Studying the accuracy of geometrized models of ribbon electron beams

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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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作者简介

T. Sapronova

Russian Federal Nuclear Center All-Russian Scientific Research Institute of Technical Physics named after academician E.I. Zababakhin

编辑信件的主要联系方式.
Email: red@cplire.ru

All-Russian Electrotechnical Institute

俄罗斯联邦, Krasnokazarmennaya Str., 12, Moscow, 111250

V. 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

俄罗斯联邦, Krasnokazarmennaya Str., 12, Moscow, 111250

参考

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1. JATS XML
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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. 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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5. Fig. 5. Functions characterizing approximate models for periodic flow.

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6. Fig. 6. Flow with hyperbola trajectories in a homogeneous magnetic field.

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7. 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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8. 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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9. 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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10. 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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11. 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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12. 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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13. Fig. 13. Junki structures a W-shaped theory for determination using hybrid algorithms at Ω = 10, f(0) = 0.2.

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14. Fig. 14. Flow with elliptical orbits in a homogeneous magnetic field.

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15. Fig. 15. Derivatives of x, y by x1, x2 for a flow with elliptical orbits at Ω = 0.16.

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16. 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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