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Probability of inelastic nuclear interactions of high-energy protons in a bent crystal
Nuclear Instruments and Methods in Physics Research B 268 (2010) 2655–2659
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Probability of inelastic nuclear interactions of high-energy protons in a bent crystal W. Scandale a, R. Losito a, M. Silari a, E. Bagli b, S. Baricordi b, P. Dalpiaz b, M. Fiorini b, V. Guidi b, A. Mazzolari b, D. Vincenzi b, R. Milan c, Gianantonio Della Mea d, E. Vallazza e, A.G. Afonin f, Yu.A. Chesnokov f, V.A. Maisheev f, I.A. Yazynin f, S.V. Afanasiev g, A.D. Kovalenko g, A.M. Taratin g,*, V.V. Uzhinsky g, A.S. Denisov h, Yu.A. Gavrikov h, Yu.M. Ivanov h, L.P. Lapina h, L.G. Malyarenko h, V.V. Skorobogatov h, V.M. Suvorov h, S.A. Vavilov h, D. Bolognini i,j, S. Hasan i,j, M. Prest i,j a
CERN, European Organization for Nuclear Research, CH-1211 Geneva 23, Switzerland INFN Sezione di Ferrara, Dipartimento di Fisica, Universita‘ di Ferrara Via Saragat 1, 44100 Ferrara, Italy c INFN Laboratori Nazionali di Legnaro, Viale Universita‘ 2, 35020 Legnaro (PD), Italy d Dipartimento di Ingegneria dei Materiali e Tecnologie Industriali, Universita‘ di Trento, Via Mesiano 77, 38050 Trento, Italy e INFN Sezione di Trieste, Via Valerio 2, 34127 Trieste, Italy f Institute of High Energy Physics, Moscow Region, RU-142284 Protvino, Russia g Joint Institute for Nuclear Research, Joliot-Curie 6, 141980 Dubna, Moscow Region, Russia h Petersburg Nuclear Physics Institute, 188300 Gatchina, Leningrad Region, Russia i Universita‘ dell’Insubria, via Valleggio 11, 22100 Como, Italy j INFN Sezione di Milano Bicocca, Piazza della Scienza 3, 20126 Milano, Italy b
a r t i c l e
i n f o
Article history: Received 30 June 2010 Available online 11 July 2010 Keywords: Crystal Channeling Volume reflection Nuclear interactions
a b s t r a c t Probability of inelastic nuclear interactions in a short bent silicon crystal for its orientations optimal for channeling and volume reflection was investigated using 400 GeV/c protons of the CERN SPS. The contribution of nuclear interactions from channeled protons was observed to be about 3–4% of the probability for the amorphous orientation. For the crystal orientation optimal for volume reflection the nuclear interaction probability of protons was a few percents larger than in the amorphous case. It was shown that in the limiting case of a quasi parallel beam realizing for the collider beam halo the inelastic nuclear losses should decrease by more than five times, which is an additional advantage of a crystal as a primary collimator for the LHC collimation system. Ó 2010 Elsevier B.V. All rights reserved.
When high-energy charged particles enter a crystal with small angles relative to the crystal planes their transverse motion is governed by the crystal potential averaged along the planes U(x). If the particle angles are smaller than the critical channeling angle hc = (2Uo/pv)1/2, where p, v are the particle momentum and velocity and Uo the depth of the planar potential well, they can be captured into the channeling regime [1]. Channeled positive particles move through a crystal oscillating between two neighboring planes. Therefore, all the processes requiring close collisions with the crystal atoms are strongly suppressed in a crystal well aligned with the beam. Bent crystals can deflect channeled particles by the bend angle a when their bend radius R > Rc, where Rc is the critical bend radius [2]. Particles can be also deflected due to volume reflection [3] in the tangency area of their momentum with the bent crystal planes. Bent crystals are successfully used in circular accelerators for beam extraction and for splitting of the extracted beam [4]. * Corresponding author. Tel.: +7 496 21 65 612; fax: +7 496 21 65 180. E-mail address: [email protected] (A.M. Taratin). 0168-583X/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2010.07.002
There are plans to use the crystal deflectors for the beam halo collimation of the LHC [5]. A bent crystal used as a primary collimator will deflect particles and direct them deeply onto the absorber. This should possibly increase the collimation efficiency. Experiments on beam halo collimation with a crystal primary collimator have been already performed at RHIC [6] and Tevatron [7]. The crystal collimator orientation was performed using the indications of the beam loss monitors (BLM), which registered secondary particles generated by inelastic nuclear interactions of the beam halo particles in the crystal. A large decrease of the BLM count was registered at the crystal orientation corresponding to the maximum capture of particles into the channeling regime. A decrease of the BLM rate by a factor of five was observed in the UA9 runs, the experiment on the crystal collimation ongoing at the CERN SPS [8]. It should be noted that in circular accelerators this ratio is determined both by the decrease of the nuclear interaction rate in the aligned crystal and by the increase of the number of particle passages through the crystal for its amorphous orientation. A few experiments on the study of nuclear interactions of highenergy protons and heavy nuclei in the aligned crystals have been
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also performed at the external accelerator beams [9–12]. Nuclear interactions of high-energy protons in germanium crystals aligned by the h1 1 0i axis with the beam had been studied in [9,10]. A considerable decrease of the nuclear interaction probability was registered in the aligned crystals. Recently, the reduced interaction probability has been observed for 33 TeV/c Pb nuclei in a bent silicon crystal aligned by the (1 1 0) planes with the beam [11]. A strong suppression by a factor of more than 20 has been observed in [12] for nuclear-charge changing interactions of 18 TeV/c In ions channeled through a bent Si crystal. In the present work, the probability of inelastic nuclear interactions in the silicon crystal with the length 1.94 mm bent along the (1 1 0) planes has been studied with 400 GeV/c protons at the H8 beam line of the CERN SPS. The probabilities for the crystal orientations optimal for channeling and volume reflection were measured. The experiment allowed to observe the contribution of channeled protons, which was 3–4% of the probability value for the amorphous orientation of the crystal. The limit of the inelastic interaction reduction for a quasi parallel beam has been determined. The probability of inelastic nuclear interactions of protons in a short crystal at its amorphous orientation is
Pin rin N am L:
ð1Þ
The cross-section of inelastic nuclear interactions of 400 GeV/c protons with silicon nuclei in the Glauber approach calculated according to [13] rin = 0.506 b, the atomic density in a silicon crystal Nam = 0.05 1024 cm3. Therefore, for the crystal with length L = 1.94 mm the probability Pin = 0.49%. The atomic density changes along the particle trajectory in the aligned crystal. Thus the nuclear interaction probability changes as well. The atomic density N(x) is quickly reduced with the distance x from the planes according to a Gaussian distribution
NðxÞ ¼ Nam Pn ðxÞ;
dp x2 Pn ðxÞ ¼ qffiffiffiffiffiffiffiffiffiffiffi exp 2 ; 2u1 2pu21
ð2Þ
Atomic density (N/Nam)
there u1 is the amplitude of thermal vibrations of the crystal atoms, u1 = 0.075 Å for a silicon crystal at a room temperature, dp is the planar channel width. The density at the plane positions is 10 times larger than the average density Nam. The ‘‘nuclear corridor” width, where the atomic nuclei of the plane are concentrated, is much smaller than the channel width, for the (1 1 0) Si dp = 1.92 Å and 6u1/dp = 0.23. Fig. 1 shows the dependence of the atomic density averaged along the particle trajectory in the (1 1 0) silicon crystal on the particle transverse energy Ex. The maximum density at Ex = Uo is three times larger than the average one. For stable chan-
3
2
neled states with small transverse energies the atomic density along the trajectories is very small or equals zero. For above-barrier particles with Ex > Uo the atomic density averaged along the trajectory approaches the average one with increasing Ex. For volume reflection of particles in a bent crystal the atomic density averaged along the particle trajectory in a tangency area is significantly larger than Nam. However, the density approaches to the average one when the distance of particles from the tangency point is increased. As a result, the averaged atomic density is only a few percents larger than Nam for a whole crystal length of 1.94 mm. Our experimental setup was mainly the same as in [14], see Fig. 2. Four microstrip silicon detectors, two upstream and two downstream of the crystal, were used to detect the particle trajectories with an angular resolution of about 3 lrad. Two large scintillation detectors with transverse dimensions 100 100 mm2 were placed 60 cm downstream the crystal on both sides from the primary proton beam to register secondary particles generated in inelastic nuclear interactions of protons in the crystal. The distance between the scintillation detectors was 10 mm. So, the angle of the inner edge of both scintillation detectors from the crystal location was hed = 8.33 mrad. It is sufficient to exclude the contributions of primary protons scattered due to elastic nuclear interactions, because hel hed. A 70 1.94 0.5 mm3 silicon strip crystal with the largest faces parallel to the (1 1 0) crystallographic planes fabricated according to the methodology [15,16] was bent along its length and placed vertically, so that the anticlastic bending induced along the crystal width was used to deflect particles in the horizontal plane (see Fig. 2b in [14]). A high precision goniometer was used to orient the (1 1 0) crystal planes parallel to the beam direction. The optimal crystal orientation, which gives the maximum of the deflected beam fraction, was found. The RMS deviation value measured for the horizontal angular distribution of the incident beam was rx = (13.368 ± 0.003) lrad. It is larger than the critical channeling angle, hc 10 lrad. However, the beam part deflected due to channeling in the crystal can be considerably increased by decreasing the angular size of the incident beam when only particles with the incident angles |hxo| < hcut are considered. Fig. 3 shows the deflection angle distribution of protons observed with the cutting angle hcut = 1.5 lrad. The Gaussian fit in Fig. 3a gives the deflection angle value hxm = (189 ± 0.02) lrad, which equals the crystal bend angle a. The deflected beam fraction Pd = (72.5 ± 0.117)% is hatched. Nuclear interactions occur mainly with undeflected particles either not captured into the channeling regime at the crystal entrance or dechanneled during the crystal passage. Fig. 4 shows the dependence of the undeflected beam part Pnd = 1 Pd on the cutting angle of the incident beam. It should be mentioned that some instability of the angular position of the goniometer (as large as a few microradians) observed over a long period of measurements and the crystal torsion (different crystal orientations along its height) decreased the deflection efficiency. The analysis of the amplitude spectra of the scintillation detectors registering secondary particles from the crystal allowed to
1
0
0
25
50
75
100
Transverse energy (eV) Fig. 1. The dependence of the atomic density averaged along the particle trajectory in the (1 1 0) silicon crystal on the particle transverse energy.
Fig. 2. Experimental layout at the external beam H8 of the CERN SPS. Here Si1–Si4 are the silicon microstrip detectors, g is the goniometer with a bent crystal. S1 and S2 are the scintillation detectors.
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F in ¼ N12 ðA > Ab Þ=N o ;
40
20
0 -100
0
100
200
Angle (µrad)
10
4
10
3
10
2
where N12(A > Ab) is the number of the coincidence events in S1 and S2 with amplitudes A > Ab, No is the number of particles with |hxo| < hcut, which hit the crystal. Let us note that the registered number of the coincidence events is not equal to the number of all inelastic interactions of protons in the crystal. The part of all events generated charged particles, which hit both the detectors, the coincidence frequency F12 = 0.655 ± 0.005, was determined by simulation using the FRITIOF model [17]. Fig. 5 shows the measured dependencies of the inelastic nuclear interaction frequency of protons on the cutting angle value hcut of the incident beam for the amorphous orientation (1) and for the aligned crystal (2), as well as without the crystal in the beam that is the experimental background (3). The interaction frequencies without the crystal and with the crystal in its amorphous orientation are practically constant. Whereas the frequency registered in the aligned crystal is considerably smaller than for its amorphous orientation and it decreases with decreasing hcut due to the increase of the fraction of well channeled protons, which do not experience close collisions with the crystal atoms. The probability of inelastic nuclear interactions of protons in the crystal was calculated by subtraction of the experimental background Fin(BG) and taking into account the coincidence frequency F12 estimated by the simulation above
Pin ¼ ðF in F in ðBGÞÞ=F 12 :
10
-100
0
100
200
Angle (µrad) Fig. 3. The deflection angle distributions of 400 GeV/c protons by the silicon crystal bent along the (1 1 0) planes. Only particles with the incident angles |hxo| < hcut = 1.5 lrad were considered. (a) In a linear scale, (b) in a logarithmic scale. Here the boundaries of the dechanneling area are marked by the solid circles.
0.6
0.5
0.4
ð4Þ
Fig. 6 shows the dependences of the inelastic nuclear interaction probability of protons in the crystal on the value of hcut in the cases of the amorphous orientation (1) and volume reflection (2) as well as in the aligned crystal (3). The measured probability value for the amorphous orientation is P am in = (0.505 ± 0.005)%, which is in a good agreement with the theoretical estimation made above using (1). For the symmetric case of volume reflection (2) considered in the experiment when the tangency area of the particle momentums with the bent planes is in the middle of the crystal length and practically all particles pass the whole crystal in abovebarrier states the probability is 3–4% larger than for the amorphous orientation. In the aligned crystal for the smallest angular width of the incident beam the probability is more than 3.5 times smaller than Pam in . The inelastic nuclear interaction probability of protons in the aligned crystal has been also studied by simulation using the model [18]. The calculated dependence is shown by the curve 4. There is a significant discrepancy with the experiment for small values of
0.3
0.6 0.2
0
10
20
Cutting angle (µrad) Fig. 4. The dependence of the undeflected part of protons on the cutting angle hcut of the incident beam.
determine the amplitude discrimination thresholds Ab, which cut the intrinsic detector background. Secondary particles were registered also in the case when the crystal was removed from the beam. They were generated by inelastic nuclear interactions of protons upstream the crystal and form the experimental background. The coincidence of the events with the amplitude A > Ab registered by the left and right scintillation detectors were used to subtract efficiently the experimental background including delectrons. The frequency of the inelastic nuclear interactions of protons in the crystal was defined as
Interaction frequency (%)
Counts
(b) 10 5
Beam fraction Pnd (%)
ð3Þ
60
3
Counts (10 )
(a)
0.4
0.2
0
0
10
20
Cutting angle (µrad) Fig. 5. The dependencies of the inelastic nuclear interaction frequency of protons on the cutting angle value of the incident beam for the amorphous orientation (1), the aligned crystal (2) and for the case without the crystal in the beam – the experimental background (3).
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Interaction probability ( %)
0.6
0.4
0.2
0
0
10
20
Cutting angle (µrad) Fig. 6. The dependencies of the inelastic nuclear interaction probability of protons in the crystal on the value of the cutting angle hcut of the incident beam for the amorphous orientation (1), for the case of volume reflection (2) and in the aligned crystal (3). The dependence (4) was obtained by simulation for the aligned crystal.
hcut because the goniometer instability and the crystal torsion were not taken into account in the simulation. However, for large values of hcut when the angular size of the incident beam is larger than the angular parameters of the goniometer instability and the crystal torsion the agreement with the experiment is good. The simulation allows to register the state of particles before their inelastic interactions with the crystal nuclei. According to the simulation the contribution value of inelastic interactions from channeled protons is in the interval (0.015–0.02)%, that is (3–4)% of the probability for the amorphous orientation. Let us remember that only channeled protons with large oscillation amplitudes, which approach closely to the channel walls (r < rc = 2.5u1), can have inelastic interactions with the crystal nuclei. Fig. 7 shows the calculated particle distributions in the transverse energy at the crystal entrance for the different values of hcut. Channeled particles with Ex > Exc = U(rc), whose value is shown by the arrow, enter the nuclear corridor of the channel walls. The beam fraction P(Ex > Exc) increases a little with increasing hcut and is maximum at hcut = hc. Then it decreases again. The maximum difference of the fraction values for a quasi parallel beam and the beam with hcut = hc is about 30%. This explains a little difference observed in the simulation for the inelastic interaction numbers of channeled protons with the different angular sizes hcut of the incident beam.
Let us try to determine a possible contribution of channeled protons to the inelastic interactions registered in the aligned crystal. Particles, which passed the whole crystal in channeling or above-barrier states, form the maxima at hx = a or hx = hvr, respectively, where hvr is the deflection angle due to volume reflection (see Fig. 3a). Dechanneled particles between two maxima were in channeling states only some part of the crystal length, which is determined by their deflection angle – hx/a. These particles are better seen with using a logarithmic scale (Fig. 3b). Here the Gaussian fit for the left maximum allows to separate volume reflected and dechanneled particles. The total number of particles passed through the whole crystal in above-barrier states with taking into account the contributions of dechanneled particles can be determined as
Nnch ¼
i1 X
ni þ
i2 X
i¼1
i1
ð5Þ
i1
0.6
Probability Pin/Pinam
60 3
N (10 )
i2 X ðni yi Þð1 hxi =aÞ;
where ni is the particle number of the ith histogram bin, yi is the Gaussian fit value in the middle of the ith bin hxi. The boundaries (i1,i2) of the dechanneling area are shown by the solid circles in Fig. 3b. Two first members of (5) determine the beam part, which was not captured into the channeling regime at the crystal entrance and passed the whole crystal in above-barrier states. The third member determines the contribution of dechanneled particles. Fig. 8 shows the inelastic interaction probability of protons measured in the aligned crystal as a function of the beam fraction passed the crystal in above-barrier states, Pnch = Nnch/No (solid circles). The different circles correspond to the different angular cuts of the incident beam hcut. The probability is shown as a ratio to its in ¼ Pin =Pam . value for the amorphous orientation P in in ¼ Pnch , is a hypoThe dependence shown by a dashed line, P thetic one when the probability is the same as in the amorphous case for all above-barrier protons and the contribution from channeled protons is absent. The probability values measured in the experiment are larger than the hypothetic ones. The difference is about 8% for the large angular sizes hcut of the incident beam. A half of this difference, about 4%, is due to the fact that the interaction probability for above-barrier protons is larger than for the amorphous orientation (see 2 in Fig. 6). The remaining difference, about 4% for the large values of hcut, is due to the contribution of channeled protons, which is in a good agreement with the value predicted by the simulation. The difference decreases for the small values of hcut because of the decrease of both the contributions. The contribution from channeled protons decreases because their
80
40
20
0
yi þ
0.5
0.4
0.3 0.3
0
5
10
15
Ex (eV) Fig. 7. Particle distributions in the transverse energy at the crystal entrance for the different angular sizes hcut of the incident beam: 3 lrad (1), 6 lrad (2), 12 lrad (3), and 20 lrad (4).
0.4
0.5
Beam part Pnch Fig. 8. The dependence of the inelastic nuclear interaction probability in the aligned crystal on the non-channeled part of the beam. The probability as a ratio to the value for the amorphous orientation is presented, Pin/P am in . The dashed line is a hypothetic linear dependence of Pin/P am in = Pnch.
W. Scandale et al. / Nuclear Instruments and Methods in Physics Research B 268 (2010) 2655–2659
part with large oscillation amplitudes decreases as it was shown in Fig. 7. The contribution from above-barrier particles decreases because they more quickly leave the tangency area where the atomic density averaged along their trajectories is higher than Nam. The measurements have shown that the probability of inelastic nuclear interactions of high-energy protons in the crystal depends strongly on its orientation. For the orientation optimal for volume reflection the probability is a few percents larger than for the amorphous one. The probability is significantly smaller in the aligned crystal because well channeled protons move through the crystal far from the crystallographic planes where the atomic nuclei are concentrated. Our experimental data show that the contribution of inelastic interactions from channeled protons is about 3–4% of the probability for the amorphous orientation. In the limiting case with a quasi parallel beam, which should be realized in the collider beam halo, the deflection efficiency in a single passage can approach 85%. Therefore, the probability of inelastic nuclear interactions of the beam halo protons in a perfectly aligned crystal should decrease more than five times (see 4 in Fig. 6). This is an additional advantage of a crystal primary collimator in comparison with the ordinary amorphous one. We are grateful to Professor L. Lanceri (INFN and University of Trieste) who provided the tracking detectors, to V. Carassiti and M. Melchiorri for the design and fabrication of the crystal holders.
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We acknowledge partial support by the INFN NTA-HCCC and MIUR 2006028442 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-CERN 08-02-91020. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18]
J. Lindhard, K. Dan, Vidensk. Selsk. Mat. Fys. Medd. 34 (14) (1965). E.N. Tsyganov, Preprint TM-682, TM-684, Fermilab, Batavia (1976). A.M. Taratin, S.A. Vorobiev, Nucl. Instrum. Methods B 26 (1987) 512. A.G. Afonin et al., Nucl. Instrum. Methods B 234 (2005) 14. V.M. Biryukov et al., Nucl. Instrum. Methods B 234 (2005) 23. R.P. Fliller et al., Nucl. Instrum. Methods B 234 (2005) 47. R.A. Carrigan Jr. et al., Fermilab-CONF-06-309-AD. W. Scandale, UA9 Report, 2009. S.K. Andersen et al., Nucl. Phys. B 144 (1978) 1. R.A. Carrigan Jr. et al., Nucl. Phys. B163 (1980) 1. C. Binno et al., Nucl. Instrum. Methods B 194 (2002) 417. U.I. Uggerhoj et al., Phys. Lett. B 619 (2005) 240. S.Yu. Shmakov, V.V. Uzhinskii, A.M. Zadorozgny, Comput. Phys. Commun. 54 (1989) 125. W. Scandale et al., Phys. Rev. Lett. 101 (2008) 234801. S. Baricordi et al., Appl. Phys. Lett. 91 (2007) 061908. S. Baricordi et al., J. Phys. D: Appl. Phys. 41 (2008) 245501. M.I. Adamovich et al., Z. Phys. A 358 (1997) 337. A.M. Taratin, S.A. Vorobiev, Sov. Phys. Tech. Phys. 30 (1985) 927.
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Probability of inelastic nuclear interactions of high-energy protons in a bent crystal W. Scandale a, R. Losito a, M. Silari a, E. Bagli b, S. Baricordi b, P. Dalpiaz b, M. Fiorini b, V. Guidi b, A. Mazzolari b, D. Vincenzi b, R. Milan c, Gianantonio Della Mea d, E. Vallazza e, A.G. Afonin f, Yu.A. Chesnokov f, V.A. Maisheev f, I.A. Yazynin f, S.V. Afanasiev g, A.D. Kovalenko g, A.M. Taratin g,*, V.V. Uzhinsky g, A.S. Denisov h, Yu.A. Gavrikov h, Yu.M. Ivanov h, L.P. Lapina h, L.G. Malyarenko h, V.V. Skorobogatov h, V.M. Suvorov h, S.A. Vavilov h, D. Bolognini i,j, S. Hasan i,j, M. Prest i,j a
CERN, European Organization for Nuclear Research, CH-1211 Geneva 23, Switzerland INFN Sezione di Ferrara, Dipartimento di Fisica, Universita‘ di Ferrara Via Saragat 1, 44100 Ferrara, Italy c INFN Laboratori Nazionali di Legnaro, Viale Universita‘ 2, 35020 Legnaro (PD), Italy d Dipartimento di Ingegneria dei Materiali e Tecnologie Industriali, Universita‘ di Trento, Via Mesiano 77, 38050 Trento, Italy e INFN Sezione di Trieste, Via Valerio 2, 34127 Trieste, Italy f Institute of High Energy Physics, Moscow Region, RU-142284 Protvino, Russia g Joint Institute for Nuclear Research, Joliot-Curie 6, 141980 Dubna, Moscow Region, Russia h Petersburg Nuclear Physics Institute, 188300 Gatchina, Leningrad Region, Russia i Universita‘ dell’Insubria, via Valleggio 11, 22100 Como, Italy j INFN Sezione di Milano Bicocca, Piazza della Scienza 3, 20126 Milano, Italy b
a r t i c l e
i n f o
Article history: Received 30 June 2010 Available online 11 July 2010 Keywords: Crystal Channeling Volume reflection Nuclear interactions
a b s t r a c t Probability of inelastic nuclear interactions in a short bent silicon crystal for its orientations optimal for channeling and volume reflection was investigated using 400 GeV/c protons of the CERN SPS. The contribution of nuclear interactions from channeled protons was observed to be about 3–4% of the probability for the amorphous orientation. For the crystal orientation optimal for volume reflection the nuclear interaction probability of protons was a few percents larger than in the amorphous case. It was shown that in the limiting case of a quasi parallel beam realizing for the collider beam halo the inelastic nuclear losses should decrease by more than five times, which is an additional advantage of a crystal as a primary collimator for the LHC collimation system. Ó 2010 Elsevier B.V. All rights reserved.
When high-energy charged particles enter a crystal with small angles relative to the crystal planes their transverse motion is governed by the crystal potential averaged along the planes U(x). If the particle angles are smaller than the critical channeling angle hc = (2Uo/pv)1/2, where p, v are the particle momentum and velocity and Uo the depth of the planar potential well, they can be captured into the channeling regime [1]. Channeled positive particles move through a crystal oscillating between two neighboring planes. Therefore, all the processes requiring close collisions with the crystal atoms are strongly suppressed in a crystal well aligned with the beam. Bent crystals can deflect channeled particles by the bend angle a when their bend radius R > Rc, where Rc is the critical bend radius [2]. Particles can be also deflected due to volume reflection [3] in the tangency area of their momentum with the bent crystal planes. Bent crystals are successfully used in circular accelerators for beam extraction and for splitting of the extracted beam [4]. * Corresponding author. Tel.: +7 496 21 65 612; fax: +7 496 21 65 180. E-mail address: [email protected] (A.M. Taratin). 0168-583X/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2010.07.002
There are plans to use the crystal deflectors for the beam halo collimation of the LHC [5]. A bent crystal used as a primary collimator will deflect particles and direct them deeply onto the absorber. This should possibly increase the collimation efficiency. Experiments on beam halo collimation with a crystal primary collimator have been already performed at RHIC [6] and Tevatron [7]. The crystal collimator orientation was performed using the indications of the beam loss monitors (BLM), which registered secondary particles generated by inelastic nuclear interactions of the beam halo particles in the crystal. A large decrease of the BLM count was registered at the crystal orientation corresponding to the maximum capture of particles into the channeling regime. A decrease of the BLM rate by a factor of five was observed in the UA9 runs, the experiment on the crystal collimation ongoing at the CERN SPS [8]. It should be noted that in circular accelerators this ratio is determined both by the decrease of the nuclear interaction rate in the aligned crystal and by the increase of the number of particle passages through the crystal for its amorphous orientation. A few experiments on the study of nuclear interactions of highenergy protons and heavy nuclei in the aligned crystals have been
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W. Scandale et al. / Nuclear Instruments and Methods in Physics Research B 268 (2010) 2655–2659
also performed at the external accelerator beams [9–12]. Nuclear interactions of high-energy protons in germanium crystals aligned by the h1 1 0i axis with the beam had been studied in [9,10]. A considerable decrease of the nuclear interaction probability was registered in the aligned crystals. Recently, the reduced interaction probability has been observed for 33 TeV/c Pb nuclei in a bent silicon crystal aligned by the (1 1 0) planes with the beam [11]. A strong suppression by a factor of more than 20 has been observed in [12] for nuclear-charge changing interactions of 18 TeV/c In ions channeled through a bent Si crystal. In the present work, the probability of inelastic nuclear interactions in the silicon crystal with the length 1.94 mm bent along the (1 1 0) planes has been studied with 400 GeV/c protons at the H8 beam line of the CERN SPS. The probabilities for the crystal orientations optimal for channeling and volume reflection were measured. The experiment allowed to observe the contribution of channeled protons, which was 3–4% of the probability value for the amorphous orientation of the crystal. The limit of the inelastic interaction reduction for a quasi parallel beam has been determined. The probability of inelastic nuclear interactions of protons in a short crystal at its amorphous orientation is
Pin rin N am L:
ð1Þ
The cross-section of inelastic nuclear interactions of 400 GeV/c protons with silicon nuclei in the Glauber approach calculated according to [13] rin = 0.506 b, the atomic density in a silicon crystal Nam = 0.05 1024 cm3. Therefore, for the crystal with length L = 1.94 mm the probability Pin = 0.49%. The atomic density changes along the particle trajectory in the aligned crystal. Thus the nuclear interaction probability changes as well. The atomic density N(x) is quickly reduced with the distance x from the planes according to a Gaussian distribution
NðxÞ ¼ Nam Pn ðxÞ;
dp x2 Pn ðxÞ ¼ qffiffiffiffiffiffiffiffiffiffiffi exp 2 ; 2u1 2pu21
ð2Þ
Atomic density (N/Nam)
there u1 is the amplitude of thermal vibrations of the crystal atoms, u1 = 0.075 Å for a silicon crystal at a room temperature, dp is the planar channel width. The density at the plane positions is 10 times larger than the average density Nam. The ‘‘nuclear corridor” width, where the atomic nuclei of the plane are concentrated, is much smaller than the channel width, for the (1 1 0) Si dp = 1.92 Å and 6u1/dp = 0.23. Fig. 1 shows the dependence of the atomic density averaged along the particle trajectory in the (1 1 0) silicon crystal on the particle transverse energy Ex. The maximum density at Ex = Uo is three times larger than the average one. For stable chan-
3
2
neled states with small transverse energies the atomic density along the trajectories is very small or equals zero. For above-barrier particles with Ex > Uo the atomic density averaged along the trajectory approaches the average one with increasing Ex. For volume reflection of particles in a bent crystal the atomic density averaged along the particle trajectory in a tangency area is significantly larger than Nam. However, the density approaches to the average one when the distance of particles from the tangency point is increased. As a result, the averaged atomic density is only a few percents larger than Nam for a whole crystal length of 1.94 mm. Our experimental setup was mainly the same as in [14], see Fig. 2. Four microstrip silicon detectors, two upstream and two downstream of the crystal, were used to detect the particle trajectories with an angular resolution of about 3 lrad. Two large scintillation detectors with transverse dimensions 100 100 mm2 were placed 60 cm downstream the crystal on both sides from the primary proton beam to register secondary particles generated in inelastic nuclear interactions of protons in the crystal. The distance between the scintillation detectors was 10 mm. So, the angle of the inner edge of both scintillation detectors from the crystal location was hed = 8.33 mrad. It is sufficient to exclude the contributions of primary protons scattered due to elastic nuclear interactions, because hel hed. A 70 1.94 0.5 mm3 silicon strip crystal with the largest faces parallel to the (1 1 0) crystallographic planes fabricated according to the methodology [15,16] was bent along its length and placed vertically, so that the anticlastic bending induced along the crystal width was used to deflect particles in the horizontal plane (see Fig. 2b in [14]). A high precision goniometer was used to orient the (1 1 0) crystal planes parallel to the beam direction. The optimal crystal orientation, which gives the maximum of the deflected beam fraction, was found. The RMS deviation value measured for the horizontal angular distribution of the incident beam was rx = (13.368 ± 0.003) lrad. It is larger than the critical channeling angle, hc 10 lrad. However, the beam part deflected due to channeling in the crystal can be considerably increased by decreasing the angular size of the incident beam when only particles with the incident angles |hxo| < hcut are considered. Fig. 3 shows the deflection angle distribution of protons observed with the cutting angle hcut = 1.5 lrad. The Gaussian fit in Fig. 3a gives the deflection angle value hxm = (189 ± 0.02) lrad, which equals the crystal bend angle a. The deflected beam fraction Pd = (72.5 ± 0.117)% is hatched. Nuclear interactions occur mainly with undeflected particles either not captured into the channeling regime at the crystal entrance or dechanneled during the crystal passage. Fig. 4 shows the dependence of the undeflected beam part Pnd = 1 Pd on the cutting angle of the incident beam. It should be mentioned that some instability of the angular position of the goniometer (as large as a few microradians) observed over a long period of measurements and the crystal torsion (different crystal orientations along its height) decreased the deflection efficiency. The analysis of the amplitude spectra of the scintillation detectors registering secondary particles from the crystal allowed to
1
0
0
25
50
75
100
Transverse energy (eV) Fig. 1. The dependence of the atomic density averaged along the particle trajectory in the (1 1 0) silicon crystal on the particle transverse energy.
Fig. 2. Experimental layout at the external beam H8 of the CERN SPS. Here Si1–Si4 are the silicon microstrip detectors, g is the goniometer with a bent crystal. S1 and S2 are the scintillation detectors.
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F in ¼ N12 ðA > Ab Þ=N o ;
40
20
0 -100
0
100
200
Angle (µrad)
10
4
10
3
10
2
where N12(A > Ab) is the number of the coincidence events in S1 and S2 with amplitudes A > Ab, No is the number of particles with |hxo| < hcut, which hit the crystal. Let us note that the registered number of the coincidence events is not equal to the number of all inelastic interactions of protons in the crystal. The part of all events generated charged particles, which hit both the detectors, the coincidence frequency F12 = 0.655 ± 0.005, was determined by simulation using the FRITIOF model [17]. Fig. 5 shows the measured dependencies of the inelastic nuclear interaction frequency of protons on the cutting angle value hcut of the incident beam for the amorphous orientation (1) and for the aligned crystal (2), as well as without the crystal in the beam that is the experimental background (3). The interaction frequencies without the crystal and with the crystal in its amorphous orientation are practically constant. Whereas the frequency registered in the aligned crystal is considerably smaller than for its amorphous orientation and it decreases with decreasing hcut due to the increase of the fraction of well channeled protons, which do not experience close collisions with the crystal atoms. The probability of inelastic nuclear interactions of protons in the crystal was calculated by subtraction of the experimental background Fin(BG) and taking into account the coincidence frequency F12 estimated by the simulation above
Pin ¼ ðF in F in ðBGÞÞ=F 12 :
10
-100
0
100
200
Angle (µrad) Fig. 3. The deflection angle distributions of 400 GeV/c protons by the silicon crystal bent along the (1 1 0) planes. Only particles with the incident angles |hxo| < hcut = 1.5 lrad were considered. (a) In a linear scale, (b) in a logarithmic scale. Here the boundaries of the dechanneling area are marked by the solid circles.
0.6
0.5
0.4
ð4Þ
Fig. 6 shows the dependences of the inelastic nuclear interaction probability of protons in the crystal on the value of hcut in the cases of the amorphous orientation (1) and volume reflection (2) as well as in the aligned crystal (3). The measured probability value for the amorphous orientation is P am in = (0.505 ± 0.005)%, which is in a good agreement with the theoretical estimation made above using (1). For the symmetric case of volume reflection (2) considered in the experiment when the tangency area of the particle momentums with the bent planes is in the middle of the crystal length and practically all particles pass the whole crystal in abovebarrier states the probability is 3–4% larger than for the amorphous orientation. In the aligned crystal for the smallest angular width of the incident beam the probability is more than 3.5 times smaller than Pam in . The inelastic nuclear interaction probability of protons in the aligned crystal has been also studied by simulation using the model [18]. The calculated dependence is shown by the curve 4. There is a significant discrepancy with the experiment for small values of
0.3
0.6 0.2
0
10
20
Cutting angle (µrad) Fig. 4. The dependence of the undeflected part of protons on the cutting angle hcut of the incident beam.
determine the amplitude discrimination thresholds Ab, which cut the intrinsic detector background. Secondary particles were registered also in the case when the crystal was removed from the beam. They were generated by inelastic nuclear interactions of protons upstream the crystal and form the experimental background. The coincidence of the events with the amplitude A > Ab registered by the left and right scintillation detectors were used to subtract efficiently the experimental background including delectrons. The frequency of the inelastic nuclear interactions of protons in the crystal was defined as
Interaction frequency (%)
Counts
(b) 10 5
Beam fraction Pnd (%)
ð3Þ
60
3
Counts (10 )
(a)
0.4
0.2
0
0
10
20
Cutting angle (µrad) Fig. 5. The dependencies of the inelastic nuclear interaction frequency of protons on the cutting angle value of the incident beam for the amorphous orientation (1), the aligned crystal (2) and for the case without the crystal in the beam – the experimental background (3).
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Interaction probability ( %)
0.6
0.4
0.2
0
0
10
20
Cutting angle (µrad) Fig. 6. The dependencies of the inelastic nuclear interaction probability of protons in the crystal on the value of the cutting angle hcut of the incident beam for the amorphous orientation (1), for the case of volume reflection (2) and in the aligned crystal (3). The dependence (4) was obtained by simulation for the aligned crystal.
hcut because the goniometer instability and the crystal torsion were not taken into account in the simulation. However, for large values of hcut when the angular size of the incident beam is larger than the angular parameters of the goniometer instability and the crystal torsion the agreement with the experiment is good. The simulation allows to register the state of particles before their inelastic interactions with the crystal nuclei. According to the simulation the contribution value of inelastic interactions from channeled protons is in the interval (0.015–0.02)%, that is (3–4)% of the probability for the amorphous orientation. Let us remember that only channeled protons with large oscillation amplitudes, which approach closely to the channel walls (r < rc = 2.5u1), can have inelastic interactions with the crystal nuclei. Fig. 7 shows the calculated particle distributions in the transverse energy at the crystal entrance for the different values of hcut. Channeled particles with Ex > Exc = U(rc), whose value is shown by the arrow, enter the nuclear corridor of the channel walls. The beam fraction P(Ex > Exc) increases a little with increasing hcut and is maximum at hcut = hc. Then it decreases again. The maximum difference of the fraction values for a quasi parallel beam and the beam with hcut = hc is about 30%. This explains a little difference observed in the simulation for the inelastic interaction numbers of channeled protons with the different angular sizes hcut of the incident beam.
Let us try to determine a possible contribution of channeled protons to the inelastic interactions registered in the aligned crystal. Particles, which passed the whole crystal in channeling or above-barrier states, form the maxima at hx = a or hx = hvr, respectively, where hvr is the deflection angle due to volume reflection (see Fig. 3a). Dechanneled particles between two maxima were in channeling states only some part of the crystal length, which is determined by their deflection angle – hx/a. These particles are better seen with using a logarithmic scale (Fig. 3b). Here the Gaussian fit for the left maximum allows to separate volume reflected and dechanneled particles. The total number of particles passed through the whole crystal in above-barrier states with taking into account the contributions of dechanneled particles can be determined as
Nnch ¼
i1 X
ni þ
i2 X
i¼1
i1
ð5Þ
i1
0.6
Probability Pin/Pinam
60 3
N (10 )
i2 X ðni yi Þð1 hxi =aÞ;
where ni is the particle number of the ith histogram bin, yi is the Gaussian fit value in the middle of the ith bin hxi. The boundaries (i1,i2) of the dechanneling area are shown by the solid circles in Fig. 3b. Two first members of (5) determine the beam part, which was not captured into the channeling regime at the crystal entrance and passed the whole crystal in above-barrier states. The third member determines the contribution of dechanneled particles. Fig. 8 shows the inelastic interaction probability of protons measured in the aligned crystal as a function of the beam fraction passed the crystal in above-barrier states, Pnch = Nnch/No (solid circles). The different circles correspond to the different angular cuts of the incident beam hcut. The probability is shown as a ratio to its in ¼ Pin =Pam . value for the amorphous orientation P in in ¼ Pnch , is a hypoThe dependence shown by a dashed line, P thetic one when the probability is the same as in the amorphous case for all above-barrier protons and the contribution from channeled protons is absent. The probability values measured in the experiment are larger than the hypothetic ones. The difference is about 8% for the large angular sizes hcut of the incident beam. A half of this difference, about 4%, is due to the fact that the interaction probability for above-barrier protons is larger than for the amorphous orientation (see 2 in Fig. 6). The remaining difference, about 4% for the large values of hcut, is due to the contribution of channeled protons, which is in a good agreement with the value predicted by the simulation. The difference decreases for the small values of hcut because of the decrease of both the contributions. The contribution from channeled protons decreases because their
80
40
20
0
yi þ
0.5
0.4
0.3 0.3
0
5
10
15
Ex (eV) Fig. 7. Particle distributions in the transverse energy at the crystal entrance for the different angular sizes hcut of the incident beam: 3 lrad (1), 6 lrad (2), 12 lrad (3), and 20 lrad (4).
0.4
0.5
Beam part Pnch Fig. 8. The dependence of the inelastic nuclear interaction probability in the aligned crystal on the non-channeled part of the beam. The probability as a ratio to the value for the amorphous orientation is presented, Pin/P am in . The dashed line is a hypothetic linear dependence of Pin/P am in = Pnch.
W. Scandale et al. / Nuclear Instruments and Methods in Physics Research B 268 (2010) 2655–2659
part with large oscillation amplitudes decreases as it was shown in Fig. 7. The contribution from above-barrier particles decreases because they more quickly leave the tangency area where the atomic density averaged along their trajectories is higher than Nam. The measurements have shown that the probability of inelastic nuclear interactions of high-energy protons in the crystal depends strongly on its orientation. For the orientation optimal for volume reflection the probability is a few percents larger than for the amorphous one. The probability is significantly smaller in the aligned crystal because well channeled protons move through the crystal far from the crystallographic planes where the atomic nuclei are concentrated. Our experimental data show that the contribution of inelastic interactions from channeled protons is about 3–4% of the probability for the amorphous orientation. In the limiting case with a quasi parallel beam, which should be realized in the collider beam halo, the deflection efficiency in a single passage can approach 85%. Therefore, the probability of inelastic nuclear interactions of the beam halo protons in a perfectly aligned crystal should decrease more than five times (see 4 in Fig. 6). This is an additional advantage of a crystal primary collimator in comparison with the ordinary amorphous one. We are grateful to Professor L. Lanceri (INFN and University of Trieste) who provided the tracking detectors, to V. Carassiti and M. Melchiorri for the design and fabrication of the crystal holders.
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We acknowledge partial support by the INFN NTA-HCCC and MIUR 2006028442 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-CERN 08-02-91020. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18]
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