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Mechanisms of High-Energy Beam Deflection by Bent Crystals

Explore mechanisms of charged particles motion near crystal planes, including hyperchanneling, stochastic scattering, and above barrier motion. Learn about beam deflection due to plane channeling in bent crystals.

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Mechanisms of High-Energy Beam Deflection by Bent Crystals

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  1. Mechanisms of high-energy beam deflection by bent crystals N.F.Shul’ga Akhiezer Institute for Theoretical Physics of NSC KIPT, Kharkov, Ukraine N.F.Shul’ga Akhiezer Institute for Theoretical Physics of NSC KIPT, Kharkov, Ukraine e-mail: shulga@kipt.kharkov.ua Orsay, 2013

  2. Mechanisms of ChargedParticles Motion near <100> Axis y z x c) b) a) d) e) x e • Hyperchanneling (e+, e–) • Stochastic multiple scattering • Planar channeling • Above barrier motion • Above barrier motion d c z 2

  3. Plane Channeling (Regular Motion)Lindhard (1965) y x z x U(x) pz=const≈p x z 5

  4. y x z Beam Deflection of fast Charged Particles due to Plane Channeling Effect in Bent Crystal E.Tsyganov (1976) Plane channeling Lindhard 1965

  5. The Motion of Relativistic Particle in Central Field of Bent Crystal Planes E0 Finite motion, precession b=R+x0 r(t)=R+x(t) A. Akhiezer, N.Shul’ga, A.Greenenko et al., Sov.Phys. Usp. 1995 7 J. Ellison, Nucl. Phys. B 206 (1982) 205

  6. z Above barrier motion Akhiezer, Shul’ga 1978 “Volume reflection” effectA. Taratin, S. Vorobiev 1987 x

  7. Deflection Functions for Beam Reflection in Crystal N.F. Shul’ga, V.I. Truten’, V.V. Boyko, 2009 E=300 GeVα=2. E=3000 GeV α=0.2 12

  8. Scattering on one bent crystal plane e+ e- 14

  9. Potential for Beam Reflection by Bent Crystal Planes Condition for bending: 15

  10. Stochastic Mechanism of Beam Deflectionby Bent Crystal N.F. Shul’ga, V.I. Truten’, I.V. Kirillin (2008-2013) z z΄ N. Shul’ga, A.Greenenko, JETP Lett., 1991. 18

  11. Multiple Scattering on Atomic strings V. Beloshitskii, M. Kumakhov (1973), 19 N. Shul’ga, V. Truten’, S. Fomin (1982),

  12. Dynamical Chaos at Multiple Scattering for e Z=0.5 Z=0.7 Z=1.5 Z=2, Z=2, Z=1 A. Akhiezer, N Shul’ga, V. Truten’, Physics Reports, 1991 20

  13. Multiple Scattering in Oriented Crystal (simulation) Si, <111>, E=450 GeV A. Greenenko, N. Shul’ga, NIM B193(2002) 133 21

  14. CERN Experiment (1996) on 450 GeV Proton Beam by a Bent Crystal

  15. Simulationfor CERN Experiment Experimental Situation A.Greenenko, N. Shul’ga (1999)

  16. α=0.9 α=3.6 α=14.4 Condition for beam deflection A.A. Greenenko, N.F. Shul'ga, NIM B 173 (2001) 178 l=crystal lenght along the beam l┴=equalization length 450GeV proton beam angular distribution at the exit of a bent silicon crystal with the curvature radius R=30 m near (110) axis: (a) l=3 mm; α=0.9; (b) l=12 mm; α=3.6; (c) l=48 mm; α=14.4

  17. Angular distribution of 400 GeVprotonsafter passing2 mmof bent Si crystal with R=40 m CERN experiment W. Scandale et al. Phys. Rev. Lett. 101 (2008), 164801 Simulation results 28

  18. Angular distribution of 150 GeVπ–-mesonsafter passing 1.172 mmof bent Si crystal with R=40 m CERN experiment Simulation results W. Scandale et al. PhysicsLettersB680(2009)301-304 29

  19. y z' z x DYNAMICAL CHAOS PHENOMENON IN NEGATIVELY-CHARGED PARTICLE BEAM SCATTERING ON BENT CRYSTAL N.F. Shul’ga, I.V. Kirillin, V.I. Truten’ (PHYSICS LETTERS B, 2011) angular distribution of beam particles after passing 8 mm of silicon crystal, bent at 185 mkradalong thex axis: experiment(W. Scandale, A. Vomiero et al., Phys. Lett. B, v. 693, 2010, p. 545) simulation in real crystal geometry simulation in random string approximation angular distribution of the initial beam

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