Possibilities of application of the effects of multiple volume reflection in one crystal and of the channeling efficiency increase by the crystal cut or buried oxide layer are applied for the first time to the problem of crystal collimation. It is demonstrated that both these effects decrease the nuclear reaction rate in the crystal

scraper and increase the average impact parameter of collisions of deflected protons with an absorber. However the crystal cut is efficient at precise crystal orientation

corresponding to the channeling conditions while the MVROC effect can be applied at relatively rough crystal alignment

Guidi, V.

Mazzolari, A.

Tikhomirov, V. V.

English

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DOI 10.1393/ncc/i2011-10954-2Colloquia: Channeling 2010IL NUOVO CIMENTO Vol. 34 C, N. 4 Luglio-Agosto 2011New approaches to the crystal collimationV. Guidi(1), A. Mazzolari(1) and V. V. Tikhomirov(2)(∗)(1) Dipartimento di Fisica dell’Universita` and INFN, Sezione di Ferrara - Ferrara, Italy(2) Research Institute for Nuclear Problems, Belarus State University - Minsk, Belarus(ricevuto il 22 Dicembre 2010; pubblicato online il 9 Settembre 2011)Summary. — Possibilities of application of the effects of multiple volume reflectionin one crystal and of the channeling efficiency increase by the crystal cut or buriedoxide layer are applied for the first time to the problem of crystal collimation. It isdemonstrated that both these effects decrease the nuclear reaction rate in the crystalscraper and increase the average impact parameter of collisions of deflected protonswith an absorber. However the crystal cut is efficient at precise crystal orientationcorresponding to the channeling conditions while the MVROC effect can be appliedat relatively rough crystal alignment.PACS 29.27.-a – Beams in particle accelerators.PACS 61.85.+p – Channeling phenomena (blocking, energy loss, etc.).PACS 41.75.-i – Charged-particle beams.1. – IntroductionParticle deflection in bent crystals can greatly enhance the collimation efficiency atthe LHC and other modern accelerators. The UA9 experiment dedicated to the studyof crystal collimation of a stored beam has been started at CERN [1]. Though both thechanneling and volume reflection effects are already used in crystal collimators, furtherpossibilities to increase the efficiency of both these effects exist.First, either the microscopic crystal cut [2] or the buried oxide layer [3] can be appliedto increase the probability of proton capture into the channeling regime up to 99%. In thispaper we present the results of the first simulations of the SPS stored beam collimationby the crystal with cut demonstrating a tenfold decrease of the nuclear reaction rate inthe collimator. A technique of fabrication of the necessary micrometer-size cuts is beingdeveloped by the Sensor and Semiconductor Laboratory of Ferrara University.The largest increase in collimation efficiency is reached at the cost of a very precisecrystal-beam alignment. It is commonly accepted that, for safety reasons, high-efficiency(∗) E-mail: vvtikh@mail.ruc© Societa` Italiana di Fisica 399400 V. GUIDI, A. MAZZOLARI and V. V. TIKHOMIROVcrystal collimators which need a precise alignment should be used in parallel with amor-phous ones which do not need it. However the crystal collimators based on the volumereflection (VR) effect also need much less precise alignment than that using channeling.The recently predicted effect of multiple VR from different planes of one crystal [4],observed at the SPS [5] and studied in further detail in [6], allows to increase the VRangle about five times. Therefore the crystal collimators using the effect [4-6] are alsogood candidates for the use in parallel with channeling-based collimators for safety andreliability reasons. The results of first simulations of collimators using the multiple VRin one crystal are also discussed in this paper for the first time.2. – Increase of the probability of particle capture into the channeling regimeThe channeling phenomenon in bent crystals has been long studied to steer charged-particle beams. The fraction of particles being deflected by the crystal over the totalflux of the particles traversing the latter is restricted by an incomplete beam captureinto the regime of stable channeling motion occurring at the entry face of the crystal.The maximal observed value for the probability of positively charged particle capture isclose to 85% [7] being limited by the strong nuclear and electron scattering in the regions|x| < xc, where xc = 0.15 ∼ 0.20 A˚ is the critical approach distance measured from thecrystal plane position.The channeling phenomenon is effectively treated in terms of the averaged potentialconcept. The averaged planar potential V (x) (potential energy, rigorously speaking) isobtained by an atomic potential averaging along the plane (and also over the thermalvibrations) and depends only on the transverse coordinate x measured along the normalto the planes. The V (x) translational invariance ensures the conservation of the trans-verse energy ε⊥ = εv2x/2 + V (x), where ε and vx = vx(x) are the total particle energyand velocity (measured in c units) at point x, respectively. The planar channeling is alimited transverse motion which occurs if ε⊥ ≤ Vmax, where Vmax is the maximal valueof the averaged potential.The ε⊥ conservation, however, is violated by the difference of the real intracrystalpotential from the averaged one. This difference is most pronounced in the regions ofmaximal nuclear and electron number densities like the region |x| < xc near the planesituated at x = 0. If a particle has sufficiently large transverse energy ε⊥ ≥ 0.5Vmax itregularly reaches such a region and experiences a strong incoherent scattering on bothnuclei and electrons causing a fast ε⊥ increase leading to the particle dechanneling.However the particles with ε⊥ ≤ 0.5Vmax, unable to reach the regions with high nuclearand electron number densities, experience a continuous stable channeling motion.Unfortunately, the initial transverse energy ε⊥ = εv2x0/2 + V (x0), which a particleacquires entering the crystal, cannot be considerably less than Vmax in the incidenceregions |x0| ≤ xc even if the initial transverse velocity vx0 is minimal. Such particlesinevitably dechannel leading to the limitation of the probability of particle capture intothe regime of stable channeling motion by the mentioned value of 85%. However a fastε⊥ reduction caused by the special type violation of the planar potential translationalinvariance could improve the situation.A corresponding method of increase of the particle capture probability into the regimeof stable channeling motion was recently suggested [2]. It consists in placing a very thin“focusing” crystalline plate parallel to the entry face of the crystal that channels theparticles. The plate must have the same inter-planar periodicity as the crystal and beperfectly aligned with it. Intuitively, such a combination may be realized by performingNEW APPROACHES TO THE CRYSTAL COLLIMATION 401-101230 20 40 60 80 100-10123  400 GeV, z1=4μm, z2=16μm Oz, μmcutx, AOx, AFig. 1. – The facilitation of 400GeV proton capture into the channeling regime by the cut, situ-ated between 4 and 16μm, or by a buried 400 nm amorphous layer applied under the conditionsof an oblique incidence at α  0.033 rad.a cut parallel to the entry surface of a crystal, i.e., by removing the atoms betweenz = z1 and z = z2. Thereby, a common crystalline structure is realized at 0 ≤ z ≤ z1and z ≥ z2. The dynamics of the particles entering the crystal near the maxima of theplanar potential is such that a decrease in the transverse kinetic energy ε⊥ occurs.The mechanism of transverse energy compaction can be explained as follows [2]. Let usconsider a “ready to dechannel” particle with V (x0)  Vmax and |vx0| < 0.25√2Vmax/ε.As the particle crosses the thin crystalline plate [0, z1], it experiences a force directedtowards a V (x) minimum. However, the interaction time in this region is so short thatthe particle does not reach the potential minimum and acquires only a transverse velocityv(x1) which satisfies the condition |v(x0)| < v(x1) < 0.5√2Vmax/ε. As the particle exitsthe plate at z = z1, both the potential energy V (x) and local crystal field vanish andthe transverse velocity component v(x2) = v(x1) remains unchanged until the crystalbulk is reached at z = z2. The width z2 − z1 should be chosen in such a way thatthe particle re-enters the crystal at z = z2 close to the potential minimum, acquiring apotential energy V (x2) < 0.25Vmax. Since the particle approaches the re-entrance point(x2, z2) with the reduced kinetic energy 0.5εv2(x2) < 0.25Vmax, the total transverseenergy ε⊥(z2) = 0.5εv2(x2) + V (x2) decreases at least down to 0.5Vmax ensuring, thus,a further stable channeling motion at z > z2.The described proton motion within 0 ≤ z ≤ z2 resembles that on a quarter of thechanneling oscillation length λ. The method assumes the width of the empty space z2−z1to range between z2/2 and 2z2/3 (depending considerably on the inevitable incidentbeam angular divergence), and the plate thickness z1 between z2/3 and z2/2, namelyz2− z1 ∈ [λ/8, λ/6] and z1 ∈ [λ/12, λ/8], which correspond to tens of micrometers at theLHC energy of ε = 7TeV and to z1 = 4μm and z2 = 16μm at the SPS energy—see fig. 1.At such high energy the fabrication of a crystal with an empty space between z1 and z2can be accomplished through photolithography. However the width of the empty spacescales with λ nearly proportionally to√ε and at lower energies the photolithographybecomes inefficient. To circumvent this problem, the placing of a thin amorphous layerbetween z1 and z2 to play the same role as the empty space was suggested [6]. Thelayer can be reliably fabricated through the Separation by IMplanted OXygen (SIMOX)402 V. GUIDI, A. MAZZOLARI and V. V. TIKHOMIROVtechnique [8]. The influence of the particle scattering in the buried amorphous Si layeron its focusing effect becomes negligible starting from hundreds of MeV [6]. Note thatan oblique particle incidence at an angle α < π/2 on the entrance crystal plane and theburied amorphous Si layer, parallel to the latter, allows to effectively increase the plateand layer thicknesses proportionally to cscα, making it possible to use the most readilyavailable SIMOX wafers with z2 − z1  400 nm in a wider interval of particle energies,including that of the SPS at α  0.033 rad—see fig. 1. Another, even more importantadvantage of an oblique particle incidence, allowing to effectively increase the thicknessesof the thin plate and either the cut or buried amorphous layer, is the possibility to usethe same crystal in a wide energy region, including the whole interval 450GeV–7TeV ofproton acceleration at the LHC.The main idea of this paper is to apply the possibility of increase of the probabilityof capture into the channeling regime by the cut or buried amorphous layer as well as bythe effect of multiple volume reflection from planes of one bent crystal (MVROC) to theproblem of beam collimation. Remind that VR occurs as a particle trajectory becomestangential to a bent crystalline plane [9]. Since a crystalline axis is parallel to the lineof intersection of various crystal planes, a reflection from most of them becomes possibleas a proton moves at a small angle with respect to such an axis [4]. This MVROC effectincreases the total particle deflection angle about five times [5,6] and is described in moredetail in these proceedings [10].3. – Performance of the new types of crystal collimatorsModern accelerators use the two-stage collimator scheme, the primary scraper ofwhich deflects the halo particles to an absorber. If a bent crystal is used as the scraper,both the channeling and VR effects can be applied to facilitate the particle deflectionto the absorber. Namely the nuclear reaction rate in the scraper decreases while theaverage particle impact parameter to the absorber increases. The first crystal collimationexperiment [1] has recently demonstrated the former effect.To widen the benefits of the crystal scraping we suggest to apply both the crystal cutand MVROC. To make a comparison with the “normal” crystal scraper we undertookthe simulation for both the layout of the experiment [1] and 1mm crystal length alongthe beam. The crystal bending radius R was chosen equal to 6.67m both for the normalcrystal and the crystal with cut and to 2m for the crystal with the MVROC orientation.The channeling plane (110) was chosen to be normal to the bending plane of both thenormal crystal and crystal with cut.To choose the optimal orientation of the MVROC scraper we proceed from the factthat the optimal conditions for the 120GeV proton MVROC in a crystal with l = 1mmand R = 2m arise at the incidence angles ΘX0  275μrad and ΘY 0  100μrad withrespect to the 〈111〉 axis. To make the MVROC efficient in all the experimental VRangular interval we chose the mentioned optimal MVROC orientation to correspond tothe normal crystal scraper rotation angle θcr = −70μrad. Thus, the angle of MVROCscraper rotation in the bending plane, measured from the direction of its vertical (11¯0)plane at the entrance surface, will be equal to θcr = −205μrad. The positive rotationdirection coincides with that of crystal bending in all the cases.The simulated dependences of the fraction of particles lost in inelastic reactions in thecrystal scraper versus the crystal rotation angle are shown in figs. 2 and 3 for the normalcrystal, crystal with cut and crystal in MVROC orientation. The normal crystal curvedemonstrates the same behavior as that in ref. [1] with the dip corresponding to the mostNEW APPROACHES TO THE CRYSTAL COLLIMATION 403-200 -100 0 1000123cut  Nr/N, %θcr normal crystal,    cut,   MVROC MVROCFig. 2. – Inelastic loss fraction as a function of the angle θcr of crystal rotation in the horizontalplane in a normal crystal with R = 6.67m (short dash), a crystal with the cut between 2 and8μm and R = 6.67m (solid) and a multiply reflecting crystal with bending radius R = 2mand the 〈111〉 axis forming the angles −ΘX0 = θcr − 205μrad, −ΘY 0 = −100μrad with thechanneling beam direction (long dash).efficient deflection of channeled protons, the plateau in the region−180 < θcr < −20μrad,corresponding to the VR manifestation, and that at the level of 2.5% correspondingto practically amorphous-type scattering. The “crystal with cut curve” demonstratesan order of magnitude deeper “channeling dip” directly explained by the increase ofprobability of proton capture into the channeling regime by the cut. The “MVROCcurve”, on the opposite, is distinguished by its stable behavior near the inelastic losslevel lying in between the channeling dip and the VR plateau of the “normal crystal”curve. Such a behavior reflects the high deflection efficiency of the MVROC effect in awide angular region [6].The cut, in fact, facilitates the collimation efficiency in quite a complementary wayto the MVROC effects. Namely, the former needs very precise crystal fabrication andalignment and allows to improve the normal crystal collimator functioning only near theperfect channeling alignment. The MVROC effect, on the contrary, allows to improvethe collimation efficiency in the angular interval comparable in width with that of theVR effect manifestation. Such a complementarity makes reasonable a simultaneous useof the collimators based on the cut and MVROC effects.-30 -15 0 15 3010-310-210-1100    Nr/N, %θcrFig. 3. – The same as fig. 2 for a narrow angular interval near the channeling crystal orientation.404 V. GUIDI, A. MAZZOLARI and V. V. TIKHOMIROV0 5 10 15110100100010000  normal crystal cut   NpassNFig. 4. – Distribution of the number of crystal crossings before hitting the absorber in normal Sicrystal (dashed) and crystal with cut between 2 and 8μm (solid), R = 6.67m, l = 1mm. Thecut decreases the crystal crossing number.Let us dwell on a detailed comparison of the different types of crystal collimators.Figures 4 and 5 allow to compare a normal crystal and “the cut” scrapers in the case ofperfect channeling alignment. Figure 4 presents the proton distribution in a numberof crystal scraper crossings before hitting the absorber. One can see that the “cutcollimator” deflects about 99% of the protons to the absorber at the first crossing. Thenumbers of protons which experience more crossings also decreases fast with the numberof the latter. Figure 5 presents the distribution of the proton impact parameters with theabsorber demonstrating a great decrease in the number of protons hitting the absorberwith small impact parameters by the “cut scraper”.Since the “MVROC collimator” is applicable in a wide angular region it will benatural to compare its performance with that of the normal crystal collimator at a roughalignment for the representation of which we chose the normal crystal orientation atθcr = −70μrad, corresponding to the proton incidence at the horizontal angle ΘX0 =70 + 205 = 275μrad to the 〈111〉 axis of the “MVROC scraper”. Figure 6 demonstrateshow the MVROC scraper decreases the number of scraper crossings, while fig. 7 illustratesthe decrease of the number of protons hitting the absorber near its edge.0.0 0.2 0.4 0.6 0.8 1.00.1110    x, cm(1/N)dN/dx, cm-1Fig. 5. – Distribution of the impact parameter of an absorber hit under the same conditions asfig. 4. The cut diminishes the number of protons hitting the absorber near its edge.NEW APPROACHES TO THE CRYSTAL COLLIMATION 4050 5 10 15 20 2502000400060008000    NNpass normal crystal MVROC Fig. 6. – Distribution of the number of crystal crossings before hitting the absorber in usualSi crystal oriented with θcr = −70μrad (thin dashed), and in the multiply reflecting crystalwith bending radius R = 2m and the 〈111〉 axis forming the angles ΘX0 = −275μrad, ΘY 0 =−100μrad with the channeling beam direction. MVROC process decreases the crystal crossingnumber.0.0 0.2 0.4 0.6 0.8 1.0036912    (1/N)dN/dx, cm-1x, cmFig. 7. – Distribution of the impact parameter of the absorber hit under the same conditions offig. 6. MVROC process considerably increases the average impact parameter.4. – ConclusionsIn summary we have demonstrated that the increase of both the probability of pro-ton capture into the channeling regime by either crystal cut or buried amorphous SiO2layer and the proton deflection angle by the multiple volume reflection in one crystal canimprove the efficiency of the primary crystal scraper of the two-stage collimator system.The crystal cut should be used at precise crystal orientation corresponding to the chan-neling condition while the MVROC effect, on the contrary, at relatively rough crystalalignment. Both the crystal cut and MVROC scrapers can drastically reduce both thenumber of their proton crossings and that of protons which hit the absorber near itsedge.REFERENCES[1] Scandale W. et al., Phys. Lett. B, 692 (2010) 78; doi:10.1016/j.physletb.2010.07.023.[2] Tikhomirov V. V., JINST, 2 (2007) P08006.[3] Guidi V., Mazzolari A. and Tikhomirov V. V., J. Phys. D, 42 (2009) 165301;doi:10.1088/0022-3727/42/16/165301.406 V. GUIDI, A. MAZZOLARI and V. V. TIKHOMIROV[4] Tikhomirov V. V., Phys. Lett. B, 655 (2007) 217.[5] Scandale W. et al., Phys. Lett. B, 682 (2009) 274.[6] Guidi V., Mazzolari A. and Tikhomirov V. V., J. Appl. Phys., 107 (2010) 114908;DOI: 10.1063/1.3407526.[7] Scandale W. et al., Phys. Lett. B, 680 (2009) 129.[8] Bruel M., Margail J., Jaussaud C., Auberton-Herve´ A. J. and Stoemenos J.,Microelectron. Eng., 8 (1988) 149.[9] Taratin A. M. and Vorobiev S. A., Phys. Lett. A, 119 (1987) 425.[10] Guidi V., Mazzolari A. and Tikhomirov V. V., Electromagnetic RadiationAccompanying Multiple Volume Reflection in One Crystal, these proceedings.

New approaches to the crystal collimation

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New approaches to the crystal collimation

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