Studying the accuracy of geometrized models of ribbon electron beams

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription or Fee Access

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.

Full Text

Restricted Access

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, 111250

V. 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, 111250

References

  1. Сыровой В.А. // Прикл. физика. 1997. № 2–3. С. 69.
  2. Акимов П.И., Гаврилин А.А., Никитин А.П. и др. // РЭ. 2018. Т. 63. № 11. С. 1303.
  3. Гамаюнов Ю.Г., Патрушева Е.В., Тореев А.И., Шаталина С.А. // РЭ. 2008. Т. 53. № 3. С. 344.
  4. Гамаюнов Ю.Г., Патрушева Е.В. // РЭ. 2017. Т. 62. № 11. С. 1126.
  5. Гамаюнов Ю.Г., Патрушева Е.В. // РЭ. 2020. Т. 65. № 5. С. 507.
  6. Сыровой В.А. Введение в теорию интенсивных пучков заряженных частиц. М.: Энергоатомиздат, 2004.
  7. Овчаров В.Т. // РЭ. 1962. Т. 7. № 8. С. 1368.
  8. Овчаров В.Т., Пензяков В.В. // РЭ. 1970. Т. 15. № 8. С. 1651.
  9. Данилов В.Н. // Журн. прикл. механики и техн. физики. 1968. № 5. С. 3.
  10. Пензяков В.В., Олейников В.И. // РЭ. 1975. Т. 20. № 5. С. 1049.
  11. Сыровой В.А. // РЭ. 2008. Т. 53. № 8. С. 999.
  12. Сыровой В.А. // РЭ. 2011. Т. 56. № 1. С. 111.
  13. Сыровой В.А. // РЭ. 2016. Т. 61. № 7. С. 692.
  14. Сыровой В.А. Теория интенсивных пучков заряженных частиц. М.: Энергоатомиздат, 2004.
  15. Сыровой В.А. // РЭ. 2013. Т. 58. № 6. С. 614.
  16. Сыровой В.А. // РЭ. 2017. Т. 62. № 5. С. 502.
  17. Сыровой В.А. // РЭ. 2019. Т. 64. № 1. С. 82.
  18. Сыровой В.А. // РЭ. 2022. Т. 67. № 6. С. 615.
  19. Вашковский А.В., Неганова Л.А., Сыровой В.А. // Прикл. физика. 1998. № 3–4. С. 33.
  20. Сапронова Т.М., Сыровой В.А. // РЭ. 2010. Т. 55. № 6. С. 726.
  21. Сапронова Т.М., Сыровой В.А. // РЭ. 2020. Т. 65. № 12. С. 1209.
  22. Meltzer B. // J. Electr. Contr. 1956. V. 2. № 2. P. 118.
  23. Kirstein P.T., Kino G.S. // J. Appl. Phys. 1958. V. 29. № 12. P. 1758.
  24. Kirstein P.T. // J. Appl. Phys. 1958. V. 4. № 5. P. 425.
  25. Meltzer B. // Proc. Phys. Soc. 1949. V. 62B. № 355. P. 431.

Supplementary files

Supplementary Files
Action
1. JATS XML
Download
2. Fig. 1. Flow with circular trajectories from the half-plane ψ = 0, p is the mode.

Download (89KB)
Indexing metadata
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).

Download (165KB)
Indexing metadata
4. Fig. 3. Flat periodic electrostatic flow, dashed lines represent equipotentials, solid lines represent trajectories.

Download (169KB)
Indexing metadata
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.

Download (143KB)
Indexing metadata
6. Fig. 5. Functions characterizing approximate models for periodic flow.

Download (262KB)
Indexing metadata
7. Fig. 6. Flow with hyperbola trajectories in a homogeneous magnetic field.

Download (94KB)
Indexing metadata
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).

Download (314KB)
Indexing metadata
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.

Download (289KB)
Indexing metadata
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.

Download (78KB)
Indexing metadata
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.

Download (286KB)
Indexing metadata
12. Fig. 11. Functions characterizing the W-representation of the geometrized theory for flows with hyperbolic trajectories at Ω = 5, f(0) = 0.2.

Download (272KB)
Indexing metadata
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).

Download (293KB)
Indexing metadata
14. Fig. 13. Junki structures a W-shaped theory for determination using hybrid algorithms at Ω = 10, f(0) = 0.2.

Download (257KB)
Indexing metadata
15. Fig. 14. Flow with elliptical orbits in a homogeneous magnetic field.

Download (68KB)
Indexing metadata
16. Fig. 15. Derivatives of x, y by x1, x2 for a flow with elliptical orbits at Ω = 0.16.

Download (121KB)
Indexing metadata
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.

Download (306KB)
Indexing metadata

Copyright (c) 2024 Russian Academy of Sciences