Abstract
This paper provides an explanation of the key effects behind the deflection of ultra-relativistic electron beams by means of oriented ‘quasi-mosaic’ Bent Crystals (qmBC). It is demonstrated that accounting for specific geometry of the qmBC and its orientation with respect to a collimated electron beam, its size and emittance is essential for an accurate quantitative description of experimental results on the beam deflection by such crystals. In an exemplary case study, a detailed analysis of the recent experiment at the SLAC facility is presented. The methodology developed has enabled to understand the peculiarities in the measured distributions of the deflected electrons. Also, this achievement constitutes an important progress in the efforts toward the practical realization of novel gamma-ray crystal-based light sources and puts new challenges for the theory and experiment in this research area.
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References
A.V. Korol, A.V. Solov’yov, Crystal-based intensive gamma-ray light sources. Eur. Phys. J. D. 74, 201 (2020)
A.V. Korol, A.V. Solov’yov, All-atom relativistic molecular dynamics simulations of channeling and radiation processes in oriented crystals. Eur. Phys. J. D. 75, 207 (2021)
M. Krasny, The gamma factory proposal for CERN. CERN Proc. 1, 249 (2018)
TECHNO-CLS project (GA: 101046458) within the HORIZON-EIC Framework
A.V. Korol, A.V. Solov’yov, W. Greiner, Channeling and Radiation in Periodically Bent Crystals, 2nd edn. (Springer-Verlag, Berlin, Heidelberg, 2014)
A. Mazzolari, E. Bagli, L. Bandiera, V. Guidi, H. Backe, W. Lauth, V. Tikhomirov, A. Berra, D. Lietti, M. Prest, E. Vallazza, D. De Salvador, Steering of a sub-GeV electron beam through planar channeling enhanced by rechanneling. Phys. Rev. Lett. 112, 135503 (2014)
U. Wienands, T.W. Markiewicz, J. Nelson, R.J. Noble, J.L. Turner, U.I. Uggerhøj, T.N. Wistisen, E. Bagli, L. Bandiera, G. Germogli, V. Guidi, A. Mazzolari, R. Holtzapple, M. Miller, Observation of deflection of a beam of multi-GeV electrons by a thin crystal. Phys. Rev. Lett. 114, 074801 (2015)
L. Bandiera, E. Bagli, G. Germogli, V. Guidi, A. Mazzolari, H. Backe, W. Lauth, A. Berra, D. Lietti, M. Prest, D. De Salvador, E. Vallazza, V. Tikhomirov, Investigation of the electromagnetic radiation emitted by sub-GeV electrons in a bent crystal. Phys. Rev. Lett. 115, 025504 (2015)
L. Bandiera, E. Bagli, V. Guidi, A. Mazzolari, A. Berra, D. Lietti, M. Prest, E. Vallazza, D. De Salvador, V. Tikhomirov, Broad and intense radiation accompanying multiple volume reflection of ultrarelativistic electrons in a bent crystal. Phys. Rev. Lett. 111, 255502 (2013)
A. Mazzolari, M. Romagnoni, R. Camattari, E. Bagli, L. Bandiera, G. Germogli, V. Guidi, G. Cavoto, Bent crystals for efficient beam steering of multi TeV-particle beams. Eur. Phys. J. C. 78, 720 (2018)
A.I. Sytov, V. Guidi, V.V. Tikhomirov, E. Bagli, L. Bandiera, G. Germogli, A. Mazzolari, Planar channeling and quasichanneling oscillations in a bent crystal. Eur. Phys. J. C. 76, 77 (2016)
T.N. Wistisen, U.I. Uggerhøj, U. Wienands, T.W. Markiewicz, R.J. Noble, B.C. Benson, T. Smith, E. Bagli, L. Bandiera, G. Germogli, V. Guidi, A. Mazzolari, R. Holtzapple, S. Tucker, Channeling, volume reflection, and volume capture study of electrons in a bent silicon crystal. Phys. Rev. Acc. Beams. 19, 071001 (2016)
V. Guidi, A. Mazzolari, D. De Salvador, A. Carnera, Silicon crystal for channelling of negatively charged particles. J. Phys. D: Appl. Phys. 42, 182005 (2009)
R. Camattari, V. Guidi, V. Bellucci, A. Mazzolari, The quasi-mosaic effect in crystals and its application in modern physics. J. Appl. Cryst. 48, 977 (2015)
A. Mazzolari, M. Romagnoni, R. Camattari, E. Bagli, L. Bandiera, G. Germogli, V. Guidi, G. Cavoto, R. Camattari, V. Guidi, V. Bellucci, A. Mazzolari, Bent crystals for efficient beam steering of multi TeV-particle beams. Eur. Phys. J. C. 78, 720 (2018)
S. Lekhnitskii, Theory of Elasticity of an Anisotropic Body (Mir Publishers, Moscow, 1981)
O.I. Sumbaev, Reflection of gamma-rays from bent quartz plates. JETP. 5, 1042 (1957)
Y. Ivanov, A. Petrunin, V. Skorobogatov, Observation of the elastic quasi-mosaicity effect in bent silicon single crystals. JETP Lett. 81, 977 (2005)
J. Lindhard, Influence of crystal lattice on motion of energetic charged particles. K. Dan. Vidensk. Selsk. Mat. Fys. Medd. 34, 1–64 (1965)
A.M. Taratin, S.A. Vorobiev, Volume trapping of protons in the channeling regime in a bent crystal. Phys. Lett. 115, 398 (1986)
A.M. Taratin, S.A. Vorobiev, Volume reflection of high-energy charged particles in quasi-channeling states in bent crystals. Phys. Lett. 119, 425 (1987)
P.A. Doyle, P.S. Turner, Relativistic Hartree-Fock X-ray and electron scattering factors. Acta Cryst. A. 24, 390–397 (1968)
I.A. Solov’yov, A.V. Yakubovich, P.V. Nikolaev, I. Volkovets, A.V. Solov’yov, MesoBioNano explorer—a universal program for multiscale computer simulations of complex molecular structure and dynamics. J. Comp. Phys. 33, 2412 (2012)
G.B. Sushko, V.G. Bezchastnov, I.A. Solov’yov, A.V. Korol, W. Greiner, A.V. Solov’yov, Simulation of ultra-relativistic electrons and positrons channeling in crystals with MBN explorer. J. Comp. Phys. 252, 404 (2013)
I.A. Solov’yov, A.V. Korol, A.V. Solov’yov, Multiscale Modeling of Complex Molecular Structure and Dynamics with MBN Explorer (Springer International Publishing, Cham, 2017)
G.B. Sushko, I.A. Solov’yov, A.V. Solov’yov, Modeling MesoBioNano systems with MBN Studio made easy. J. Mol. Graph. Model. 88, 247 (2019)
E. Bagli, V. Guidi, DYNECHARM++: a toolkit to simulate coherent interactions of high-energy charged particles in complex structures. Nucl. Instrum. Methods B. 309, 124 (2013)
V.V. Tikhomirov, Quantum features of high energy particle incoherent scattering in crystals. Phys. Rev. Accel. Beams 22, 054501 (2019) (Erratum: Phys. Rev. Accel. Beams 23, 039901 (2020))
Funding
The work was supported in part by the DFG Grant (Project No. 413220201) and by the H2020 RISE-NLIGHT project (GA 872196). We acknowledge helpful discussions with Andrea Mazzolari, Vincenzo Guidi, Hartmut Backe and Werner Lauth. Frankfurt Center for Scientific Computing (CSC) is acknowledged for providing computer facilities. We are grateful to the anonymous referee for constructive comments.
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Sushko, G.B., Korol, A.V. & Solov’yov, A.V. Ultra-relativistic electron beams deflection by quasi-mosaic crystals. Eur. Phys. J. D 76, 236 (2022). https://doi.org/10.1140/epjd/s10053-022-00567-4
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DOI: https://doi.org/10.1140/epjd/s10053-022-00567-4