application/xmlMultiple volume reflections of high-energy protons in a sequence of bent silicon crystals assisted by volume captureW. ScandaleA. VomieroE. BagliS. BaricordiP. DalpiazM. FioriniV. GuidiA. MazzolariD. VincenziR. MilanGianantonio Della MeaE. VallazzaA.G. AfoninYu.A. ChesnokovV.A. MaisheevI.A. YazyninA.D. KovalenkoA.M. TaratinA.S. DenisovYu.A. GavrikovYu.M. IvanovL.P. LapinaL.G. MalyarenkoV.V. SkorobogatovV.M. SuvorovS.A. VavilovD. BologniniS. HasanM. PrestCrystalChannelingVolume reflectionBeamDeflectionPhysics Letters B 688 (2010) 284-288. doi:10.1016/j.physletb.2010.04.044journalPhysics Letters BCopyright © 2010 Elsevier B.V. All rights reserved.Elsevier B.V.0370-26936884-510 May 20102010-05-10284-28828428810.1016/j.physletb.2010.04.044http://dx.doi.org/10.1016/j.physletb.2010.04.044doi:10.1016/j.physletb.2010.04.044http://vtw.elsevier.com/data/voc/oa/OpenAccessStatus#Full2014-01-01T00:14:32ZSCOAP3 - Sponsoring Consortium for Open Access Publishing in Particle Physicshttp://vtw.elsevier.com/data/voc/oa/SponsorType#FundingBodyhttp://creativecommons.org/licenses/by/3.0/JournalsS300.2PLB26734S0370-2693(10)00507-110.1016/j.physletb.2010.04.044Elsevier B.V.ExperimentsFig. 1(Color online.) Schematic picture of the sequence of two bent crystals with the particle trajectories. 1 – a particle having volume reflections in both crystals near the tangency points with bent planes. 2 – a particle volume captured in the first crystal and then volume reflected in the second one (for a simplicity the trajectory part after VC is shown by red as a prolongation of the trajectory before VC). θo is the crystal orientation angle, θx is the deflection angle of the particle 1, θvr is the VR deflection angle.Fig. 2(Color online.) The deflection angle distribution of the 400 GeV/c proton beam due to VR in the (110) silicon crystal bent with R=3.56 m (simulation). The Gaussian fit parameters θvr, σvr determine the boundary angle θb=θvr+3σvr. The hatched area with θx<θb defines the VR efficiency Pvr.Fig. 3(Color online.) The photograph of the multi strip deflector. All fourteen strips are the parts of one silicon plate. A small anticlastic bend along the width of each strip is produced by a primary bend along their length.Fig. 4(Color online.) The intensity distribution of the 400 GeV/c proton beam crossed the fourteen strip silicon deflector in the deflection angles of particles θx at the different goniometer positions θo. The signs 1, 2 and 14 show the positions of the deflection maxima due to channeling of protons in the corresponding strips. The horizontal arrows with the length α show the corresponding VR acceptance areas of the strips. The vertical arrow show the position with the subsequent reflections of protons in eleven strips.Fig. 5(Color online.) The distribution of protons in the horizontal deflection angles θx for the case with the multiple volume reflection of particles in the eleven strips (for the goniometer position shown by the arrow in Fig. 4). The Gaussian fit determines the deflection angle θmr and its RMS deviation σmr. The angle θb=θmr+3σmr. The hatched area with θx<θb defines the MVR efficiency. The beam part with θx>100 μrad was volume captured and deflected in channeling states.Fig. 6(Color online.) The same as in Fig. 5 obtained by simulation. The hatched area shows the contribution of particles, which had been volume captured at least in one of the strips.Multiple volume reflections of high-energy protons in a sequence of bent silicon crystals assisted by volume captureW.ScandaleaA.VomierobE.BaglicS.BaricordicP.DalpiazcM.FiorinicV.GuidicA.MazzolaricD.VincenzicR.MilandGianantonioDella MeaeE.VallazzafA.G.AfoningYu.A.ChesnokovgV.A.MaisheevgI.A.YazyningA.D.KovalenkohA.M.Taratinh⁎alexander.taratin@cern.chA.S.DenisoviYu.A.GavrikoviYu.M.IvanoviL.P.LapinaiL.G.MalyarenkoiV.V.SkorobogatoviV.M.SuvoroviS.A.VaviloviD.BologninijkS.HasanjkM.PrestjkaCERN, European Organization for Nuclear Research, CH-1211 Geneva 23, SwitzerlandbINFM-CNR, Via Vallotti 9, 25133 Brescia, ItalycINFN Sezione di Ferrara, Dipartimento di Fisica, Università di Ferrara Via Saragat 1, 44100 Ferrara, ItalydINFN Laboratori Nazionali di Legnaro, Viale Università 2, 35020 Legnaro (PD), ItalyeDipartimento di Ingegneria dei Materiali e Tecnologie Industriali, Università di Trento, Via Mesiano 77, 38050 Trento, ItalyfINFN Sezione di Trieste, Via Valerio 2, 34127 Trieste, ItalygInstitute of High Energy Physics, Moscow Region, RU-142284 Protvino, RussiahJoint Institute for Nuclear Research, Joliot-Curie 6, 141980 Dubna, Moscow Region, RussiaiPetersburg Nuclear Physics Institute, 188300 Gatchina, Leningrad Region, RussiajUniversità dell'Insubria, via Valleggio 11, 22100 Como, ItalykINFN Sezione di Milano Bicocca, Piazza della Scienza 3, 20126 Milano, Italy⁎Corresponding author.Editor: W.-D. SchlatterAbstractMultiple volume reflections of the 400 GeV/c proton beam by the sequence of fourteen bent silicon strips has been studied at the CERN SPS. The sequence is close to be parallel that is the spread of the strip orientation angles is much smaller than their bend angle and eleven strips working coherently in the regime of volume reflections deflected the beam by 110 μrad with the efficiency 88%, which is significantly larger than the estimation based on independent reflections. The mechanism giving the efficiency increase has been studied by simulation. It appears that many particles volume captured in one of the strips take part in volume reflections in the subsequent ones. Such a crystal multi reflector can be successfully used as a primary collimator for the beam halo collimation of high-energy accelerators.KeywordsCrystalChannelingVolume reflectionBeamDeflectionWhen a high-energy charged particle enters a crystal with a small angle relative to some crystallographic planes its motion is governed by the crystal potential averaged along the planes [1]. If the angle is smaller than the critical channeling angle θc=(2Uo/pv)1/2, where p and v are the particle momentum and velocity, Uo is the depth of the planar potential well, the particle can be captured into the planar channeling regime oscillating between two neighboring crystal planes. Particle channeling is still possible if the crystal is bent with a radius larger than the critical one, R>Rc[2]. A bent crystal with a length L deflects channeled particles by the bend angle α=L/R.For particles entering a bent crystal with angles θxo>θc the effect of volume reflection (VR) predicted by Taratin and Vorobiev [3] takes place. The reflection of a particle by the planar potential occurs in the crystal volume near the place where the particle momentum direction becomes tangent to the bent planes (tangency area). The particle is deflected due to VR to the side opposite to the crystal bend by the angle, which is determined by the planar potential.Volume reflection of high-energy protons in bent crystals has been investigated in [4–7]. The value of the VR deflection angle increases with increasing the bend radius up to θvr=1.4θc[7]. The deflection efficiency is high and close to 100%. Its value is limited by the concurrent process of volume capture (VC) of particles into the channeling regime due to strong multiple scattering on the atomic nuclei. The VC probability increases as the bend radius is increased because the tangency (VC) area length Lvc where the particle momentum direction is close to be tangent to the bent planes is increased, Lvc≈Rθc[8–10].Let us consider the process of volume reflection of particles in a bent crystal. The crystal orientation angle θo and the deflection angles of particles θx are counted from the direction of the incident beam axis and the initial direction of the particle momentum, respectively (see Fig. 1). The direction to the crystal bend side is defined as a positive one. When the crystal orientation angles |θ(r)|<θc the beam particles can be captured into the channeling regime at the crystal entrance. VR of particles is realized when the orientation angles are in the interval (−α<θo<−θc). The particles volume captured into the channeling regime near the tangency point can follow by the bent channels and be deflected by the angles up to α−|θo|.Fig. 2 shows the deflection angle distribution of 400 GeV/c protons by the (110) silicon crystal with the length L=0.96 mm bent with R=3.56 m, which was obtained by simulation according to the model [11]. The proton beam shifts as a whole due to volume reflection. The Gaussian fit gives the VR deflection angle θvr=(−10.64±0.04) μrad and its RMS deviation σvr=(5.83±0.05) μrad. The distribution tail stretched to the bend side is produced by particles captured into the channeling regime in the tangency area. Some part of volume captured particles quickly leaves the channeling regime due to the same multiple scattering but others pass by the bent channels up to the crystal exit. The VR efficiency Pvr defined as in [7] is the beam part shifting as a whole with the deflection angles θx<θb=θvr+3σvr, where θb is the boundary between the reflected beam and particles volume captured into the channeling states. The value of the volume captured beam part determines the VR inefficiency ε=1−Pvr. For the considered case ε=(1.91±0.08)%, which is in a good agreement with the experiment [7].The deflection angles of particles due to volume reflection are small. A possibility to increase the particle deflection angles using the sequence of a few short bent crystals working in the regime of VR was studied in the recent articles by Scandale et al. [12] and [13]. The sequences of two and five quasi-mosaic crystals were used in these studies, respectively. It was shown that the beam deflection angles increase proportional to the number of the sequence crystals. However, the beam deflection efficiency by the crystal sequence should decrease with increasing the number of reflections because of the beam fractions volume captured into the channeling states in each of the crystals. The beam deflection efficiency due to multiple volume reflections (MVR) in N crystals can be estimated in the first order approximation of independent events as(1)Pmr(N)=PvrN=(1−ε)N≈1−Nε. So, according to (1) the deflection efficiency of 400 GeV/c protons by the sequence of ten silicon crystals considered above should be about 81%.This Letter presents the investigation results for the deflection of the 400 GeV/c proton beam by the sequence of fourteen bent silicon strips working in the regime of volume reflection at the CERN SPS, which show a considerable increase of the deflection efficiency in comparison with the estimate according to (1). Eleven strips working coherently in the VR regime deflected the beam by 110 μrad with the efficiency 88% (because of some spread of the strip orientations not all of them can work coherently). The mechanism giving the efficiency increase has been studied by simulation. It appears that a large part of particles volume captured in one of the sequence crystals, which are considered as lost in (1), take part in volume reflections in the subsequent crystals.The experimental setup was the same described in [7]. Four microstrip silicon detectors, two upstream and two downstream of the crystal, were used to detect the particle trajectories with an angular resolution of 3 μrad, which is limited by the multiple scattering of particles in the detectors and the air.The sequence of crystals was realized from a 72×26.33×0.3 mm3 silicon plate with the largest faces parallel to the (110) planes fabricated according to the technologies [14,15]. The 71×0.97 windows, which were cut in the plate through the same interval, formed the sequence of fourteen strips with L=0.98 mm connected by the common bases. The multi-strip crystal was placed in a vertical position in a specially designed holder [16] (see Fig. 3). The beam entered the crystal through its side face. The preliminary alignment using a laser beam allowed making the largest faces to be parallel to the beam direction with accuracy better than 0.5 mrad. The mechanical bending along the crystal height produced the anticlastic curvature for each strip along the beam direction, which was used for deflection of protons in the horizontal plane due to one of possible mechanisms (channeling, single or multiple volume reflection). See Fig. 2b in the recent article by Scandale et al. [7] for a single strip. The bend angle measured with the interferometer had about the same value for all strips, α=(258–276) μrad.The measured RMS deviation value for the horizontal angular distribution of the incident beam was σx=(10.86±0.01) μrad. A high precision goniometer allowed orienting the multi-strip deflector in the horizontal plane with the accuracy of 2 μrad. The scan of the horizontal orientation angles of the crystal deflector θo was performed. Fig. 4 shows by color the intensity distribution of the beam passed the crystal in the deflection angles of particles θx at the different angular positions of the goniometer θo. Only particles hitting the crystal with horizontal angles counting from the direction of the incident beam axis |θxo|<10 μrad were selected.At the very beginning (right) and at the end (left) of the scan the mean deflection angle equals zero due to scattering of particles in the crystal deflector as in an amorphous substance. In the middle area of the scan the proton deflection maxima visible at θx>0 occur due to channeling in one of the strips. On the other hand, the deflections with θx<0 happen due to single or multiple volume reflections of protons in the sequence of strips. Let us note that only one deflection maximum due to channeling should be seen if all the strips have the same orientation and bend angle. In this case we have a parallel sequence of volume reflectors studied by simulation in [17]. On the other hand, all sequence crystals can be specially inclined to each other by the VR deflection angle. Such an unparallel sequence also considered in [17] is optimal for very high energies of particles allowing to reduce the crystal length. Our crystal deflector has some spread of the strip orientations. Therefore, a few maxima due to channeling are seen in Fig. 4.The analysis of the deflection angle distributions for every step of the scan gave us the information about the strip orientations and the deflection processes realized at the different goniometer positions. The first maximum (marked by 1) with the mean deflection angle θx≈210 μrad on the right side of the scan at the crystal orientation angle θo=θo1 was formed due to channeling of protons in the first strip. These protons after the deflection in the first strip cross the next strips. Therefore, the maximum is broadening due to multiple scattering of protons and shifts in the negative direction due to VR in a few strips. On the left from θo1 the horizontal arrow shows the region of the angular acceptance α for volume reflection of protons in the first strip. The negative deflection by the angle about 10 μrad due to a single VR in the first strip is really seen at the orientation angles θo⩽θo1.The deflection maximum due to channeling of protons in the second strip at the orientation angle θo2 is marked by 2 in Fig. 4. The horizontal arrow on the left from θo2 shows the VR acceptance region for the second strip. The deflection maxima due to channeling of protons in the next twelve strips are positioned at the goniometer positions θon on the left from θo2 with small dividing distances. The corresponding VR acceptance regions for all these strips are overlapped. Therefore, starting from θo2 the number of subsequent reflections of protons in the sequence of strips continuously increases, which is visible through the gradual increase of the MVR deflection angles at θx<0. At the end of the VR acceptance of the first strip the VR region of the thirteenth strip begins. Here the deflection occurs due to twelve subsequent reflections of protons in the strips 2–13. Then on the left from the end of the VR acceptance of the second strip there is a small plateau of θx with eleven subsequent reflections of protons in the strips 3–13. The deflection maximum 14 due to channeling of protons in the fourteenth strip is positioned on the left far from the others. Channeling is observed here for a wider range of the goniometer positions (compare with the maximum 1) because the beam is broadened by multiple scattering in the previous thirteen strips. It is the only one maximum, which gives the whole value of the strip bend angle α, because there is not any strip behind the last one and its VR region is not overlapped with the regions of the previous strips. With the Gaussian fit the maximum value θx(14)=(278.4±2.2) μrad, which is in a good agreement with the value of α obtained with the interferometer. The orientations of the strips 1 and 14 were a little far from the orientations of the other strips because they are at the edges where some deformations in the support elements can arise.Fig. 5 shows the distribution of protons in the horizontal deflection angles θx for the fixed goniometer position marked in Fig. 4 by the vertical arrow where the multiple volume reflection of particles occurs in the eleven strips. The distribution was obtained with a considerably larger statistics than for the scan step. The Gaussian fit gives for the maximum and the RMS values θmr=(−110.65±0.16) μrad and σmr=(19.69±0.15) μrad, respectively. With the boundary angle for the maximum θb=θmr+3σmr the beam deflection efficiency as a whole due to subsequent volume reflections of protons in the eleven strips Pmr(θx<θb)=(88±0.22)%. The efficiency of one side deflection Pmr(θx<0)=(94.25±0.14)%. The distribution in Fig. 2 was obtained by simulation for a single strip with the parameters, which are the same as in our multi-strip deflector. The inefficiency of single reflection obtained in the simulation ε=1.91%. Therefore, according to the first order approximation (1) the efficiency of eleven reflections should be about 79%. So, the MVR efficiency observed in the experiment is considerably larger than the estimate according to (1). The reason of this is explained below.The deflection of protons by the same multi-strip crystal for the conditions of the experiment was studied by simulation based on the model [11]. Fig. 6 shows the distribution of the deflection angles of protons for the same orientation of the multi-strip deflector as in Fig. 5 when the subsequent reflections of protons occur in the eleven strips 3–13. The distribution looks like the experimental one. The maximum and the RMS values of the Gaussian fit are θmr=(−110.73±0.17) μrad and σmr=(20.19±0.14) μrad, respectively. The MVR deflection angle and its RMS spread are in a good agreement with the experiment. The deflection efficiency P(θx<θb)=(91.2±0.18)%, which is also close to the experimental one. The history of every particle can be registered in simulation. The hatched area shows the deflection angle distribution for particles, which had been volume captured at least in one of the strips. So, they also participate in the process of multiple volume reflections in the strip sequence. Their contribution in the deflection efficiency is (11.74±0.2)%.Fig. 1 helps to understand the situation. The beam part marked 1, which was only considered for the estimate (1), makes two subsequent reflections with the mean angle θvr passing two bent crystals and obtains the mean deflection angle 2θvr. A smaller beam part 2 is volume captured in the first crystal but has a tangency point with the bent planes in the second crystal. Here many of the particles 2 are reflected obtaining the mean deflection angle θvr. So, particles volume captured in one of the sequence crystals also participate in the multiple volume reflection but they obtain a smaller deflection.Our experimental results have shown a high efficient deflection of protons due to multiple reflections in the sequence of bent silicon strips. A large increase of the MVR efficiency in comparison with a first order estimate occurs due to the participation of particles volume captured in one of the sequence crystals in the multi reflection process.The experiment is a part of the investigation program on channeling and volume reflection in short bent crystals at the external beams of protons and secondary negative particles of the CERN SPS (the collaborations of H8RD22 and UA9). It was shown that the 400 GeV/c proton beam is deflected by the angle larger than θc=10 μrad with the efficiency close to 100% due to VR in a bent silicon crystal of about 1 mm length. Then a possibility to increase the deflection angle using subsequent reflections of protons in a few bent crystals was shown. The crystal multi reflector described here allows to deflect high-energy protons in the series of more than ten reflections with the efficiency about 90%. Such a crystal reflector used as a primary collimator can improve significantly the beam halo collimation in high-energy accelerators.AcknowledgementsWe are grateful to Professor L. Lanceri (INFN & University of Trieste) who provided the tracking detectors, to V. Carassiti and M. Melchiorri for the design and fabrication of the crystal holders. We acknowledge the partial support by the INFN NTA-HCCC and MIUR 2008 TMS4Z8 projects, the INTAS program, the Russian Foundation for Basic Research Grants 05-02-17622 and 06-02-16912, the RF President Foundation Grant SS-3057-2006-2, the “Fundamental Physics Program of Russian Academy of Sciences” and the grant RFBR-CERN08-02-91020.References[1]J.LindhardK. Dan. Vidensk. Selsk. Mat. Fys. Medd.34196514[2]E.N. Tsyganov, Preprint TM-682, TM-684, Fermilab, Batavia, 1976[3]A.M.TaratinS.A.VorobievPhys. Lett. A1191987425[4]Yu.M.IvanovPhys. Rev. Lett.972006144801[5]Yu.M.IvanovJETP Lett.842006372[6]W.ScandalePhys. Rev. Lett.982007154801[7]W.ScandalePhys. Rev. Lett.1012008234801[8]A.M.TaratinS.A.VorobievNucl. Instrum. Methods B471990247[9]Yu.A.ChesnokovNucl. Instrum. Methods B691992247[10]V.M.BiryukovYu.A.ChesnokovNucl. Instrum. Methods B731993153[11]A.M.TaratinS.A.VorobievSov. Phys. Tech. Phys.301985927[12]W.ScandalePhys. Lett. B6582008109[13]W.ScandalePhys. Rev. Lett.1022009084801[14]S.BaricordiAppl. Phys. Lett.912007061908[15]S.BaricordiJ. Phys. D: Appl. Phys.412008245501[16]V. Carassiti, et al., unpublished[17]A.M.TaratinW.ScandaleNucl. Instrum. Methods B2622007340