CHANNELING EFFECT SIMULATION AND ITS POSSIBLE APPLICATIONS FOR FUTURE HIGH ENERGY ACCELERATORS

1. CHANNELING EFFECT SIMULATION AND ITS POSSIBLE APPLICATIONS FOR FUTURE HIGH ENERGY ACCELERATORS ALEXEI SYTOV Belarusian State University, Research Institute for Nuclear Problems

2. Different effects in crystal θL0 Volume reflection Channeling

3. Different effects in crystal θL0 Amorphous scattering Volume reflection Channeling

4. Basic channeling principles Transverse energy conservation: z => => x

5. Basic channeling principles Condition of particle capture into the regime of channeling motion: z => => x θL

6. Channeling in bent crystal

7. Averaged planar potential Straight crystal Bent crystal Amorphous-like crystal penetration Volume reflection Dechanneling channeling channeling channeling channeling

8. Dechanneling causes

9. Dechanneling causes • Scattering on nuclei

10. Dechanneling causes • Scattering on nuclei • Scattering on electrons

11. Simulation program

12. Channeling simulation • Monte-Carlo simulation of initial incident coordinates and angles before the first particle pass through crystal. • Solving of the second-order linear differential equation at each space step. • Monte-Carlo simulation of coulomb scattering on both nucleiand electrons and initial angle changing at each space step. • Simulation of possibility of the inelastic nuclear scattering in crystal.

13. Bent crystal Initial coordinates and angles x0, θx0, y0, θy0 xi+1= xi+1(xi, θxi), θxi+1 = θxi+1 (xi, θxi) yi+1= yi +dy, θyi+1 = θyi Yes Was an escape from the crystal? No Was a scattering? Yes No Final coordinates and angles xf, θxf, yf, θyf Simulation by Monte-Carlo dθx, dθy; θxi+1= θxi+1 + dθx, θyi+1= θyi+1 + dθy

14. Simulation of channeling efficiency Simulation of the initial coordinates and angles by Monte-Carlo Bent crystal No Yes i>Nparticles? Calculation of channeling efficiency

15. Additional extension of the simulation tool

16. A technique to improve crystal channelingefficiency of charged particles till 99,9%* • A narrow plane cut near the crystal surface considerably increases the probability of capture into the stable channeling motion of positively charged particles. Crystal z Beam cut z2 z3 z1 0 *V.V.Tikhomirov. JINST, 2 P08006, 2007. zc

17. z=z1 z=z2 z=0 1 2 3 Phase space transformations θ/θch z>z1 z>z2 2' 4 θ/θch x, Å θ/θch With cut z=zc z=zc Without cut 3' 5 θ/θch θ/θch *V.V.Tikhomirov . JINST, 2 P08006, 2007. x, Å x, Å

18. Dependence of the 7 TeV proton dechanneling probability in a 1cm bent Si crystal on the r.m.s. incidence angle* Without cut With cut *V.V.Tikhomirov. JINST, 2 P08006, 2007.

19. Simulation of channeling efficiency Simulation of the initial coordinates and angles by Monte-Carlo No Yes Is there the cut? xi+1= xi+1(xi, θxi), θxi+1 = θxi+1 (xi, θxi) yi+1= yi +dy, θyi+1 = θyi Yes No Was an enter in the cut? Bent crystal Motion in the cut No Yes i>Nparticles? Calculation of channeling efficiency

20. Problems of the channeling effect for the collimation

21. Crystal collimation Absorber

22. experiment simulation UA9experiment at SPS (CERN) * • Dependence of inelasticnuclear interactionnumber of protonson the angular position of the crystal C1: The UA9 experimental layout: *W.Scandale et al. Phys. Let., B692 78-82, 2010.

23. Miscut angle

24. First crystal hit UA9: more than 90% of particles for both miscut cases

25. Probability of nuclear reactions in the crystal collimator vs miscut angle at perfect crystal alignment* UA9 ×4,5 *V. Tikhomirov, A. Sytov, arXiv:1109.5051 [physics.acc-ph]; V. Tikhomirov, A. Sytov, “VANT” (57), 2012, N1, p. 88-92.

26. Simulation of collimation efficiency Simulation of the initial coordinates and angles by Monte-Carlo Does particle hit the face of the crystal? No Yes Does particle hit the lateral surface of the crystal? No Yes Bent crystal Calculation of probability of inelastic nuclear scattering in crystal No Does particle hit the absorber? Yes Yes No Motion in accelerator Calculation of collimation efficiency i>Nparticles?

27. Future projects

28. Beam extraction from the Recycler Ring* *V. Shiltsev. FNAL, No. DE-AC02-07CH11359.

29. Two (111) Si crystals in standard IHEP holders

30. STRUCT STRUCT Does particle hit the face of the crystal? Yes No Does particle hit the lateral surface of the crystal? No Yes Bent crystal Calculation of probability of inelastic nuclear scattering in crystal

31. X-Ray accelerator

34. Code modification for X-Ray accelerator Initial coordinates and angles x0, θx0, y0, θy0 xi+1= xi+1(xi, zi, θxi), θxi+1 = θxi+1 (xi,zi, θxi) yi+1= yi +dy, θyi+1 = θyi, (pv/2)i+1= (pv/2)i+eEz(x,z)dz Yes No Was an escape from the crystal? Was a scattering? Yes No Final coordinates and angles xf, θxf, yf, θyf Simulation by Monte-Carlo dθx, dθy; θxi+1= θxi+1 + dθx, θyi+1= θyi+1 + dθy

35. Conclusions • Numericalmethods were developed anda program of channeling simulation was created. • A technique of improving of crystal channeling efficiency with cut was studied. A drastic increase of the channeling efficiency due to this method was showed. • The dependence of inelasticnuclear interactionnumber obtained at the Super Proton Synchrotron at CERN was simulated and explained. The usual miscut angle can increase the probability of nuclear reactions with a factor 4,5 for the UA9 case. • The simulation code will be combined with STRUCT and will be used for the analysis for the experiment of the crystal extraction from the Recycler Ring. • Some modifications of the simulation code will allow to simulate the project of X-Ray accelerator