Folded waveguide slow wave structure, traveling wave tube and design method

By adjusting the position and structural parameters of the inner arc boundary, the slow wave structure of the folded waveguide was optimized, solving the problems of bandwidth and loss limitations in the traditional structure. This resulted in higher coupling impedance, flatter dispersion, and lower loss, thus improving the performance of the terahertz traveling wave tube.

CN120048708BActive Publication Date: 2025-12-05BEIJING VACUUM ELECTRONIC TECH RES INST (THE 12TH RES INST OF CHINA ELECTRONICS TECH CORP)
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Patent Information

Application Number
CN202510156325.7
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2025-02-12
Publication Date
2025-12-05
Estimated Expiration
2045-02-12

AI Technical Summary

Technical Problem

In traditional folded waveguide slow wave structures, the electron beam channel radius limits bandwidth expansion, coupling impedance improvement, and loss reduction, thus restricting the performance improvement of terahertz traveling wave tubes.

Method used

A folded waveguide slow-wave structure is designed by adjusting the position of the inner arc boundary so that its center and junction are located inside the electron beam channel and the arc tip is located outside the electron beam channel. The structural parameters, including the spacing height between the inner arc boundary and the straight waveguide section, are optimized using three-dimensional electromagnetic field simulation software to form a multi-periodic structure.

Benefits of technology

It improves the coupling impedance and dispersion characteristics of the high-frequency slow-wave structure, expands the bandwidth and reduces losses, enhances the interaction strength and output power, and achieves greater bandwidth and lower line loss.

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Abstract

The application provides a folded waveguide slow wave structure, a traveling wave tube and a design method. The folded waveguide slow wave structure comprises a multi-periodic structure formed by a plurality of upper grid bodies and a plurality of lower grid bodies staggered with each other, and the folded waveguide slow wave structure comprises a straight waveguide section, a curved waveguide connecting section and an electron beam channel. The curved waveguide connecting section comprises an inner circular arc boundary. The inner circular arc boundary and the straight waveguide section comprise an inner circular arc joint. The center of the inner circular arc boundary and the inner circular arc joint are located within the boundary defined by the electron beam channel, and the arc top end point of the inner circular arc boundary is located outside the boundary defined by the electron beam channel. The folded waveguide slow wave structure can improve the performance of a terahertz traveling wave tube.
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Description

Technical Field

[0001] This invention relates to the field of microwave vacuum electronics technology. More specifically, it relates to a folded waveguide slow-wave structure, a traveling wave tube, and a design method thereof. Background Technology

[0002] Terahertz traveling-wave tubes (TWTs) are a type of vacuum amplifier used to amplify the power of terahertz waves, playing a crucial role in the development of terahertz technology. The slow-wave structure is where the microwave signal exchanges energy with the electron beam within the TWT. Currently, the folded waveguide slow-wave structure is the most suitable for a circular beam in the terahertz band. This is an all-metal structure with strong heat dissipation, a large bandwidth, a simple and easy-to-fabricate input-output coupling structure, and low high-frequency loss, making it extremely promising for future development.

[0003] Traditional folded waveguide slow-wave structures are pipe structures formed by bending the E-plane of a rectangular waveguide and arranging it periodically along the axial direction. Its basic structural unit and its main views are shown below. Figures 1A-1C As shown, the central circular channel is the electron beam channel 30. The microwave signal propagates along a tortuous path within the waveguide cavity 10, thereby reducing the phase velocity. In this structure, the centers of the inner and outer circular arcs coincide, the inner and outer walls of the straight waveguide section are at the same height, and the centers of the inner and outer circular arcs are located at the top of the inner and outer walls of the straight waveguide. The dimensional parameters of this structure are as follows: electron beam channel radius r; slow wave structure half-cycle length p (full cycle length 2p); straight waveguide section length h; waveguide wide side length a; waveguide narrow side length b. The channel diameter is 2r, and the channel penetrates the inner and outer walls of the straight waveguide section and is closed. In this structure, the island region 20 is a combination of a straight waveguide and an ideal semicircle. In traditional structures, because h > 2r, the movement of the inner circle center towards the channel center is restricted, thus limiting bandwidth expansion, coupling impedance improvement, and loss reduction. This significantly limits the performance improvement of terahertz traveling wave tubes. Summary of the Invention

[0004] To address the above problems, this invention provides a folded waveguide slow-wave structure to improve the performance of terahertz traveling wave tubes.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] This invention provides a folded waveguide slow wave structure, comprising a multi-periodic structure defined by a plurality of upper gratings and a plurality of lower gratings arranged in an alternating manner. The folded waveguide slow wave structure includes a connected straight waveguide section, a curved waveguide connecting section, and an electron beam channel. The curved waveguide connecting section includes an inner circular arc boundary. An inner circular arc junction is included between the inner circular arc boundary and the straight waveguide section.

[0007] The center of the inner arc boundary and the junction of the inner arc are both located within the boundary defined by the electron injection channel, while the apex of the inner arc boundary is located outside the boundary defined by the electron injection channel.

[0008] The preferred embodiment is that the inner arc boundary is a semi-circular arc.

[0009] The preferred embodiment is that the electron beam channel radius is r, the half-cycle length of the slow wave structure is p, the narrow side length of the straight waveguide section is b, and the first interval height between the center of the inner arc boundary and the axis of the electron beam channel in the radial direction of the electron beam channel is h1; 2r-p+b

[0010] In a preferred embodiment, the curved waveguide connection segment further includes an outer circular arc boundary, and the second interval height between the center of the outer circular arc boundary and the axis of the electron beam channel in the radial direction of the electron beam channel is greater than the radius of the electron beam channel.

[0011] A preferred embodiment is that the outer arc boundary is a semi-circular arc or a superior arc.

[0012] The preferred embodiment is that the first interval height between the center of the inner arc boundary and the axis of the electron injection channel in the radial direction of the electron injection channel is h1, and the second interval height between the center of the outer arc boundary and the axis of the electron injection channel in the radial direction of the electron injection channel is h2; h1 < h2.

[0013] The present invention also provides a traveling wave tube, comprising the folded waveguide slow wave structure described above.

[0014] This invention also provides a design method for a folded waveguide slow-wave structure, the design method comprising:

[0015] An initial folded waveguide slow wave structure is designed according to requirements. This initial folded waveguide slow wave structure includes a connected straight waveguide section, a curved waveguide connecting section, and an electron beam channel.

[0016] Using three-dimensional electromagnetic field simulation software, the center of the inner arc boundary and the junction of the inner arc boundary and the straight waveguide segment are moved down so that the center of the inner arc boundary and the junction of the inner arc are both located within the boundary defined by the electron beam channel, and the apex of the inner arc boundary is located outside the boundary defined by the electron beam channel.

[0017] The preferred embodiment is that the inner arc boundary is a semi-circular arc; the electron beam channel radius is r, the half-cycle length of the slow wave structure is p, the narrow side length of the straight waveguide section is b, and the first interval height between the center of the inner arc boundary and the axis of the electron beam channel in the radial direction of the electron beam channel is h1; 2r-p+b

[0018] ​​The preferred approach is to adjust the coupling impedance and loss of the folded waveguide slow wave structure by changing the first interval height between the center of the inner arc boundary and the axis of the electron beam channel in the radial direction of the electron beam channel, thereby optimizing the performance of the folded waveguide slow wave structure.

[0019] The beneficial effects of this invention are as follows:

[0020] This invention improves the coupling impedance, dispersion, and loss of the high-frequency slow-wave structure by shifting the center of the inner arc boundary and the junction between the inner arc boundary and the straight waveguide segment downwards. This ensures that the center of the inner arc boundary and the junction between the inner arc boundary and the straight waveguide segment are located within the boundary defined by the electron beam channel, while the apex of the inner arc boundary is located outside the boundary defined by the electron beam channel, thus preserving the integrity of the electron beam channel. Compared to traditional folded waveguide slow-wave structures, the coupling impedance of the slow-wave structure of this invention increases by up to 40% at low frequencies and up to 11% at high frequencies within the operating frequency band, exhibiting stronger interaction strength and enabling the traveling wave tube to have greater output power. The dispersion flatness of the slow-wave structure of this invention is significantly improved, resulting in a flatter dispersion curve, thus providing a larger bandwidth and a loss reduction of up to 30%, significantly reducing line loss. Attached Figure Description

[0021] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0022] Figures 1A-1C This is a schematic diagram of a traditional folded waveguide slow wave structure.

[0023] Figures 2A-2C This is a schematic diagram of the folded waveguide slow wave structure of the present invention.

[0024] Figure 3 This is a comparison diagram of the coupling impedance curves of the present invention and the traditional folded waveguide slow wave structure.

[0025] Figure 4 This is a comparison diagram of the dispersion curves of the present invention and the traditional folded waveguide slow wave structure.

[0026] Figure 5 This is a comparison of the loss characteristic curves of the present invention and the traditional folded waveguide slow wave structure.

[0027] Figure 6 This is a structural schematic diagram of one half of the structure of the present invention.

[0028] Figure 7 This is a schematic diagram showing the variation of the in-band coupling impedance of the folded waveguide slow wave structure of the present invention with the first spacing height h1.

[0029] Figure 8 This is a schematic diagram showing the change in loss characteristics of the folded waveguide slow wave structure of the present invention with the first gap height h1. Detailed Implementation

[0030] Various exemplary embodiments of the present invention will now be described in detail with reference to the accompanying drawings. It should be noted that, unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps set forth in these embodiments do not limit the scope of the invention.

[0031] The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the invention or its application or use.

[0032] Technologies and equipment known to those skilled in the art may not be discussed in detail, but where appropriate, such technologies and equipment should be considered part of the specification.

[0033] In all the examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values.

[0034] It should be noted that similar labels and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be discussed further in subsequent figures.

[0035] To improve the performance of terahertz traveling wave tubes, this invention provides a folded waveguide slow-wave structure, combined with... Figures 1A to 8As shown, the folded waveguide slow-wave structure specifically includes a multi-periodic structure defined by multiple upper and lower gratings arranged in an alternating pattern. The folded waveguide slow-wave structure includes a connected straight waveguide segment 1, a curved waveguide connecting segment 2, and an electron beam channel 3, wherein the electron beam channel 3 is a circular cross-section channel. The curved waveguide connecting segment 2 includes an inner circular arc boundary C1; an inner circular arc junction Q1 is included between the inner circular arc boundary C1 and the straight waveguide segment 1; the center O1 corresponding to the inner circular arc boundary and the inner circular arc junction Q1 are both located within the boundary defined by the electron beam channel 3, and the apex of the inner circular arc boundary C1 is located outside the boundary defined by the electron beam channel 3. This invention can improve the slow-wave structure without increasing structural complexity, giving the slow-wave structure advantages such as high coupling impedance, low loss, and flat dispersion, which can significantly increase power capacity, reduce line loss, and expand bandwidth. The straight waveguide segment 1 includes an inner straight boundary and an outer straight boundary. The inner circular arc boundary C1 and the inner straight boundary of the straight waveguide segment 1 include an inner circular arc junction Q1. This invention adjusts the height h1 of the first interval between the center O1 of the inner circular arc boundary and the electron beam channel axis L0 by adjusting only the height of the inner straight boundary of the straight waveguide segment 1. This achieves the adjustment of the position of the center O1 of the inner circular arc boundary and the position of the inner circular arc junction Q1, thereby improving the performance of the slow-wave structure. It can be understood that, taking a single-cycle folded waveguide slow-wave structure as an example, the heights of the inner boundaries of the two straight waveguide segments 1 are adjusted simultaneously, and the heights of the inner boundaries of the two straight waveguide segments 1 are always equal.

[0036] In the above embodiment, the inner arc boundary C1 is a semi-circular arc. In this case, the center O1 corresponding to the inner arc boundary is located on the line connecting the two inner arc junctions Q1. That is, the inner arc boundary C1 and the boundary defined by the electron beam channel 3 include two junction points; in the height direction of the slow-wave structure, the two junction points are located between the inner arc junction Q1 and the apex point of the inner arc boundary C1.

[0037] Furthermore, the inner circular arc boundary C1 satisfies the following relationship: 2r-p+b

[0038] In one specific embodiment, the curved waveguide connection segment further includes an outer circular arc boundary C2. The second interval height h2 between the center O2 of the outer circular arc boundary and the electron beam channel axis L0 in the radial direction of the electron beam channel is greater than the electron beam channel radius. The second interval height h2 is formed between the center O2 of the outer circular arc boundary and the electron beam channel axis L0 in the radial direction of the electron beam channel. The first interval height h1 between the center O1 of the inner circular arc boundary and the electron beam channel axis L0 in the radial direction of the electron beam channel, and the second interval height h2 between the center O2 of the outer circular arc boundary and the electron beam channel axis L0 in the radial direction of the electron beam channel, satisfy the following relationship: h1 < h2.

[0039] Furthermore, to ensure the electrical performance of the slow-wave structure, the outer circular arc boundary C2 is a semi-circular arc or a superior arc. This is because designing the outer circular arc boundary as a inferior arc would lead to a decrease in the electrical performance of the slow-wave structure.

[0040] The center of the inner arc boundary is designated O1, and its position is determined by the first gap height h1 between the center of the inner arc boundary and the electron beam channel axis. The center of the outer arc boundary is designated O2, and its position is determined by the second gap height h2. By adjusting h1 and h2, the positions of the centers O1 and O2 of the inner and outer arc boundaries can be controlled, thereby directly affecting the performance of the slow-wave structure.

[0041] The present invention also provides a traveling wave tube, comprising the folded waveguide slow wave structure described above.

[0042] ​This invention also provides a design method for a folded waveguide slow-wave structure. The method includes: designing an initial folded waveguide slow-wave structure as needed, the initial folded waveguide slow-wave structure including a connected straight waveguide segment 1, a curved waveguide connecting segment 2, and an electron beam channel 3; using three-dimensional electromagnetic field simulation software, shifting down the center O1 corresponding to the inner arc boundary and the inner arc junction Q1 between the inner arc boundary C1 and the straight waveguide segment 1, so that the center O1 corresponding to the inner arc boundary and the inner arc junction Q1 are both located within the boundary defined by the electron beam channel 3, and the apex point of the inner arc boundary C1 is located outside the boundary defined by the electron beam channel 3. The slow-wave structure obtained through this design method can improve the overall performance of terahertz band slow-wave structures and increase the design freedom of slow-wave structures.

[0043] Furthermore, the inner circular arc boundary C1 is a semi-circular arc; the electron beam channel radius is r, the half-cycle length of the slow wave structure is p, the narrow side length of the straight waveguide section is b, and the first interval height between the center O1 corresponding to the inner circular arc boundary and the electron beam channel axis L0 in the radial direction of the electron beam channel is h1; 2r-p+b

[0044] More specifically, by changing the first gap height h1 in the radial direction of the electron beam channel between the center O1 of the inner arc boundary and the electron beam channel axis L0, the coupling impedance and loss of the folded waveguide slow-wave structure are adjusted, thus optimizing the performance of the folded waveguide slow-wave structure. Reducing the first gap height h1 of the center O1 of the inner arc boundary increases the width of the curved waveguide, enhances the electromagnetic field in the electron beam direction of the straight waveguide gap, thereby improving the coupling impedance; simultaneously, reducing the first gap height h1 shortens the equivalent transmission path of the electromagnetic wave, thereby reducing transmission loss. The slow-wave structure is the site where the electron beam and microwave signal exchange energy; the shape and size of the slow-wave structure determine the field distribution and transmission. The study of the slow-wave structure's performance mainly focuses on three major characteristics: coupling impedance characteristics, loss characteristics, and dispersion characteristics. Using three-dimensional electromagnetic field simulation software, the effect of continuously shifting the position of the center O1 of the inner arc boundary on the coupling impedance and loss characteristics was simulated. (Refer to...) Figure 7 As shown, the distance h2 between the center O2 of the outer arc boundary of the slow-wave structure and the electron beam channel axis L0 in the radial direction of the electron beam channel remains constant. As the first distance h1 gradually decreases, the position of the center O1 of the inner arc boundary continuously shifts downward. The coupling impedance of the slow-wave structure of this invention increases significantly, indicating a stronger interaction strength and suggesting that the traveling wave tube has greater output power. (Refer to...) Figure 8 ​As shown, the distance between the center O2 of the outer arc boundary of the slow wave structure and the electron beam channel axis L0 in the radial direction of the electron beam channel remains constant at h2. As the first distance height h1 gradually decreases, the position of the center O1 of the inner arc boundary continuously moves downward, and the line loss of the present invention gradually decreases, indicating that it has greater output power.

[0045] The following is an embodiment of the present invention with specific structural parameters. First, a conventional folded waveguide slow-wave structure is designed, yielding the following dimensions: a = 0.74 mm, b = 0.12 mm, r = 0.12 mm, p = 0.275 mm, h = 0.3 mm. Based on this conventional folded waveguide slow-wave structure, the positions of the first and second interval heights h1 and h2 between the center O1 of the inner arc boundary and the electron beam channel axis—that is, the center O1 of the inner arc boundary and the center O2 of the outer arc boundary—are adjusted. According to the design of the present invention, lowering the center O1 of the inner arc boundary significantly improves the three major characteristics of the slow-wave structure. As the center O1 of the inner arc boundary is continuously lowered, when h1 = (2r - p + b) = (2 * 0.12 - 0.275 + 0.12) = 0.085 mm, the island region 4 will be in a critical state. To ensure the three main characteristics, h1 > (2r - p + b). In this invention, the slow-wave structure takes h1 = 0.15. h2 remains unchanged at h2 = 0.3. p remains unchanged at p = 0.275 mm. The value of a is optimized based on maintaining a synchronous voltage comparable to that of the conventional structure, i.e., the normalized phase velocity, and is finally determined to be a = 0.755 mm. Therefore, the main parameters of the slow-wave structure of this invention are a = 0.755 mm, h1 = 0.15 mm, h2 = 0.3 mm, b = 0.12 mm, p = 0.27 mm, and r = 0.12 mm. The calculation results of the three main performance characteristics (coupling impedance characteristics, dispersion characteristics, and loss characteristics) of the slow-wave structure based on the above structural parameters are as follows: Figures 3-5 As shown.

[0046] Specifically, using three-dimensional electromagnetic field simulation software, the performance comparison of the two circuits in this application—the slow-wave structure and the conventional folded waveguide slow-wave structure—was simulated and compared. Figure 3 The figure shows a comparison of the coupling impedance curves of the slow-wave structure of this application and the conventional folded waveguide slow-wave structure. Compared with the conventional folded waveguide slow-wave structure, the coupling impedance in the frequency band of this invention is increased from 2-5.2Ω to 2.8-5.8Ω, with an increase of up to 40% at the low-frequency end and 11% at the high-frequency end, which indicates a stronger interaction strength and suggests that the traveling wave tube has greater output power. Figure 4This is a comparison of the dispersion curves of the slow-wave structure of this application and the conventional folded waveguide slow-wave structure, which characterize the operating voltage and bandwidth of the traveling wave tube. At 217 GHz, both have the same normalized phase velocity, indicating that the traveling wave tube has the same voltage. Within the bandwidth, the phase velocity change rate of the slow-wave structure of this application is 0.0012 C / GHz, while that of the conventional slow-wave structure is 0.0018 C / GHz. The dispersion flatness of the slow-wave structure of this application is significantly improved, indicating that the slow-wave structure of this application has a larger bandwidth. Figure 5 This diagram compares the loss characteristics of the slow-wave structure of this application with those of a conventional folded waveguide slow-wave structure. Compared to the conventional folded waveguide slow-wave structure, the loss of the present invention is reduced from 310-440 dB / m to 230-310 dB / m within the frequency band, a reduction of up to 30%, indicating a significant reduction in line loss. In summary, the slow-wave structure of this invention has significant advantages over the conventional folded waveguide slow-wave structure in terms of coupling impedance, dispersion characteristics, and loss characteristics, while also being compatible with existing precision machining processes.

[0047] In the actual fabrication process, the slow-wave structure of this invention can be divided into two semi-circular copper pillars by splitting the entire circular copper pillar along the yz plane. A row of folded waveguide grooves and half an electron beam channel are then fabricated on each semi-circular copper pillar. The actual fabrication model of the semi-circular copper pillar is shown below. Figure 6 As shown. After processing, the two semi-circular copper pillars are joined together and pressure-diffused welded into one piece to obtain the slow-wave structure of this application. The area enclosed by the folded waveguide grooves on the two semi-circular copper pillars forms the waveguide cavity of the folded waveguide slow-wave structure; the area enclosed by the electron beam channels on the two semi-circular copper pillars forms the electron beam channel of the folded waveguide slow-wave structure.

[0048] In summary, this invention improves the coupling impedance, dispersion, and loss of the high-frequency slow-wave structure by shifting the center of the inner arc boundary and the junction between the inner arc boundary and the straight waveguide segment downwards. This ensures that the center of the inner arc boundary and the junction between the inner arc boundary and the straight waveguide segment are located within the boundary defined by the electron beam channel, while the apex of the inner arc boundary is located outside the boundary defined by the electron beam channel, thus preserving the integrity of the electron beam channel. Compared to traditional folded waveguide slow-wave structures, the coupling impedance of the slow-wave structure of this invention increases by up to 40% at low frequencies and up to 11% at high frequencies within the operating frequency band, exhibiting stronger interaction strength and enabling the traveling wave tube to have greater output power. The dispersion flatness of the slow-wave structure of this invention is significantly improved, resulting in a flatter dispersion curve, thus providing a larger bandwidth and a loss reduction of up to 30%, significantly reducing line loss.

[0049] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. For those skilled in the art, other variations or modifications can be made based on the above description. It is impossible to exhaustively list all the implementation methods here. All obvious variations or modifications derived from the technical solutions of the present invention are still within the protection scope of the present invention.

Claims

1. A folded waveguide slow wave structure, characterized by, The folded waveguide slow wave structure comprises a plurality of upper gate bodies and a plurality of lower gate bodies staggered with each other, a straight waveguide section, a curved waveguide connecting section and an electron beam channel; the curved waveguide connecting section comprises an inner circular arc boundary; the inner circular arc boundary and the straight waveguide section comprise an inner circular arc joint; The center of the inner circular arc boundary and the inner circular arc joint are located within the boundary of the electron beam channel, and the arc top point of the inner circular arc boundary is located outside the boundary of the electron beam channel. The radius of the electron beam channel is r, the half-period length of the slow wave structure is p, the narrow side length of the straight waveguide section is b, and the first interval height between the center of the inner circular arc boundary and the axis of the electron beam channel in the radial direction of the electron beam channel is h1; 2r-p+b<h1<r.

2. The folded waveguide slow wave structure of claim 1, wherein, The inner circular arc boundary is a semicircular arc.

3. The folded waveguide slow wave structure of claim 1, wherein, The curved waveguide connecting section further comprises an outer circular arc boundary, and the second interval height between the center of the outer circular arc boundary and the axis of the electron beam channel in the radial direction of the electron beam channel is greater than the radius of the electron beam channel.

4. The folded waveguide slow wave structure of claim 3, wherein, The outer circular arc boundary is a semicircular arc or an optimal arc.

5. The folded waveguide slow wave structure of claim 3, wherein, The first interval height between the center of the inner circular arc boundary and the axis of the electron beam channel in the radial direction of the electron beam channel is h1, and the second interval height between the center of the outer circular arc boundary and the axis of the electron beam channel in the radial direction of the electron beam channel is h2; h1<h2.

6. A traveling wave tube, characterized by, The design method comprises:

7. A method of designing a folded waveguide slow wave structure, characterized by, The design method comprises: The design method comprises: The design method comprises: The inner circular arc boundary is a semicircular arc; the radius of the electron beam channel is r, the half-period length of the slow wave structure is p, the narrow side length of the straight waveguide section is b, and the first interval height between the center of the inner circular arc boundary and the axis of the electron beam channel in the radial direction of the electron beam channel is h1; 2r-p+b<h1<r.

8. The design method of claim 7, wherein, By changing the first interval height between the center of the inner circular arc boundary and the axis of the electron beam channel in the radial direction of the electron beam channel, the coupling impedance and loss of the folded waveguide slow wave structure are adjusted, and the performance of the folded waveguide slow wave structure is optimized.

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