crit f MB ( v )d v | {z } h v i , (8)with the analytical solution of the integral in the numer-ator equal toˆ v × √ π × (cid:18) − (cid:20) (cid:16) v crit ˆ v (cid:17) (cid:21) × exp (cid:2) − ( v crit / ˆ v ) (cid:3)(cid:19) , (9)and the solution of the integral in the denominator beingerf (cid:16) v crit ˆ v (cid:17) − √ π × (cid:16) v crit ˆ v (cid:17) × exp (cid:0) − [ v crit / ˆ v ] (cid:1) . (10)Eq. 8 is tantamount to calculating the mean velocity h v i of the velocity distribution and multiplying it by thetotal neutron density. This is exactly the definition ofthe integral neutron flux Φ.For a perfect MB distribution, the weighted mean ve-locities h v i from the aluminum cut-off (3.2 m/s) to thesteel cutoff (6.0 m/s) are 4.74 m/s for the PF2-UCNbeam, 4.75 m/s (PF2-EDM), and 4.76 m/s (PF2-TEST).The weighted mean velocities extracted from the exper-imental spectrum are 5.13 m/s for the PF2-UCN beam,5.01 m/s (PF2-EDM), and 5.04 m/s (PF2-TEST). Theylie slightly higher than the velocities from the MB fit dueto the aluminum cut-off of the slowest UCNs. At thealuminum safety foil, even UCNs slightly faster than thecritical velocity of aluminum are reflected if they impingeon the foil at an angle other than 90°. The roughness ofthe aluminum foil also has an effect on the transmissionof UCNs [18, 19].Tab. I shows the values for neutron densities (total andup to the critical velocities of steel and Ni-58), fluxes, andtemperatures of the measured spectra of the beam portsPF2-UCN, PF2-EDM, and PF2-TEST as extracted by1. Maxwell–Boltzmann (MB) fits using the mathe-matical relations explained above2. numerical integration and direct extraction fromthe experimental data.It is easy to see that both the beam ports PF2-UCNand PF2-EDM provide comparable UCN densities. Bothare thus equally suitable for UCN storage experiments.The UCN density up to the critical velocity of steel v steelcrit at the EDM beam port ( outside the Turbine), 9 . ± .
48 cm − , is about a factor of two larger than thedensity of 4 . ± .
02 cm − measured in a storage exper-iment for a similar beamline configuration, including thealuminum safety foil, as reported by Ries et al. [12]. Thedifference might be due to differences in the UCN trans-port and detection efficiencies between these two typesof experiments.Steyerl et al. [9] reported the UCN density up to6.2 m/s inside the Turbine to be 87 cm − as derivedfrom TOF data and to be 36 cm − as measured withan iron storage bottle. Here, again, the neutron densitymeasured by the TOF method lies about a factor of twohigher than the density measured with a storage bottle. V. CONCLUSIONS
Using the same experimental equipment, we have mea-sured and compared the differential neutron fluxes atthree out of the four beam ports of the UCN Turbine atthe Institut Laue–Langevin. From these data, we wereable to calculate the integral neutron fluxes and extractthe total neutron densities up to any arbitrary criticalneutron velocity v crit . Our measured values for the PF2-UCN and PF2-EDM beams indicate that both have asimilar UCN density below the steel cut-off (6.0 m/s)of 10.4 cm − and 9.87 cm − , respectively. These are inline with earlier measurements of the UCN density insidethe Turbine vessel. The density of UCNs below the steelcut-off at the PF2-TEST beam is 0.69 cm − . These arethe first published comparative neutron density measure-ments outside the Turbine.The experimental results for this paper were producedas part of the Ph.D. theses of Stefan Döge [18] and TobiasRechberger [20]. ACKNOWLEDGMENTS
We wish to thank the instrument scientists of PF2for their advice and Dr. Tobias Rechberger for sup-port during the experiment. The PhD thesis of S. D.was done within a collaboration between the InstitutLaue–Langevin (ILL), Grenoble, France and Technis-che Universität München, Munich, Germany. It re-ceived financial support from both the ILL and FRM II/Heinz Maier-Leibnitz Zentrum (MLZ), Garching, Ger-many. Furthermore, J. H. and S. D. acknowledge fundingfrom Dr.-Ing. Leonhard-Lorenz-Stiftung, Munich, undergrant no. 930/16. [1] V. K. Ignatovich,
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