CERN 9 March 2006Biryukov: crystal collimation1 Simulations and interpretation of crystal collimation experiments at RHIC and Tevatron CERN, 9 March 2006 Valery M. Biryukov Institute for High Energy Physics Protvino, Russia

CERN 9 March 2006Biryukov: crystal collimation2 Most of the presented studies are available as e-print Arxiv:physics/ at Here we added more analysis and illustrations and made new predictions.

CERN 9 March 2006Biryukov: crystal collimation3 In IHEP crystal collimation experiment (1999) the rates in the ring were measured downstream of the scraper Typical angular scans and background rate distribution shown: [ A.G. Afonin et al. Talk given at PAC 1999 (New York) ]

CERN 9 March 2006Biryukov: crystal collimation4 In RHIC crystal collimation experiment the emphasis was on the local rate, i.e. interaction rate in the crystal (shown) Both the accelerator experiment in RHIC and the numerical experiment with CATCH have shown an unexpected plateau… Interpretation is an issue for ab initio numerical experiment as much as for a real experiment !..

CERN 9 March 2006Biryukov: crystal collimation5 At least 3 effects automatically give plateau in the right angular range..! a) Volume capture: flat within ~0.4 mrad b) Volume reflection flat within ~0.4 mrad c) Miscut angle: flat within ~0.3 mrad

CERN 9 March 2006Biryukov: crystal collimation6 a) Volume capture happens with low probability but – if happens – makes a strong bending. b) Volume reflection happens with very high probability but makes miserable bending effect – a few microradian. c) Miscut angle plays a role only when particles come within ~0.3 mr X 5 mm = 1.5 micron w.r.t. the surface All 3 effects are well known but none of them gives obvious explanation at first glance :

CERN 9 March 2006Biryukov: crystal collimation7 Miscut angle makes a flat effect in the range ~0.3 mrad … But in simulations for RHIC the miscut was switched off … So I had to drop it from the list

CERN 9 March 2006Biryukov: crystal collimation8 Volume capture is often neglected at high energies … How can it explain the effect? Probability of VC at RHIC is ~0.1% per 1 encounter with crystal. Proton survives in Si ~450 mm equivalent to 90 encounters with 5 mm crystal until inelastic interaction. Probability of VC in circulating beam is up to ~9% and would be seen within wide range. At the same time, channeling peak depends on divergence and was % in RHIC, i.e. 2-3 times higher than 9% but seen in a very narrow range. So, you would even say that VC is much more visible than plain channeling at 250 GeV in circulating beam !

CERN 9 March 2006Biryukov: crystal collimation9 Explanation based on volume capture could work for RHIC in a certain case. Two problems: VC probability drops with E like E -3/2. So the ~9% (RHIC)  ~1% (Tevatron), not enough to explain Tevatron data. Aperture (secondary collimator) suppresses VC by cutting off the number of particle encounters with crystal.

CERN 9 March 2006Biryukov: crystal collimation10 Volume reflection deflects beam by ~0-2 critical angle RHIC: crit. angle ~10 urad m.s. angle ~13 urad Tevatron: crit. angle ~5 urad m.s. angle ~3 urad Taratin, Vorobiev (1987) Cf.: a 5 mm W target scatters at ~20-40 urad. Crystal bends at 440 urad. How a 5-10 urad effect can play a role ?

CERN 9 March 2006Biryukov: crystal collimation11 To answer the questions, we modeled crystal collimation with the O-shaped crystal and Tevatron lattice Crystal was set at 5σ and collimator at 5.5σ in hor.plane We calculated nuclear interaction rate in the crystal: Indeed, it showed the same signature!.. The rate is suppressed by 95% at the dip (87% within +-5 urad) and by 50% at plateau. The dip width ~30 urad.

CERN 9 March 2006Biryukov: crystal collimation12 Why it goes this way? For 100 protons incident on the crystal, very rough distribution of losses is: at random: 69 die in crystal, 31 in collimator; at the dip: 77 channeled, 4 die in crystal, 19 in collimator; at plateau: 2 channeled, 35 die in crystal, 63 in collimator. The plateau effect is not due to channeling! It is due to increased losses at the aperture caused by stronger diffusion of beam in crystal scatterings. For plateau effect, two things are necessary: 1)Coherent scattering in crystal. 2)Close secondary aperture.

CERN 9 March 2006Biryukov: crystal collimation13 Figure shows exit x’ angular distibutions of 250 GeV and 1 TeV protons downstream of the O-shaped crystal w.r.t. the entrance angle, at the middle of “plateau” 2 remarkable features: a) is not 0 ! = -16 urad (RHIC) = -4.2 urad (TeV) b) r.m.s. x’ is increased! = 18 urad (RHIC) [cf. 13 urad random] = 6.4 urad (TeV) [cf. 3.3 urad random]

CERN 9 March 2006Biryukov: crystal collimation14 In circulating beam, coherent scatterings result in diffusion. It is governed by r.m.s. x’ rather than by reflections. By every encounter with a crystal, beam emittance grows by about  (Δθ) 2, where  is accelerator beta function and Δθ is the scattering angle in crystal. We have found that in RHIC case the emittance grows faster by factor of 2 in the plateau region than outside of this region, and a factor of 3.7 faster than at random alignment, in Tevatron case. Our simulations show that at the 7-TeV LHC this factor can be as high as

CERN 9 March 2006Biryukov: crystal collimation15 Figures show how diffusion develops at plateau. Phase space after 1, 2, 3, 4, 5, 6 encounters with crystal

CERN 9 March 2006Biryukov: crystal collimation16 Diffusion compared at plateau vs random. Phase space after 1, 3, 6 encounters with crystal

CERN 9 March 2006Biryukov: crystal collimation17 The proposed interpretation can be validated by Tevatron data. Courtesy: V. Shiltsev.

CERN 9 March 2006Biryukov: crystal collimation18 Reviewing the possible effects causing plateau, we conclude that secondary aperture is crucial element. If you have no apertures (many sigmas far), you see no effect of reflections but you can see volume capture…(subject to E). When you close the aperture, it suppresses volume capture but then you can see the effect of reflections !

CERN 9 March 2006Biryukov: crystal collimation19 To test it, we make further predictions for Tevatron. The same plot for crystal set at 5σ but collimator at 7σ: The dip slightly affected but plateau moves up. Suppression at plateau is now 30% instead of 50%

CERN 9 March 2006Biryukov: crystal collimation20 More predictions for possible tests: (x,x’) distribution at collimator – plateau case

CERN 9 March 2006Biryukov: crystal collimation21 (x, x’) distribution at peak

CERN 9 March 2006Biryukov: crystal collimation22 Prediction for the new crystal: strip 3 mm, 0.15 mrad. Suppression at plateau is 65%.

CERN 9 March 2006Biryukov: crystal collimation23 Reflection angle in the new strip is urad (cf. with 4.2 urad in the O-shaped one) at 1 TeV. In the 7 TeV LHC the reflection in the 3 mm strip is just 0.3 urad for 150 urad bending angle, but 2.3 urad for 50 urad bending angle, and 2.9 urad for 25 urad bending angle. This makes it feasible to achieve ~15 urad bending of 7 TeV beam with 5 reflections …

CERN 9 March 2006Biryukov: crystal collimation24 How to refer the reflections to critical angle? What is usually called critical angle is solely for stable channeling, i.e. critical energy of ~12 eV. This domain is quite different from reflections. Reflections are governed by the full potential well of ~23 eV (Si). The corresponding critical angle is (2*23eV/E) 1/2 which is 2.6 urad at 7 TeV, 6.8 urad at 1 TeV Typical reflection of beam in the above examples is on the order of ~1 critical angle. Expect ~10 urad at 400 GeV, ~25 at 70 GeV

CERN 9 March 2006Biryukov: crystal collimation25 We can conclude that crystal collimation studies, besides promising a very high efficiency of the technique in colliders, reveal a new interesting physics of beam reflection on the coherent field of the atomic planes of bent crystal. This reflection, theoretically predicted almost 20 years ago, causes a strong perturbation of beam in the conditions of crystal collimation experiments at RHIC and Tevatron and is observed as a very strong factor affecting particle loss in the accelerator ring. This revealed physics is essential in designing crystal applications for colliders. This strong scattering effect could even serve itself as a basis of a new collimation design.