Technical Physics Letters, Vol. 27, No. 12, 2001, pp. 1055–1057. Translated from Pis’ma v Zhurnal Tekhnichesko

œ

Fiziki, Vol. 27, No. 24, 2001, pp. 64–70.Original Russian Text Copyright © 2001 by Ezhov, Bazarov, Geltenbort, Kovrizhnykh, Krygin, Ryabov, Serebrov.

Permanent-Magnet Trap for Ultracold Neutron StorageV. F. Ezhova, B. A. Bazarovb, P. Geltenbortc, N. A. Kovrizhnykhd,

G. B. Krygina,*, V. L. Ryabova, and A. P. Serebrovaa St. Petersburg Institute of Nuclear Physics, Russian Academy of Sciences, Gatchina, Leningrad oblast, Russia

b DOMEN Research Institute, St. Petersburg, Russiac Max von Laue–Paul Langevin Institute, Grenoble, France

d Efremov Institute of Electrophysical Equipment, St. Petersburg, Russia* e-mail: krygin@pnpi.spb.ru

Received June 6, 2001; in final form, August 2, 2001

Abstract—The design of a permanent-magnet trap for ultracold neutron (UCN) storage is described. This trapexcludes neutron collisions with the walls and, hence, eliminates anomalous losses. Used in the experiments onthe neutron lifetime determination such UCN traps remove the main systematic error related to the anomalousneutron losses on the walls. © 2001 MAIK “Nauka/Interperiodica”.

In recent years, considerable progress has beenachieved in the experiments on determining the neutronhalflife. This was provided by using the basic propertyof ultracold neutrons (UCNs), according to which theseneutrons can be stored in closed vessels. Presently, thevalue averaged over all data reported in the literatureamounts to τ1/2 = 886.7 ± 1.9 s [1]. However, a furtherincrease in the experimental accuracy is hindered by asystematic error related t the presence of anomalousUCN losses upon reflection from the container walls.The nature of this phenomenon is still not completelyclear, which gives little hope for an increase in the accu-racy of traditional experiments in the nearest future.

However, in the very early days upon the discoveryof UCNs, Vladimirskiœ [2] considered the possibility ofUCN storage in magnetic traps. In such a system,UCNs possessing a certain polarization are reflectedfrom a magnetic barrier and, hence, do not strike thewalls. Therefore, the use of magnetic traps may princi-pally eliminate the problem of anomalous losses. Thus,the problem reduces to creating a magnetostatic systemin which the magnetic field strength increases in alldirections.

Such traps are widely used in the atomic physics.The most known design is offered by traps of the Ioffe–Pritchard type [3, 4]. This device comprises a magneticquadrupole, creating a reflecting barrier in the radialdirection, and two gate coils at the quadrupole ends cre-ating reflecting gradients on the quadrupole axis nearedges. The particle admission and extraction can becontrolled by switching current in one of the gate coils.

In application to UCNs, a system of this type wasdesigned and constructed in Los Alamos [5]. The maindifficulty in creating a UCN trap is related to the factthat the magnetic moment of a neutron is lower by threeorders of magnitude as compared to that of an atom.

1063-7850/01/2712- $21.00 © 21055

Accordingly, the magnetic fields necessary to holdUCNs must be three orders larger. In the Los Alamossystem [5], the magnetic trap implemented supercon-ductor-based magnets.

However, the superconductor-based magnetic sys-tems possess two significant disadvantages. The first isa relatively slow current variation. As a result, it takes atoo long time to close the inlet hole. For this reason,designers of the Los Alamos system refused from usinginlet and outlet holes and used to generate UCNs imme-diately inside the magnetic trap by means of thermalneutron scattering on a superfluid helium film coveringthe trap walls.

The second disadvantage is a relatively small vol-ume of superconductor-based magnetic systems, sincethe statistical accuracy of the experimental neutron life-time determination depends primarily on the trap vol-ume. An increase in the superconductor-based mag-netic system volume would lead to enormous growth ofthe cost of experiments. The volume of the Los Alamostrap was as small as 0.28 dm3 (diameter, 3 cm; length,40 cm) at a magnetic barrier of 1.1 T. For a UCN num-ber density of 1.8 ± 0.3 cm–3, the total number oftrapped UCNs was 400 ± 65 per cycle. From a practicalstandpoint, this system design is overcomplicated,since the magnetic systems employing nonsupercon-ducting elements allow the same magnetic fieldstrengths to be obtained in traps of a significantlygreater size. Moreover, using modern magnetic materi-als, it is possible to create UCN traps with the samemagnetic field strength and greater volume based onpermanent magnets.

The magnetic potential m · B must correspond to aneutron energy of 0.6 × 10–7 eV/T (for comparison, thenuclear potential for beryllium is equivalent to 2.5 ×10−7 eV). Thus, the magnetic barrier with a height of

001 MAIK “Nauka/Interperiodica”

1056

EZHOV

et al

.

1 T reflects neutrons possessing a certain polarizationup to a velocity of 3.4 m/s. The force acting upon themagnetic moment of a particle moving in an inhomoge-neous magnetic field is

where the plus and minus signs refer to the cases of themagnetic moment oriented along the magnetic field andin the opposite direction, respectively. Let us estimatethe possible magnitude of a magnetic field gradientreflecting UCNs. The magnetic moment precession inthe field is described by the Bloch equation

where γn = 1.83 × 108 s–1 T–1 is the gyromagnetic ratio.The spin of a neutron moving at a velocity v in the mag-netic field will retain the orientation provided that thefollowing adiabaticity condition is obeyed [6]:

For B = 1 T, a field gradient of ∇ B = 1 T/mm, and a neu-tron velocity of v = 3.4 m/s, the adiabaticity conditionis obeyed to within 1.83 × 108 @ 3.4 × 103. Evidently, aspecial point only corresponds to the site where themagnetic field turns zero. At this point, the adiabaticitycondition is violated and the magnetic moment projec-tion onto the magnetic field direction may change.Vladimirskiœ [2] estimated the probability of a nonadi-abatic reversal of the neutron spin under the conditionswhen one field component (Hz) is constant and the other(Hx) performs rapid rotation. In this case, the neutron

F ∇ U– ∇ m B⋅( ) µ∇ B ,±= = =

dmdt------- γnm B,×=

γnB @ dB/dt( )/B v ∇ B /B.⋅=

1

2

3

4 5

Fig. 1. A general schematic diagram of the permanent-mag-net UCN trap: (1) neutron guides; (2) gate coil; (3) magnetyoke; (4) permanent magnets; (5) magnetic guide.

TE

spin reversal probability is

where ω = µHz/" is the neutron spin precession fre-

quency about the Hz direction and τ = Hz/ is the effec-tive time of the magnetic field rotation. For a neutronperforming a large number N of passages at the pointsof zero magnetic field or rapid field rotation, the adia-baticity condition will be obeyed provided that Nω ! 1.For a minimum magnetic field strength, we obtain thecondition

Thus, in any particular case, we may select a value ofHzmin such that the nonadiabatic spin reversal can beignored.

From the economic standpoint, the most favorablemagnetic system design is that in which the magneticfield strength decays over a minimum distance. Thiswould provide for a decrease in the energy (stored inthe magnet) required for creating the necessary fieldstrength and, hence, for a reduction in the permanent-magnet trap weight and cost. Moreover, this leads to anincrease in the effective volume of UCN storage.

In the atomic physics, the problem of reflectingatoms from a magnetic barrier is frequently solved byusing magnetic planes in periodic magnetic structuresmagnetized along the surface [7]. At these planes, themagnetic field decays by the exponential law exp(–kx),where x is the distance and k is a characteristic periodof the structure. In the structures employed for experi-ments on the reflection of atoms, the k value may reachup to a few microns. Accordingly, the structures with aperiod on the order of several millimeters can be usedin the experiments with UCNs. The calculation showedthat systems employing the modern magneticallyhard materials readily allow obtaining a field strengthof B = 1 T at the reflecting wall with a field gradientof ∇ B = 1 T/mm.

Thus, let us summarize the main requirements to theexperimental UCN trap setup:

(i) The magnetic trap height is determined by thegravitational potential (i.e., by the height above whichthe neutron of a given energy cannot rise in the gravita-tional field). For this reason, there is no sense in creat-ing systems with a height exceeding 60 cm. At a suffi-ciently large height, there is no need for the upper lid.

(ii) There should be no points with zero magneticfield strength inside the magnetic trap.

(iii) The neutrons must be admitted in and extractedfrom the trap through a weak magnetic field region.Upon admitting neutrons, the field strength is increasedand the UCNs are trapped.

(iv) Using gradually decreasing field for the neutronextraction, it is possible to measure the energy spec-trum of stored neutrons.

w e πωτ– ,=

H

πµHzmin2

/" H N .ln>

CHNICAL PHYSICS LETTERS Vol. 27 No. 12 2001

PERMANENT-MAGNET TRAP FOR ULTRACOLD NEUTRON STORAGE 1057

Figure 1 gives a general schematic diagram of theproposed magnetic trap. Figure 2 shows a quarter of thecross section. The trap comprises a vertical vessel witha almost square cross section of the UCN storage cav-ity. The neutrons are admitted in and extracted from thetrap via a hole in the bottom. The magnetic field in thishole region is created by a gate coil. In order to elimi-nate the points of zero magnetic field inside the trapvolume, the magnetic field of the gate coil is closed viaan external magnetic guide through the upper part andthe internal cavity of the trap. As a result, a verticalmagnetic field component appears in the whole trapvolume. Since the magnetic field of the walls is closed

1

2

3

Fig. 2. Element of the UCN trap cross section: (1) perma-nent magnets; (2) magnetic guide; (3) closing yoke.

TECHNICAL PHYSICS LETTERS Vol. 27 No. 12 20

in the horizontal plane, no magnetic field zeros can takeplace in the trap. The whole system is placed into avacuum.

The trap volume is about 20 dm3. For a neutronnumber density of 5 cm–3, this provides for the storageof up to 105 neutrons. The presence of a controlledmagnetic barrier closing the entrance allows the storedUCN spectrum to be purified from over-barrier neu-trons. By varying the current in the gate coil, it is pos-sible to control the boundary energy of stored neutrons,which is important in searching for the possible system-atic effects.

Acknowledgments. This study was performedwithin the framework of an experiment on the adiabaticcooling of atomic hydrogen, which is supported by theRussian Foundation for Basic Research projectno. 99-02-17378.

REFERENCES1. D. E. Groom et al. (Particle Data Group), Eur. Phys. J. C

15 (1-4), 1 (2000).2. V. V. Vladimirskiœ, Zh. Éksp. Teor. Fiz. 39 (4), 1062

(1960) [Sov. Phys. JETP 12, 740 (1960)].3. T. H. Bergeman, P. McNicholl, J. Kycia, et al., J. Opt.

Soc. Am. B 6, 2249 (1989).4. T. H. Bergeman, G. Erez, and H. Metcalf, Phys. Rev. A

35, 1535 (1987).5. P. R. Huffman, C. R. Brome, J. S. Butterworth, et al.,

Nature 403, 62 (2000).6. A. Abragam, The Principles of Nuclear Magnetism

(Clarendon, Oxford, 1961; Inostrannaya Literatura,Moscow, 1963).

7. E. A. Hinds and I. G. Hughes, J. Phys. D 32, R119(1999).

Translated by P. Pozdeev

01