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A Superconducting Storage Ring for Very Slow Neutrons

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A Superconducting Storage Ring for Very Slow Neutrons © 1979 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. IEEE Transactionson NuclearScience, Vol. NS-26,No, 3, June 1979 A SUPERCONDUCTINGSTORAGE RING FOR VERY SLOW NEUTRONS K. J. Kiigler, W. Paul and U. Trinks+ Physikalisches Institut der Universitat Bonn, Bonn, Germany Summarv frequency WL is large compared with the anqu- It was shown experimentally that neutrons lar frequency of rotation of is: wL=-pB/h&l/B, can be confined in a magnetic storage ring by which is satisfied everywhere except in the means of thl:ir magnetic moments. Due to the central zone r50.5 mm, where B is very small, small dipoll., = moment the energy of the neutron In case of a toroidal sextupole field with is limited to a few 10s6 eV in spite of the mean diameter 2R, as shown schematically in high field in the superconducting magnet of In many respects the beam fig. lb the particles will oscillate harmoni- 1 m diameter. cally (in first order approximation) around dynamics are similar to a storage ring for charged par Iticles. The basic field configura- circular orbits, with RzR, given by the equivalence of centrifugal and magnetic for- tion is a sextupole field superimposed of a ce: mva2/R=u6 B/6rR. Thus the central zone R=Ro strong deca:pole term in order to overcome imperfaction resonances by a non harmonic where spin flip may occur is excluded. The potential. As only neutrons in one spin state betatron frequencies are given by ,x2= 3+R0 are confined, care has to be taken to avoid (6 2B/6r2b/ (6 B/5 r) in the radial and spin flips. The neutrons are injected by a by vy 2 =R(6 2B/C;y )/(SB/i; r) in the axial direc- totally reflecting mirror system which can tion for small amplitudes. be removed out of the confinement region. 3. Beam dynamics Neutrons were detected up to a storage time Their number decreases according It is rather instructive to compare this sto- of 45 min. rage ring for neutrons with those for charged to their 1iEetime (71/2=10.6 min) due to radioactive decay. particles. For a charged particle, dipole fields provide the compensation of the centri- 1 . Introduction fugal force, quadrupole terms for the focusing A superconducting magnetic storage ring for forces, sextu- and octupoles are used for corrections of the optical system. In the very slow neutrons came into operation at neutron case using the magnetic moment one the ultracold neutron beam of the ILL Gre- has to use one order higher of multipole ex- noble. We followed an old idea of guiding pansion of the magnetic field: here the and focusing particles having a magnetic quadrupole term compensates the centrifugal moment by means of a magnetic sextupole field which was successful1 in atomic beam force, sextupole terms provide focusing , and physics (1) and proposed also for neutron we use higher (decapole) terms to introduce beams (2) . In such a field, bent to a torus nonlinearities in order to keep the amplitu- with a radius R, neutrons can be guided on des of the betatron oscillations limited (see circular orbits. Similar proposals were below) . made by Heer (3) and a Russian group (4) . However, there are strong differences between 2. Principlle the concepts. In the neutron case we have rather strong focusing (ne25) in axial and The potential energy of a particle with a radial directions at the same time and (ne- magnetic momen: 11 and a spin l/2 in a magnetic glecting field imperfactions) no azimuthal field is $=-:.B and the corresponding force: field dependence. This leads to equations F=& DgradB, the sign + for parallel and - of motion for the deviations x (and y) of the for antiparallel position of p to B. In a li- cicular orbits of the form: near sextupole with a field as indicated in fig. la the induced field is given by x”+a, X+ a2x2 -k a3x3 + . = 0 (1) with the primes denoting d2/dC2 and ai inde- pendent of 0 (with al as leading term). In the ideal case of an azimuthally symmetric field the solutions are s t a b 1 e unhar- manic oscillations with frequencies v*& and amplitudes depending mainly on the cubic term a3. As the real magnetic field has small pertur- Fig. 1 . (a) Field lines and field induction bations (of the order of 0.5%) the equations B of a linear sextupole and (b) a (1) have to be modified mainly by adding terms sextupole torus. of the form Ck * cos(kG+Bk) on the right hand side with k integer and Ek small compared B= (Bo/ro2) r2, thus the restoring force is with al. If there were no nonlinear terms a1 -r. For 11 parallel to B the particles with isI these perturbation terms would cause oscillate harmonically around the central forced oscillations with amplitudes proportio- axis r=O, if i) the kinetic energy of the nal to F~/ lk2-v2] , thus leading to infinitely motion perplendicular to the axis is less increasing amplitudes in the resonance caseeon than Ekin,L,uB,. With p,=-6.02.10 -8 eV/T and the other hand in the presence of nonlinear B,=3.5 T one gets Ekin,- d 2.1 -low7 eV corres- terms al with i ? 3 the maximum amplitude Xmax ponding to ~~~6.4 m/s. ii) i; remains parallel is limited, because the resonance curves are to 2. This condition is held, if the larmor bent due to the amplitude dependence Of the betatron frequency v(xmax), which gives the ‘) Present address: Technische Universitat characteristically triangular shaped ampli- Miinchen, Phys.Dep. El2 tude/frequency curves. As an example fig. 2 D8046 Garching, Germany 3152 0018-9499/79/0600-3152$00.750 1979 IEEE \ \ Ra555mm v, B+0.6 m/s \ \ \ 0l- I I I IA 4.3 A.4 v. 45 k 4.6 Fig. 2. Resonance curve for radial oscilla- tions at orbit radius R = 55.5 cm (NESTOR) . shows a curve which results from computer calculations of neutron paths in the ideal Fig. 3. The coil configuration and field in- field of NESTOR perturbed by typical imper- duction B (dotted). The confinement fections of different frequencies k per turn region is indicated by the broken (5). These calculations together with theo- lines. Hatching denotes copper alloy, retical considerations showed that (due to the solid area liquid He. the smallness of the perturbation term ek) this effect is strong enough to allow storage total kinetic energy up to 2.10 -’ eV . of neutrons without losses in a momentum Neutrons are injected from inside in the band as large as Ap/p=:O.35 corresponding to ring by a totally reflecting mirror system azimuthal velocities v0 = 12 . 17 m/s, if (glass nickel coated) in both directions. It the orbits of the neutrons are limited to can be removed from the confinement region the central part of the storage region. This by a pneumatic system in a time small compa- is provided by beam scrapers at the inner red to the time for one revolution. The in- and outer radius of the storage region, each jection time is ~0.2 set corresponding to of which covers about one third of the total one revolution. cross section and is removed a few seconds after the beginning of storage, thus allowing Since the vacuum between the He-cooled coil the remaining beam to blow up. Because of the support is better than 1O-11 N/m2 the beam- low incoming flux of very slow neutrons it gas collisions are no problem. is important, that a large momentum band The stored neutrons are detected by a 311e corresponding to an extended working region proportional counter moved into the ring is acceptable. after a preset time. In case of storage rings for charged partic- 5. $leasurements les the equations of motion for the ideal field without perturbations and nonlineari- Some measurements concerning the storage t:es are of thle form x” t (1 -n) x = 0 and time of the confined neutrons in the ring y t ny = 0 with n strongly depending on 0 for different positions of the beam scrapers (for strong focusing and weak focusing with are shown in fig. 4. Each point is the straight sections) . Here, in contrast to the average of several injection cycles. The neutron ring, the well known regions of in- dotted areas indicate the respective position stability resulting from first and higher of the injection system limited by the beam order resonances occur already in the ideal scrapers during the first 6.2 s (curve (b) field case. From this it follows that only and (c) only) . particles in a very small momentum band of The upper most curve (a) was made without typically Ap/p $10-3 remain in a stable beam scrapers. It shows that, after some motion, and the corresponding working region losses in the first minutes due to improper in the working diagram has to be pointlike injection parameters, the number of neutrons and is not even allowed to move near stop remaining in the ring decreases according bands. Therefore, perturbations by imper- to the lifetime of the radioactive decay: fections of the field will influence the the straight line represents this decay with particle motions much more than in the a mean lifetime of T = 918 s, it is ad justed neutron case and have to be corrected.
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