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Studying the accuracy of geometrized models of ribbon electron beams
- Authors: Sapronova T.M.1, Syrovoy V.A.1
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Affiliations:
- Russian Federal Nuclear Center All-Russian Scientific Research Institute of Technical Physics named after academician E.I. Zababakhin
- Issue: Vol 69, No 3 (2024)
- Pages: 260-287
- Section: ЭЛЕКТРОННАЯ И ИОННАЯ ОПТИКА
- URL: https://cijournal.ru/0033-8494/article/view/650702
- DOI: https://doi.org/10.31857/S0033849424030078
- EDN: https://elibrary.ru/JUZAEZ
- ID: 650702
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Abstract
Using a set of standard exact solutions described by ordinary differential equations and elementary functions, geometrized models of plane electron beams in l-, and W-representations were studied. A comparison is made of the capabilities of the geometrized approach and the paraxial theory.
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About the authors
T. M. Sapronova
Russian Federal Nuclear Center All-Russian Scientific Research Institute of Technical Physics named after academician E.I. Zababakhin
Author for correspondence.
Email: red@cplire.ru
All-Russian Electrotechnical Institute
Russian Federation, Krasnokazarmennaya Str., 12, Moscow, 111250V. A. Syrovoy
Russian Federal Nuclear Center All-Russian Scientific Research Institute of Technical Physics named after academician E.I. Zababakhin
Email: red@cplire.ru
All-Russian Electrotechnical Institute
Russian Federation, Krasnokazarmennaya Str., 12, Moscow, 111250References
- Сыровой В.А. // Прикл. физика. 1997. № 2–3. С. 69.
- Акимов П.И., Гаврилин А.А., Никитин А.П. и др. // РЭ. 2018. Т. 63. № 11. С. 1303.
- Гамаюнов Ю.Г., Патрушева Е.В., Тореев А.И., Шаталина С.А. // РЭ. 2008. Т. 53. № 3. С. 344.
- Гамаюнов Ю.Г., Патрушева Е.В. // РЭ. 2017. Т. 62. № 11. С. 1126.
- Гамаюнов Ю.Г., Патрушева Е.В. // РЭ. 2020. Т. 65. № 5. С. 507.
- Сыровой В.А. Введение в теорию интенсивных пучков заряженных частиц. М.: Энергоатомиздат, 2004.
- Овчаров В.Т. // РЭ. 1962. Т. 7. № 8. С. 1368.
- Овчаров В.Т., Пензяков В.В. // РЭ. 1970. Т. 15. № 8. С. 1651.
- Данилов В.Н. // Журн. прикл. механики и техн. физики. 1968. № 5. С. 3.
- Пензяков В.В., Олейников В.И. // РЭ. 1975. Т. 20. № 5. С. 1049.
- Сыровой В.А. // РЭ. 2008. Т. 53. № 8. С. 999.
- Сыровой В.А. // РЭ. 2011. Т. 56. № 1. С. 111.
- Сыровой В.А. // РЭ. 2016. Т. 61. № 7. С. 692.
- Сыровой В.А. Теория интенсивных пучков заряженных частиц. М.: Энергоатомиздат, 2004.
- Сыровой В.А. // РЭ. 2013. Т. 58. № 6. С. 614.
- Сыровой В.А. // РЭ. 2017. Т. 62. № 5. С. 502.
- Сыровой В.А. // РЭ. 2019. Т. 64. № 1. С. 82.
- Сыровой В.А. // РЭ. 2022. Т. 67. № 6. С. 615.
- Вашковский А.В., Неганова Л.А., Сыровой В.А. // Прикл. физика. 1998. № 3–4. С. 33.
- Сапронова Т.М., Сыровой В.А. // РЭ. 2010. Т. 55. № 6. С. 726.
- Сапронова Т.М., Сыровой В.А. // РЭ. 2020. Т. 65. № 12. С. 1209.
- Meltzer B. // J. Electr. Contr. 1956. V. 2. № 2. P. 118.
- Kirstein P.T., Kino G.S. // J. Appl. Phys. 1958. V. 29. № 12. P. 1758.
- Kirstein P.T. // J. Appl. Phys. 1958. V. 4. № 5. P. 425.
- Meltzer B. // Proc. Phys. Soc. 1949. V. 62B. № 355. P. 431.
Supplementary files
Supplementary Files
Action
1.
JATS XML
2.
Fig. 1. Flow with circular trajectories from the half-plane ψ = 0, p is the mode.
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3.
Fig. 2. Beam boundary and cathode shape in three approximations (1, 2, 3) l-representations of the geometrized theory (4 ‒ exact solution, spiral trajectories), divergent flow (a), convergent flow (b).
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4.
Fig. 3. Flat periodic electrostatic flow, dashed lines represent equipotentials, solid lines represent trajectories.
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5.
Fig. 4. Derivatives of x, y by x1, x2 for periodic flow.Fig. 4. Derivatives of x, y by x1, x2 for periodic flow.
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6.
Fig. 5. Functions characterizing approximate models for periodic flow.
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7.
Fig. 6. Flow with hyperbola trajectories in a homogeneous magnetic field.
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8.
Fig. 7. Derivatives of x, y with respect to x1, x2 for a flow with hyperbola trajectories (a) in the vicinity of the injection plane (b) at Ω = 1 (1), 5 (2) and 10 (3).
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9.
Fig. 8. Functions characterizing approximate models for electrostatic flow with hyperbola trajectories (Ω = 1); 1, 2, 3 – an approximation of the geometrized theory, a 4–paraxial model.
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10.
Fig. 9. The trajectory of the beam boundary with the hyperbola axis at Ω = 5, f(0) = 0.1; 1 is the exact solution, 2 is the paraxial model.
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11.
Fig. 10. Derivatives of x, y with respect to x1, x2 for a flow with the hyperbola axis Ω = 5 (a), in the vicinity of the injection plane (b); 1 is the l representation, 2 is the W representation.
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12.
Fig. 11. Functions characterizing the W-representation of the geometrized theory for flows with hyperbolic trajectories at Ω = 5, f(0) = 0.2.
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13.
Fig. 12. Derivatives of x, y with respect to x1, x2 for a flow with hyperbola trajectories, W is a variant of the theory (a), the vicinity of the injection plane (b), Ω = 5 (1) and 10 (2).
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14.
Fig. 13. Junki structures a W-shaped theory for determination using hybrid algorithms at Ω = 10, f(0) = 0.2.
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15.
Fig. 14. Flow with elliptical orbits in a homogeneous magnetic field.
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16.
Fig. 15. Derivatives of x, y by x1, x2 for a flow with elliptical orbits at Ω = 0.16.
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17.
Fig. 16. Functions characterizing approximate models for flows with elliptical orbits at Ω = 0.16, f(0) = 0.1, f(a) = 0.25; 1, 2, 3 – approximations of geometrized theory, 4–paraxial model.
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