Abstract
We calculate exact two-dimensional analytic expressions for the electric and magnetic fields and their potentials generated by a linear beam of relativistic charged particles between infinite ideally conducting planes and ferromagnetic poles. We use the method of summing an infinite sequence of fields of linear image charges and image currents to obtain solutions and also calculate the density distribution of the electric charge on the conductor surface induced by the charged particle beam. We obtain new formulas for the linear approximation of the fields near the beam and discuss the mathematical features of the exact solutions and the applicability constraints for the linear approximations.
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References
H. Wiedemann, Particle Accelerator Physics, Springer, Berlin (2007).
B. B. Levchenko, “Modification of relativistic beam fields under the influence of external conducting and ferromagnetic flat boundaries,” Prog. Theor. Exp. Phys., 2020, 013G01 (2020).
W. Thomson, “On electrical images,” in: Notices and Abstracts of Communications to the 17th Meeting of the British Association for the Advancement of Science (Oxford, June 1847), Vol. 1, John Murray, London (1848), pp. 6–7.
J. C. Maxwell, “Theory of electric images and electric inversion,” in: A Treatise on Electricity and Magnetism, Oxford Univ. Press, Oxford (1873), pp. 191–225.
L. J. Laslett, “On intensity limitations imposed by transverse space-charge effects in circular particle accelerators,” in: Proc. Summer Study on Storage Rings (Brookhaven Natl. Lab. Report No. 7534), Brookhaven Natl. Lab., New York (1963), pp. 324–363.
A. W. Chao, Physics of Collective Beam Instabilities in High Energy Accelerators, John Wiley and Sons, New York (1993).
B. B. Levchenko, “Electric and magnetic fields generated by a charged bunch between parallel conducting plates,” Phys. Res. Intern., 2010, 201730 (2010).
G. Apollinari, A.I. B’ejar Alonso, O. Brüning, P. Fessia, M. Lamont, L. Rossi, and L. Tavian, eds., High-Luminosity Large Hadron Collider (HL-LHC) Technical Design Report V.0.1 (CERN Yellow Reports: Monographs, Vol. 4), CERN Publ., Geneva (2017).
B. B. Levchenko, “On field emission in high energy colliders initiated by a relativistic positively charged bunch of particles,” arXiv:physics/0608135 (2006).
R. Cimino, I. R. Collins, M. A. Furman, M. Pivi, F. Ruggiero, G. Rumolo, and F. Zimmermann, “Can low-energy electrons affect high-energy physics accelerators?” Phys. Rev. Lett., 93, 014801 (2004).
W. R. Smythe, Static and Dynamic Electricity, McGraw-Hill, New York (1950).
A. Hofmann, “Tune shifts from self-fields and images,” in: Proc. 5th General Accelerator Physics Course (Jyväskylä, Finland, 7-18 September 1992, S. Turner, ed.,), Vol. 1, CERN Publ., Geneva (1994), pp. 329–348.
B. Zotter, “The Q-shift of off-center particle beams in elliptic vacuum chambers,” Nucl. Instrum. Meth., 129, 377–395 (1975).
Acknowledgments. The author thanks E. B. Oborneva for the discussions and support of this project.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 203, No. 2, pp. 311–320, May, 2020.
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Levchenko, B.B. Fields of a relativistic beam of charged particles between parallel planes: Exact two-dimensional solutions obtained by the method of images. Theor Math Phys 203, 700–708 (2020). https://doi.org/10.1134/S0040577920050116
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DOI: https://doi.org/10.1134/S0040577920050116