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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://ruspoj.com/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
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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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