volume | PIER Journals

2020-06-21

Fields of an Ultra-Relativistic Beam of Charged Particles Between Parallel Plates. Exact Two-Dimensional Solutions by the Method of Images and Applications to the HL-LHC

Boris Levchenko

Dr. Boris Levchenko

D.V. Skobeltsyn Institute of Nuclear Physics

M.V. Lomonosov Moscow State University

Russian Federation

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Progress In Electromagnetics Research C, Vol. 103, 83-95, 2020

doi:10.2528/PIERC20032903 | Google Scholar

Abstract

Exact two-dimensional (2D) analytic expressions for electric and magnetic fields and their potentials created by a linear beam of relativistic charged particles between infinite perfectly conductive plates and ferromagnetic poles are derived. The solutions are obtained by summing an infinite sequence of fields from linear charge-images and current-images in complex space. Knowledge of the normal component of the electric field on the conductor surface makes it possible to calculate the induced electric charge surface density. In addition, we derive within an improved linear approximation new analytical expressions for fields near the beam in the case of an arbitrary beam offset from the median plane. The mathematical features of exact solutions and limitations for the applicability of linear approximations are specified. The primary goals of the future high-luminosity p-p and heavy-ion Large Hadron Collider programme after the Long Shutdown 2 are the search for yet unobserved effects of physics beyond the Standard Model, searches for rare or low-sensitivity processes in the Higgs sector, and probing in more detail the mechanism of electroweak symmetry breaking. This programme relies on the stable operation of the accelerator. However, as the beam luminosity increases, a number of destabilizing phenomena occur, in particular field emission, enhancing the electron cloud effect. For the case of a proton beam, we apply the exact 2D solution for estimating the intensity of electron field emission activated by the electric field of the beam in collimators of the future high-luminosity Large Hadron Collider. Calculation shows that the field emission intensity is very sensitive to a collimator surface roughness. In addition, with a relatively small and accidental beam displacement from the median path, about 20% of the collimator half-gap, the emission intensity increases by a factor of 10⁷. This will partially neutralize the beam space charge, violating acceleration dynamics and enhancing instability effects.

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Boris Levchenko, "Fields of an Ultra-Relativistic Beam of Charged Particles Between Parallel Plates. Exact Two-Dimensional Solutions by the Method of Images and Applications to the HL-LHC," Progress In Electromagnetics Research C, Vol. 103, 83-95, 2020.
doi:10.2528/PIERC20032903

References

1. Wiedemann, H., Particle Accelerator Physics, Springer, Berlin-Heidelberg, Germany, 2007.

2. Levchenko, B. B., "Modification of relativistic beam fields under the influence of external conducting and ferromagnetic flat boundaries," Prog. Theor. Exp. Phys., Vol. 2020, No. 1, 013G01-013G29, 2020.
doi:10.1093/ptep/ptz132 Google Scholar

3. Thomson, W., "On electrical images," Report of the Seventeenth Meeting of the British Association for the Advancement of Science, Vol. 1, Part II, 6, London, 1848. Google Scholar

4. Maxwell, J. C., A Treatise on Electricity and Magnetism, Vol. 1, Ch. 11, The Calendon Press, 1873.

5. Laslett, L. J., "On intensity limitations imposed by transverse space-charge effects in circular particle accelerators," Proc. BNL Summer Study on Storage Rings, 324-363, BNL-7534, 1963. Google Scholar

6. Chao, A. W., Physics of Collective Beam Instabilities in High-energy Accelerators, John Wiley and Sons, New York, 1993.

7. Hofmann, A., "Tune shifts from selffields and images," Proceedings of the 5th General Accelerator Physics Course, Vol. 1, CERN-94-01, Jyväskylä, Finland, 1992. Google Scholar

8. Levchenko, B. B., "Electric and magnetic fields generated by a charged bunch between parallel conducting plates," Physics Research International, Vol. 2010, 201730-201735, 2010. Google Scholar

9. Brüning, O., P. Collier, P. Lebrun, S. Myers, R. Ostojic, J. Poole, and P. Proudlock, LHC Design Report. The LHC Main Ring, Vol. 1, CERN, Geneva, 2004.

10. Apollinari, G., I. B. Alonso, O. Brüning, P. Fessia, M. Lamont, L. Rossi, and L. Tavian, High-luminosity Large Hadron Collider (HL-LHC), Vol. 4, CERN-2017-007-M, CERN, Geneva, 2017.

11. "Report reveals full reach of LHC programme," CERN Courier, Vol. 59, 9, 2019, https://cerncourier.com/a/report-reveals-full-reach-of-lhc-programme. Google Scholar

12. Smythe, W. R., Static and Dynamic Electricity, McGraw-Hill Book Company, New York, 1950.

13. Zotter, B., "The Q-shift of off-center particle beams in elliptic vacuum chambers," Nucl. Instrum. Meth., Vol. 129, 377-395, 1975.
doi:10.1016/0029-554X(75)90728-4 Google Scholar

14. Cimino, R., 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., Vol. 93, 014801, 2004.
doi:10.1103/PhysRevLett.93.014801 Google Scholar

15. Fowler, R. H. and L. W. Nordheim, "Electron emission in intense electric fields," Proc. Roy. Soc. (London), Vol. A119, 173-181, 1928. Google Scholar

16. Nordheim, L.W., "The effect of the image force on the emission an reflexion of electrons by metals," Proc. Roy. Soc. (London), Vol. A121, 626-639, 1928. Google Scholar

17. Nordheim, L., "Die theorie der electronenemission der metalle," Physikalische Zeitschrift, Vol. 30, No. 7, 117-196, 1929. Google Scholar

18. Elinson, M. I. and G. F. Vasil’ev, Field Emission, Fizmatgiz, Moscow, 1958 [in Russian].

19. Fursey, G., Field Emission in Vacuum Microelectronics, Kluwer Academic Plenum Publishers, New York, 2005.

20. Sommerfeld, A., H. Bethe, and , Elektronentheorie der Metalle, Springer, Berlin, 1967.
doi:10.1007/978-3-642-95002-5

21. Murphy, E. L., R. H. Good, and Jr., "Thermionic emission, field emission and the transition region," Phys. Rev., Vol. 102, No. 6, 1464-1473, 1956.
doi:10.1103/PhysRev.102.1464 Google Scholar

22. Christov, S. G., "Recent test and new applications of the unified theory of electron emission," Surf. Sci., Vol. 70, 32-51, 1978.
doi:10.1016/0039-6028(78)90399-0 Google Scholar

23. Good, R. H., Jr. and E.W. M¨uller, "Field emission," Encyclopedia of Physics, Vol. XXI, S. Flügge (Ed.), 1956. Google Scholar

24. Shrednik, V. N., "The theory of field emission from metals," Cold Cathodes, M. I. Elinson (Ed.), Sovetskoe Radio, Moscow, 1974 [in Russian]. Google Scholar

25. Gomer, R., Field Emission and Field Ionization, AIP, New York, 1993.

26. Modinos, A., Field, Thermionic, and Secondary Electron Emission Spectroscopy, Plenum Press, New York, 1983.

27. Eidelman, S., et al. "Review of particle physics," Phys. Lett., Vol. B592, No. 1-4, 1-5, 2004.
doi:10.1016/j.physletb.2004.06.001 Google Scholar

28. Burgess, R. E., H. Kroemer, and J. M. Houston, "Corrected values of Fowler-Nordheim field emission function θ(y) and S(y)," Phys. Rev., Vol. 90, 515, 1953.
doi:10.1103/PhysRev.90.515 Google Scholar