Vol. 123
Latest Volume
All Volumes
PIERC 142 [2024] PIERC 141 [2024] PIERC 140 [2024] PIERC 139 [2024] PIERC 138 [2023] PIERC 137 [2023] PIERC 136 [2023] PIERC 135 [2023] PIERC 134 [2023] PIERC 133 [2023] PIERC 132 [2023] PIERC 131 [2023] PIERC 130 [2023] PIERC 129 [2023] PIERC 128 [2023] PIERC 127 [2022] PIERC 126 [2022] PIERC 125 [2022] PIERC 124 [2022] PIERC 123 [2022] PIERC 122 [2022] PIERC 121 [2022] PIERC 120 [2022] PIERC 119 [2022] PIERC 118 [2022] PIERC 117 [2021] PIERC 116 [2021] PIERC 115 [2021] PIERC 114 [2021] PIERC 113 [2021] PIERC 112 [2021] PIERC 111 [2021] PIERC 110 [2021] PIERC 109 [2021] PIERC 108 [2021] PIERC 107 [2021] PIERC 106 [2020] PIERC 105 [2020] PIERC 104 [2020] PIERC 103 [2020] PIERC 102 [2020] PIERC 101 [2020] PIERC 100 [2020] PIERC 99 [2020] PIERC 98 [2020] PIERC 97 [2019] PIERC 96 [2019] PIERC 95 [2019] PIERC 94 [2019] PIERC 93 [2019] PIERC 92 [2019] PIERC 91 [2019] PIERC 90 [2019] PIERC 89 [2019] PIERC 88 [2018] PIERC 87 [2018] PIERC 86 [2018] PIERC 85 [2018] PIERC 84 [2018] PIERC 83 [2018] PIERC 82 [2018] PIERC 81 [2018] PIERC 80 [2018] PIERC 79 [2017] PIERC 78 [2017] PIERC 77 [2017] PIERC 76 [2017] PIERC 75 [2017] PIERC 74 [2017] PIERC 73 [2017] PIERC 72 [2017] PIERC 71 [2017] PIERC 70 [2016] PIERC 69 [2016] PIERC 68 [2016] PIERC 67 [2016] PIERC 66 [2016] PIERC 65 [2016] PIERC 64 [2016] PIERC 63 [2016] PIERC 62 [2016] PIERC 61 [2016] PIERC 60 [2015] PIERC 59 [2015] PIERC 58 [2015] PIERC 57 [2015] PIERC 56 [2015] PIERC 55 [2014] PIERC 54 [2014] PIERC 53 [2014] PIERC 52 [2014] PIERC 51 [2014] PIERC 50 [2014] PIERC 49 [2014] PIERC 48 [2014] PIERC 47 [2014] PIERC 46 [2014] PIERC 45 [2013] PIERC 44 [2013] PIERC 43 [2013] PIERC 42 [2013] PIERC 41 [2013] PIERC 40 [2013] PIERC 39 [2013] PIERC 38 [2013] PIERC 37 [2013] PIERC 36 [2013] PIERC 35 [2013] PIERC 34 [2013] PIERC 33 [2012] PIERC 32 [2012] PIERC 31 [2012] PIERC 30 [2012] PIERC 29 [2012] PIERC 28 [2012] PIERC 27 [2012] PIERC 26 [2012] PIERC 25 [2012] PIERC 24 [2011] PIERC 23 [2011] PIERC 22 [2011] PIERC 21 [2011] PIERC 20 [2011] PIERC 19 [2011] PIERC 18 [2011] PIERC 17 [2010] PIERC 16 [2010] PIERC 15 [2010] PIERC 14 [2010] PIERC 13 [2010] PIERC 12 [2010] PIERC 11 [2009] PIERC 10 [2009] PIERC 9 [2009] PIERC 8 [2009] PIERC 7 [2009] PIERC 6 [2009] PIERC 5 [2008] PIERC 4 [2008] PIERC 3 [2008] PIERC 2 [2008] PIERC 1 [2008]
2022-08-28
A Charged Particle Model Based on Weber Electrodynamics for Electron Beam Trajectories in Coil and Solenoid Elements
By
Progress In Electromagnetics Research C, Vol. 123, 151-166, 2022
Abstract
To aid with the design, evaluation, and optimisation of charged particle instrumentation, computer modelling is often used. It is therefore of interest to obtain accurate predictions for trajectories of charged species with the help of simulation. Particularly for solenoids and coils, which are often used for guiding, deflecting or focusing particle beams, knowledge of the magnetic field is required, especially in the fringing field regions. A novel model, which is based on a direct-line-of-action force between interacting charges, is described in this paper which accurately predicts the deflection of an electron beam trajectory traversing through a coil and the fringe field region. The model is further compared with a standard field model and a commercially available software package. Additionally, a relatively straightforward experiment has been designed and implemented to verify the simulation results, where it is found that the presented direct-action model is equally as accurate as field-based simulations compared with the experimental results. Furthermore, the magnetic field of a solenoid is visualised and analysed in terms of its radial, axial, and total field strength and compared to a force map obtained from the direct-interaction model. This representation allows for further comparison of the field and force interaction models and it is found that they are qualitatively the same.
Citation
Christof Baumgärtel, and Simon Maher, "A Charged Particle Model Based on Weber Electrodynamics for Electron Beam Trajectories in Coil and Solenoid Elements," Progress In Electromagnetics Research C, Vol. 123, 151-166, 2022.
doi:10.2528/PIERC22061508
References

1. Steinhauer, L. and D. Quimby, "Advances in laser solenoid fusion reactor design," The Technology of Controlled Nuclear Fusion: Proceedings of the Third Topical Meeting on the Technology of Controlled Nuclear Fusion, Vol. 1, 121, National Technical Information Service, Santa Fe, New Mexico, May 9-11, 1978.

2. Tobita, K., S. Nishio, M. Sato, S. Sakurai, T. Hayashi, Y. Shibama, T. Isono, M. Enoeda, H. Nakamura, S. Sato, et al. "Slimcs-compact low aspect ratio demo reactor with reducedsize central solenoid," Nuclear Fusion, Vol. 47, No. 8, 892, 2007.

3. Engström, C., T. Berlind, J. Birch, L. Hultman, I. Ivanov, S. Kirkpatrick, and S. Rohde, "Design, plasma studies, and ion assisted thin film growth in an unbalanced dual target magnetron sputtering system with a solenoid coil," Vacuum, Vol. 56, No. 2, 107-113, 2000.

4. Zhang, X., J. Xiao, Z. Pei, J. Gong, and C. Sun, "Influence of the external solenoid coil arrangement and excitation mode on plasma characteristics and target utilization in a dc-planar magnetron sputtering system," Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films, Vol. 25, No. 2, 209-214, 2007.

5. Karino, T., M. Okamura, T. Kanesue, S. Ikeda, and S. Kawata, "Plasma instability inside solenoid with laser ion source," Review of Scientific Instruments, Vol. 91, No. 5, 053303, 2020.

6. Schröder, G., "Fast pulsed magnet systems," Handbook of Accelerator Physics and Engineering, A. W. Chao and M. Tigner, eds., No. CERN-SL-98-017-BT, Ch. 3, 460-466, World Scientific, Singapore, 1999.

7. Wong, L. J., K.-H. Hong, S. Carbajo, A. Fallahi, P. Piot, M. Soljacić, J. D. Joannopoulos, F. X. Kärtner, and I. Kaminer, "Laser-induced linear-field particle acceleration in free space," Scientific Reports, Vol. 7, No. 1, 11159, 2017.

8. Arnaudon, L., P. Baudrenghien, C. Bertone, Y. Body, J. Broere, O. Brunner, M. Buzio, C. Carli, F. Caspers, J. Corso, J. Coupard, A. Dallocchio, N. Dos Santos, R. Garoby, F. Gerigk, L. Hammouti, K. Hanke, M. Jones, I. Kozsar, J. Lettry, J. Lallement, A. Lombardi, L. Lopez-Hernandez, C. Maglioni, S. Mathot, S. Maury, B. Mikulec, D. Nisbet, C. Noels, M. Paoluzzi, B. Puccio, U. Raich, S. Ramberger, C. Rossi, N. Schwerg, R. Scrivens, G. Vandoni, S. Weisz, J. Vollaire, M. Vretenar, and T. Zickler, "The LINAC4 Project at CERN,", 4, Aug. 2011.

9. Dattoli, G., L. Mezi, and M. Migliorati, "Operational methods for integro-differential equations and applications to problems in particle accelerator physics," Taiwanese Journal of Mathematics, 407-413, 2007.

10. Karamyshev, O., C.Welsch, and D. Newton, "Optimization of low energy electrostatic beam lines," Proceedings of IPAC2014, 2014.

11. Papash, A., A. Smirnov, and C. Welsch, "Nonlinear and long-term beam dynamics in low energy storage rings," Physical Review Special Topics --- Accelerators and Beams, Vol. 16, No. 6, 060101, 2013.

12. Maher, S., F. P. Jjunju, and S. Taylor, "Colloquium: 100 years of mass spectrometry: Perspectives and future trends," Reviews of Modern Physics, Vol. 87, No. 1, 113, 2015.

13. Taminger, K. M., W. H. Hofmeister, and R. A. Halfey, "Use of beam deflection to control an electron beam wire deposition process,", US Patent 8,344,281, Jan. 2013.

14. Koleva, E., V. Dzharov, V. Gerasimov, K. Tsvetkov, and G. Mladenov, "Electron beam delfection control system of a welding and surface modification installation," Journal of Physics: Conference Series, Vol. 992, 012013, IOP Publishing, 2018.

15. Kasisomayajula, V., M. Booty, A. Fiory, and N. Ravindra, "Magnetic field assisted heterogeneous device assembly," Supplemental Proceedings: Materials Processing and Interfaces, Vol. 1, 651-661, 2012.

16. Fernández-Morán, H., "Electron microscopy with high-field superconducting solenoid lenses," Proceedings of the National Academy of Sciences of the United States of America, Vol. 53, No. 2, 445, 1965.

17. Fernández-Morán, H., "High-resolution electron microscopy with superconducting lenses at liquid helium temperatures," Proceedings of the National Academy of Sciences of the United States of America, Vol. 56, No. 3, 801, 1966.

18. Bordelon, D. E., R. C. Goldstein, V. S. Nemkov, A. Kumar, J. K. Jackowski, T. L. De-Weese, and R. Ivkov, "Modified solenoid coil that efficiently produces high amplitude ac magnetic fields with enhanced uniformity for biomedical applications," IEEE Transactions on Magnetics, Vol. 48, No. 1, 47-52, 2011.

19. Drees, J. and H. Piel, "Particle beam treatment system with solenoid magnets,", US Patent App. 15/203,966, Jan. 12 2017.

20. Berz, M., B. Erdélyi, and K. Makino, "Fringe field effects in small rings of large acceptance," Physical Review Special Topics --- Accelerators and Beams, Vol. 3, No. 12, 124001, 2000.

21. Makino, K. and M. Berz, "Solenoid elements in cosy infinity," Institute of Physics CS, Vol. 175, 219-228, 2004.

22. Aslaninejad, M., C. Bontoiu, J. Pasternak, J. Pozimski, and A. Bogacz, "Solenoid fringe field effects for the neutrino factory linac-mad-x investigation," Tech. Rep., Thomas Jefferson National Accelerator Facility, Newport News, VA (United States), 2010.

23. Gorlov, T. and J. Holmes, "Fringe field effect of solenoids," 9th International Particle Accelerator Conference (IPAC2018), IPAC, 3385-3387, JaCoW Publishing, Vancouver, BC, Canada, 2018.

24. Migliorati, M. and G. Dattoli, "Transport matrix of a solenoid with linear fringe field," Il Nuovo Cimento della Società Italiana di Fisica-B: General Physics, Relativity, Astronomy and Mathematical Physics and Methods, Vol. 124, No. 4, 385, 2009.

25. Cebron, D., "Magnetic fields of solenoids and magnets,", https://www.mathworks.com/matlabcentral/fileexchange/71881-magnetic-fields-of-solenoids-and-magnets, 2019, Retrieved Sept. 26, 2019.

26. Derby, N. and S. Olbert, "Cylindrical magnets and ideal solenoids," American Journal of Physics, Vol. 78, No. 3, 229-235, 2010.

27. Callaghan, E. E. and S. H. Maslen, "The magnetic field of a finite solenoid," Tech. Rep., NASA, 1960.

28. Lerner, L., "Magnetic field of a finite solenoid with a linear permeable core," American Journal of Physics, Vol. 79, No. 10, 1030-1035, 2011.

29. Muniz, S. R., V. S. Bagnato, and M. Bhattacharya, "Analysis of off-axis solenoid fields using the magnetic scalar potential: An application to a zeeman-slower for cold atoms," American Journal of Physics, Vol. 83, No. 6, 513-517, 2015.

30. Lim, M. X. and H. Greenside, "The external magnetic field created by the superposition of identical parallel finite solenoids," American Journal of Physics, Vol. 84, No. 8, 606-615, 2016.

31. Arpaia, P., B. Celano, L. De Vito, A. Esposito, A. Parrella, and A. Vannozzi, "Measuring the magnetic axis alignment during solenoids working," Scientific Reports, Vol. 8, No. 1, 11426, 2018.

32. Arpaia, P., L. De Vito, A. Esposito, A. Parrella, and A. Vannozzi, "On-field monitoring of the magnetic axis misalignment in multi-coils solenoids," Journal of Instrumentation, Vol. 13, No. 08, P08017, 2018.

33. Arpaia, P., B. Celano, L. De Vito, A. Esposito, N. Moccaldi, and A. Parrella, "Monitoring the magnetic axis misalignment in axially-symmetric magnets," 2018 IEEE International Instrumentation and Measurement Technology Conference (I2MTC), 1-6, IEEE, 2018.

34. Read, F. H. and N. J. Bowring, "The cpo programs and the bem for charged particle optics," Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 645, No. 1, 273-277, 2011.

35. Smith, R. T., F. P. Jjunju, and S. Maher, "Evaluation of electron beam deflections across a solenoid using Weber-Ritz and Maxwell-Lorentz electrodynamics," Progress In Electromagnetics Research, Vol. 151, 83-93, 2015.

36. Smith, R. T. and S. Maher, "Investigating electron beam deflections by a long straight wire carrying a constant current using direct action, emission-based and field theory approaches of electrodynamics," Progress In Electromagnetics Research B, Vol. 75, 79-89, 2017.

37. Baumgärtel, C., R. T. Smith, and S. Maher, "Accurately predicting electron beam deflections in fringing fields of a solenoid," Scientific Reports, Vol. 10, No. 1, 1-13, 2020.

38. Smith, R. T., S. Taylor, and S. Maher, "Modelling electromagnetic induction via accelerated electron motion," Canadian Journal of Physics, Vol. 93, No. 7, 802-806, 2014.

39. Smith, R. T., F. P. Jjunju, I. S. Young, S. Taylor, and S. Maher, "A physical model for low-frequency electromagnetic induction in the near field based on direct interaction between transmitter and receiver electrons," Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 472, No. 2191, 20160338, 2016.

40. Baumgärtel, C. and S. Maher, "A novel model of unipolar induction phenomena based on direct interaction between conductor charges," Progress In Electromagnetics Research, Vol. 171, 123-135, 2021.

41. Assis, A. and M. Tajmar, "Superconductivity with weber's electrodynamics: The london moment and the meissner effect," Annales de la Fondation Louis de Broglie, Vol. 42, 307, 2017.

42. Prytz, K. A., "Meissner effect in classical physics," Progress In Electromagnetics Research M, Vol. 64, 1-7, 2018.

43. Torres-Silva, H., J. Lόpez-Bonilla, R. Lόpez-Vázquez, and J. Rivera-Rebolledo, "Weber's electrodynamics for the hydrogen atom," Indonesian Journal of Applied Physics, Vol. 5, No. 01, 39-46, 2015.

44. Frauenfelder, U. and J. Weber, "The fine structure of Weber's hydrogen atom: Bohr-sommerfeld approach," Zeitschrift für angewandte Mathematik und Physik, Vol. 70, No. 4, 105, 2019.

45. Tajmar, M., "Derivation of the planck and fine-structure constant from Assis's gravity model," Journal of Advanced Physics, Vol. 4, No. 3, 219-221, 2015.

46. Baumgärtel, C. and M. Tajmar, "The planck constant and the origin of mass due to a higher order casimir effect," Journal of Advanced Physics, Vol. 7, No. 1, 135-140, 2018.

47. Weber, W. E., Wilhelm Weber's Werke,, Vol. 3 (First part), Julius Springer, Berlin, 1893.

48. Maxwell, J. C., "Xxv. on physical lines of force: Part i. --- The theory of molecular vortices applied to magnetic phenomena," The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Vol. 21, No. 139, 161-175, 1861.

49. Maxwell, J. C., A Treatise on Electricity and Magnetism Unabridged, Dover, 1954.

50. Yaghjian, A., "Reflections on Maxwell's treatise," Progress In Electromagnetics Research, Vol. 149, 217-249, 2014.

51. Assis, A. K. T., Weber's Electrodynamics, 47-77, Springer, Dordrecht, 1994.

52. Kinzer, E. and J. Fukai, "Weber's force and Maxwell's equations," Foundations of Physics Letters, Vol. 9, No. 5, 457-461, 1996.

53. O'Rahilly, A., Electromagnetic Theory: A Critical Examination of Fundamentals, Vol. I and II, Dover Publications, 1965.

54. Wesley, J. P., "Weber electrodynamics, Part I. General theory, steady current effects," Foundations of Physics Letters, Vol. 3, No. 5, 443-469, 1990.

55. Li, Q., "Electric field theory based on Weber's electrodynamics," International Journal of Magnetics and Electromagnetism, Vol. 7:039, No. 2, 1-6, 2021.

56. Slepian, J., "Lines of force in electric and magnetic fields," American Journal of Physics, Vol. 19, No. 2, 87-90, 1951.

57. Mendes, R., L. Malacarne, and A. Assis, Virial Theorem For Weber's Law, 67-70, Rinton Press, Paramus, 2004.