The aim of "beta-beams" is to produce highly energetic pure electron neutrino and anti-neutrino beams coming from β-decay of radioactive ions. In CERN baseline, after accelerating, the ions 6He2+ and 18Ne10+ are stored in a racetrack-shaped-decay ring until they are lost [1]. Consequently, the injection compensates the losses which occurred between two cycles. Two main loss sources were identified: the β decay and the injection scheme. After giving the optics, we will see how to protect the magnetic elements from the decay products. The injections scheme will be then detailed with its implications. We will see that the injection process makes a collimation section in energy necessary. Since the magnetic elements are not perfect, we will take into account the magnet misalignment and the multipole defects in the dipoles. We will talk then about the closed orbit distortion due to misalignment defects and about the long-term transverse stability with the dynamic aperture

Chance, A

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PoS(Nufact08)088Decay ring status / studiesANTOINE CHANCE∗†CEA, IRFU, SACM, Centre de Saclay, F-91191 Gif-sur-Yvette, France.E-mail: achance@cea.frThe aim of "beta-beams" is to produce highly energetic pure electron neutrino and anti-neutrinobeams coming from β -decay of radioactive ions. In CERN baseline, after accelerating, the ions6He2+ and 18Ne10+ are stored in a racetrack-shaped-decay ring until they are lost [1]. Consequently,the injection compensates the losses which occurred between two cycles. Two main loss sourceswere identified: the β decay and the injection scheme. After giving the optics, we will see howto protect the magnetic elements from the decay products. The injections scheme will be thendetailed with its implications. We will see that the injection process makes a collimation sectionin energy necessary. Since the magnetic elements are not perfect, we will take into account themagnet misalignment and the multipole defects in the dipoles. We will talk then about the closedorbit distortion due to misalignment defects and about the long-term transverse stability with thedynamic aperture.10th International Workshop on Neutrino Factories, Super beams and Beta beamsJune 30 - July 5 2008Valencia, Spain∗Speaker.†Work supported by European Community under the FP6 - Research Infrastructure Action - Structuring the Euro-pean Research Area - EURISOL DS Project Contract no. 515768 RIDS.c© Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/PoS(Nufact08)088Decay ring status / studies ANTOINE CHANCE1. OpticsThe decay ring is a 6911.5 m-long racetrack-shaped-ring with two 2468-m-long straight sec-tions, of which one is directed toward the detector situated in the Fréjus tunnel [1]. The usefulsection is around 36 % of the circumference. The parameters of the beam are given in Table 1 [2].Table 1: Nominal parameters for the decay ring.Units 6He2+ 18Ne10+γ - 100 100Bρ T.m 938 563Bdipole T 6 3.6τ at rest s 0.8 1.67Ninjected (ions/batch) - 9.05×1012 4.26×1012Nstored (ions/batch) - 9.71×1013 7.40×1013Harm. number - 924 924Bunch number - 20 20rms εx pi mm.mrad 0.11 0.11rms εy pi mm.mrad 0.06 0.06∆νx - -0.015 -0.127∆νy - -0.024 -0.201A first consequence to store high intensity beams is that the tune spread due to the spacecharge effects may not be negligible. The tune shift was calculated for 6He2+ and 18Ne10+ and isgiven in Table 1. With nominal parameters, the space charge effects can be neglected in 6He2+ casecontrary to 18Ne10+ case. A solution to decrease the space charge effect would be to increase therms emittance of the stored beam by injecting a mismatched beam. To have a negligible tune shiftfor 18Ne10+ of -0.063 in the horizontal plane and -0.055 in the vertical one, the rms emittance mustthen be enlarged up to 0.22 pi mm.mrad in both planes. In the following, we will assume this rmsemittance for 18Ne10+ to neglect space charge effects.The arcs are 2pi insertions of which the optics is given on Figure 1. Four functional partswere distinguished in the arcs [3]: a regular FODO lattice in the arc, a matching section betweenthe long straight section and the FODO lattice, which is used to extract the decay products comingfrom the long straight section too, a low β high dispersion insertion for the injection and a matchingsection between the regular FODO lattice and the insertion. Moreover, large betatron functions areneeded in the FODO lattices of the long straight sections to maximize the neutrino flux going tothe detector.2. Losses by β decayThe decay of the stored ions implies a continuous power loss with a mean value of 10.8 W/mfor 6He2+ and 11.8 W/m for 18Ne10+[4]. The relative rigidity difference between the decay productand the reference one is then around -33% for 6He2+ and +11% for 18Ne10+, which is too large to2PoS(Nufact08)088Decay ring status / studies ANTOINE CHANCEInjectionSectionMatchingSectionRegular FODOLatticesMatchingSectionExtractionSectionΒxΒyDx0 200 400 600 800 100005101520sHmLPrimaryCollimatorΒx ΒyDx0 500 1000 1500 2000-100102030sHmLFigure 1: Optical Functions in the arc (left) and in the collimation section (right).accept the decay products. They are then lost after crossing a few dipoles. Two principal problem-atics can be underlined. After the long straight sections, the deposition is equal to several tens ofkilowatts: a dedicated extraction section at the arc entry is needed. Moreover, the deposition in-side the superconducting magnets must be low enough to avoid quenching, for which two solutionswere studied. The first one consists in inserting absorbers between the magnetic elements. The sec-ond one consists in using open mid plane dipoles, which are dipoles without coils in the horizontalplane. The advantages of this solution is to enable longer dipoles, which decreases their magneticfield (5 T instead of 6 T), to reduce the needed dipole aperture (±50 mm against ±80 mm) and tomake the structure changes simpler if other ions are used.To evaluate the deposition of the decay products in the chamber, a simple 1D program wasimplemented in BETA [5]. It does not take into account any interaction with the walls. To improvethe model, a 3D simulation with the interactions was run in the case of absorbers [6]. In bothsimulations, the average value deposited in the dipoles is then less than 10 W/m. Unfortunately,peaks exceed recommended limit: 4.3 mW/cm3 for dipoles. The 3D simulation with open midplane dipoles has not been performed yet.3. Collimation in energyThe injection system relies on injecting a fresh beam in a dispersive area at an energy differentfrom the reference one. The stored beam and the injected one are then horizontally separated.The injection can be cut in four main steps. Firstly, the stored beam is deviated by four kickers.Secondly, the entering beam is injected “off momentum” at δ = 5× 10−3 on its chromatic orbit.Thirdly, the kickers are switched off. The injected beam stays on its chromatic orbit and runs underthe septum blade. Finally, both beams are merged together by a specific RF program using twovariable cavity families, of which one is at double frequency [7].Several injection cycles were simulated, which has identified two loss sources. The first onecomes from the fresh ions which are not captured at the injection. The second one is due to theblow-up in the space (l,δ ) injection after injection. On Figure 2, the survival of a beam injected att = 0 is represented as a function of the number of injection cycles. After around 15-20 injections,most ions are not accepted anymore. When the steady state is reached, the loss amount betweentwo injections is compensated by the injection itself. Around 50 % (Helium) and 20 % (Neon) of3PoS(Nufact08)088Decay ring status / studies ANTOINE CHANCEthe losses which occurred between two cycles are due to the β decay. The mean power to collimatein the ring can then be evaluated to 74 kW for 6He2+ and 248 kW for 18Ne10+. Therefore, a two-stepcollimation system is needed and was designed to collimate in energy at δ = 2.5×10−3( Figure 1).It is located in the long straight section which is not directed toward the detector.Figure 2: Loss amount as a time function. At t = 0, the beam has just been injected. In red, decay lossesand in red, losses due to the collimation in energy for Helium (left) and Neon (right).4. Defects in the magnetic elementsMisalignments and errors on the main field are to take into account in the magnetic elements.One of their consequences is a distortion of the closed orbit. The random rms errors on the magneticfield, the rms transverse misalignment and the rotation around the machine axis are respectivelyassumed to be 0.5× 10−3, 0.5 mm and 1 mrad for the dipoles. The rms error on the gradient inthe quadrupoles is assumed to be 1× 10−3. Their rms transverse misalignment is 0.4 mm. TheBPMs are assumed to be ideal. The order of magnitude of the closed orbit distortion is then a fewcentimeters, which makes the closed orbit correction necessary. 83/85 horizontal/vertical BPMswere inserted in the structure. After correction, the rms resultant of the closed orbit is then lessthan 0.4 mm. The maximum rms value for the horizontal dipole correctors is 0.042 mrad and forthe vertical ones 0.064 mrad. Since the closed orbit is corrected up to three standard deviations, theintegrated field in the dipole correctors must be respectively 0.118 T.m and 0.180 T.m.The natural chromaticity in the decay ring is respectively -1.72 and -2.35 in each plane. With-out correction, the injected beam is not accepted. After correcting the chromaticity with only twosextupole families, we obtain the dynamic aperture of the blue curve on Figure 3. The dynamicaperture is quite large but the coupling resonances are not corrected and the beam does not keep anelliptic shape. After minimizing the sextupolar resonances with six sextupole families, we obtainthe red curve on Figure 3. The dynamic aperture is much larger.However, the obtained dynamic aperture is in the case of ideal dipole magnets. The largeaperture of the dipoles implies unavoidable multipole components. Until now, only systematicmultipole components were considered. The assumed systematic multipole components in thedipoles are b3 = −1.68× 10−4, b5 = 33.02× 10−4, b7 = −50.12× 10−4 and b9 = 29.58× 10−4at the reference radius 60 mm[8]. A direct consequence is a reduction of the dynamic aperture.In order to identify the main multipole effects, the Figure 3 gives the dynamic aperture calculated4PoS(Nufact08)088Decay ring status / studies ANTOINE CHANCEfor each alone multipole component for the same reference structure. The strongest contributioncomes from the fifth and the seventh order multipole components. In order to decrease their effects,different working points were considered and an automatic enlargement program of the dynamicaperture was added in BETA, which enabled to obtain a dynamic aperture of more than 6 σ [9].2 SX6 SX-30 -20 -10 0 10 20 3005101520253035number of ΣxnumberofΣy-10 -5 0 5 100246810number of ΣxnumberofΣyFigure 3: Dynamic aperture for 1000 turns. On left, the dipoles are ideal and in blue, 2 sextupole familieswere used and in red 6 sextupole families. On right, the multipole defects of the fifth order (red), the seventhorder (blue), the ninth order (green) or every multipole component (black) were applied.5. ConclusionThe optics of the decay ring has been given at first and second orders. Some problematics havebeen studied as the decay losses, the injection system, the collimation in energy or the errors in thedipoles. In a near future, the transport of the beam in the collimation section should be simulated.The interaction with the walls and the 6D beam distribution must be taken into account. The effectof the high intensities stored on the beam dynamics (beam loading, space charge, impedances, . . .)is to study too.References[1] M. Benedikt et al., Baseline Design for a Beta-Beam Neutrino Facility,in proceedings of EPAC’04.[2] Parameter and Intensity Values, Version 2, July 2005, EURISOL DS/TASK12/TN-05-03.[3] A. Chancé, Etude et conception de l’anneau de désintégration d’une usine à neutrinos utilisant lesdécroissances beta des noyaux Hélium 6 et Néon 18 produits par un faisceau intense de protonsfrappant diverses cibles, PhD thesis, Université Paris Sud, 2007.[4] A. Chancé et al., Loss Management in the Beta-Beam Decay Ring, in proceedings of EPAC’06.[5] J. Payet, Code BETA, LNS Version.[6] F.W. Jones et al., Simulation of Decays and Secondary Ion Losses in a Betabeam Decay Ring, inproceedings of PAC’07.[7] S. Hancock et al., Stacking Simulations in the Beta-Beam Decay Ring, in proceedings of EPAC’06.[8] C. Vollinger et al., private communication, 2006.[9] A. Chancé et al., Studies of dipole field quality for the beta-beam decay ring, in proceedings ofPAC’07.5

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