Design and Method of Symmetric Grating Structure for Traveling Wave Amplifier

Design and Method of Symmetric Grating Structure for Traveling Wave Amplifier | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Design and Method of Symmetric Grating Structure for Traveling Wave Amplifier Qinwen Xue, Xuesong Yuan, Zhongtao Cui, Yunze Zhu, Matthew Thomas Cole, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6519536/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Excellent performance high frequency structures are critical to the development of millimeter wave and terahertz traveling wave amplifiers (TWAs). The plane symmetric grating structure (SGS) has the advantages of large transverse dimension, simple structure and easy to manufacture with one-dimensional processing. The TM 11 mode in SGS has characteristics of high coupling impedance and strong resonance, but its bandwidth is narrow, which limits its application in sheet beam traveling wave tube. It is found that the bandwidth of SGS can be effectively expanded by loading the coupled waveguide (operating in TE 10 mode) in parallel with the symmetric grating in this paper. The experiment of expand the bandwidth of SGS has been done in the Ka-band. The results show that the relative bandwidth of SGS can be widened from 0.03–8.3%. Besides, a G-band TWA is designed, and the cross-sectional area of its slow wave structure is more than twice that of the traditional high frequency structure. The PIC simulation results demonstrate that the maximum power is 169 W at 219 GHz, corresponding to a gain of 27.2 dB, and the − 3dB bandwidth is 10.5 GHz. Symmetric grating structure High frequency structure Traveling wave tube Vacuum electronics Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 1 Introduction Millimeter and terahertz radiation sources have proven themselves essential in high speed communications, and phased array radar applications [1], [2], [3]. When developing higher frequency radiation sources, the size of high-frequency structures is limited due to the decreased transversal dimension, which brings difficulties in designing the electron optical systems as well as in the manufacturing and processing of the high-frequency structures [4]. Folded waveguides [5], sine waveguides [6], helix [7], microstrip meander lines [8] and staggered double corrugated waveguides [9] and other structures show good performance in traveling wave amplifiers (TWAs). As a kind of classical slow wave structure, rectangular grating slow wave structure has many advantages, such as simple structure, large lateral size, and compatibility with planar micromachining technology, which is widely used in backward wave oscillator [10], extended interaction device [11], [12], traveling wave tube [13], diffraction radiation oscillator [14] and so on [15]. Rectangular grating slow wave structures are generally divided into double grating structures (symmetrical [16] and staggered) and single grating structures [17]. This paper mainly discusses the symmetric double grating structure. The common symmetric grating structure (SGS) is presented in Fig. 1 (a). There are two modes in the SGS, as shown in Fig. 1 (b) and (c), which respectively regarded as TE 10 mode and TM 11 mode. In Fig. 1 (b), TE 10 mode has a large bandwidth. However, the axial electric field is distributed asymmetrically about the plane x = 0 [18], [19], which leads to the very low coupling impedance at the gap. It is not conducive to the beam wave interaction between electrons and electromagnetic fields. In Fig. 1 (c), the axial electric field is symmetrically distributed about the plane x = 0, and it has a very strong coupling impedance, which is beneficial to the beam wave interaction between electrons and electromagnetic fields. However, its bandwidth is very narrow, and there are few works to apply this mode to TWA at present. The researchers found that the staggered grating structure can be obtained by moving the symmetric grating in the z-axis direction for a certain distance [20], as shown in Fig. 1 (d). Therefore, the electric field distribution can also change, as displayed in Fig. 1 (e) and (f), that Fig. 1 (e) corresponds to Fig. 1 (b), Fig. 1 (f) corresponds to Fig. 1 (c). A lot of research has been done on this structure. When the high-frequency structure works in the mode of Fig. 1 (e) [21], [22], [23], the cutoff frequency of this mode depends on the lateral width. Hence, affected by the size coordination effect, the device will be similar to the wavelength at high frequency. Besides, there is also leakage in the electron beam tunnel, which needs to be suppressed by the Bragg reflector. Moreover, when the high frequency structure works in the mode of Fig. 1 (f), inevitably, the backward wave oscillation of the fundamental mode and the self-excited oscillation of the 3π point will be produced [24], [25], [26]. For the SGS in Fig. 1 (c), increasing the thickness of the grating and changing the transverse dimension of beam tunnel, the electric field distribution will not be changed. It reduces the pressure of processing technology and ensures the efficiency of beam wave interaction. Then rotate it 90 degrees along the z-axis and increase the number of periods to get Fig. 1 (h). We use the coupling waveguide shown in Fig. 1 (g) to connect in parallel with the SGS depicted in Fig. 1 (h). Finally, the electric field distribution of the proposed high frequency structure is acquired, as described in Fig. 1 (i). Therefore, the vacuum model of a single cycle for proposed TWA is shown in Fig. 1 (j). 2 Beam Wave Interaction Model and Experiment Verification According to the design idea of the slow wave structure mentioned above, the ideal mode diagram of the whole high frequency system of the proposed TWA is given below, as shown in Fig. 2 . The whole circuit is mainly divided into two parts, the coupled waveguide and SGS. The specific principle is described as follows. The signal is injected into the standard waveguide from port 1, entering coupled waveguide through the transition section. When the partial signal arrives at the coupling hole, it couples into the symmetric grating continuously. The coupled signals interact with the electron beam to obtain an amplified high frequency signal. In particular, the electron beam interacts with the RF field indirectly by gratings. Then the amplified signal is diverted to the coupled waveguide. Finally, the combined power goes out from the standard waveguide port 2. To demonstrate the bandwidth enhancement intuitively, the dispersion of single period is calculated by eigenmode solver firstly in Ka-band. As shown in Fig. 3 (a), the dispersion of SGS is almost a straight line with an absolute bandwidth of 101 MHz. Furthermore, the absolute bandwidth of the single period dispersion curve obtained by expanding the coupled waveguide based on the SGS as shown in Fig. 3 (b) reaches 2.76 GHz. It can be calculated that the relative bandwidth based on the extension of coupled waveguide has increased from 0.03–8.3%. At the same time, comparing the electric field distribution of the two structures inserted in the figure, we can find that they are both TM 11 mode, which is proved that this method can effectively broaden the bandwidth of SGS. Then, to verify the feasibility of the slow wave structure in TWA, we have carried out experimental research. The fabricated models are shown in Fig. 4 (a). It has two parts. One is coupled waveguide, which digs out a part component in standard waveguide WR-28 due to its high pass characteristics. The other is SGS. It consists of two pieces of metal periodic grating, which is etched by machining and milling technology. Then two halves are bonded and assembled with coupled waveguide, as shown in Fig. 4 (b). We use a vector network analyzer (VNA, Model: AV3672C) to test the S-parameters, and the experiment results and simulation results of TWA are shown in Fig. 4 . By comparison, the resonance characteristics of S 11 and the passband characteristics of S 21 are in good agreement. The experimental findings demonstrate that S 11 -3dB in the range of 32.5–34.4 GHz as shown in Fig. 4 (d). For S 21 , it can be found that the measured results are a little lower than the simulation results. It is possible to the leakage of waves without welding and surface loss. Therefore, it is proved that the bandwidth of SGS can be expanded by coupling waveguide through the verification experiments of processing and assembly. 3 Application in G-band TWA Next, to illustrate the hot characteristics of the proposed high frequency structure, a G-band TWA is designed by PIC simulation. Figure 5 shows a cross-sectional view of the proposed circuit. Considering the conductor loss and surface roughness in the G-band, the conductivity is set to 2.2×107 S/m, which is made of copper. A summary of the geometry parameters is listed in the table I. Figure 6 (a) depicts the dispersion relationship of a single period structure. The dotted line is drawn according to the beam wave interaction theory, which is synchronism voltage, providing effective modulation with the electron beam. Figure 6 (b) describes the coupling impedance at point A, the centre of the beam tunnel, which is marked in Fig. 5 (a). Figure 7 shows the S-parameter of the TWA. Port1 is input and port 2 is output. Port 3 is set at the emission end of the electron beam tunnel, and port 4 is set at the end. S 11 is lower than − 15 dB from 214 GHz to 230 GHz. S 31 , and S 41 are both below − 155dB. The circuit operates at the forward + 1st spatial harmonic. To test the amplifier in high current density, a sheet beam is adopted. The hot performance of the TWA is simulated. The operating voltage was set to 26.8 kV, the current is 0.3 A, the cross-sectional area of beam is 0.7 × 0.1 mm, the current density is 428 A/cm2, the number of pitches is 62, and the total length of the beam tunnel is 32.9 mm, and the longitudinal magnetic field is 0.55 T. As shown in Fig. 8 (a), when the input signal is 0.32 W, the maximum power obtained at the frequency of 219 GHz is 169 W. The illustration in Fig. 8 (a) shows the Fourier transform of the frequency spectrum at 219 GHz. Note the absence of any parasitic components. The gain of the output signal is 27.2dB and the gain per unit length of the beam tunnel translates to 8.45dB/cm. Figure 8 (b) describes the variation of the gain and output power with frequency, where the particle bunching effect as an illustration is seen. The − 3dB bandwidth is 10.5 GHz. Table 1 Parameters of structure. Symbol Description Value(mm) a Long side of coupled waveguide 0.92 b Narrow side of coupled waveguide 0.34 ga Long side of grating 1.54 gb Narrow side of grating 0.78 ta Broad side of beam tunnel 1.04 tb Narrow side of beam tunnel 0.16 p Period 0.52 h Thickness of the vane 0.3 According to the maximum output power at 219 GHz, the characteristic is discussed in detail further. As shown in Fig. 9 , the power flow distribution (i.e. Poynting vector) of the proposed TWA is conducted from the perspective of microwave transmission. Figure 9 (a) describes the cold characteristic, it is obvious that the transmission signal of the waveguide is attenuated along the longitudinal direction, and the energy in the grating is also reduced because of ohmic loss. Figure 9 (b) shows the hot characteristic. After the electron beam interacts with the modes in the grating, the amplified signal is continuously coupled into the waveguide through the coupling hole and superimposed, and finally output from the waveguide. Figure 9 (c) captures the last few periods of Fig. 9 (a). It can be seen that there is no longitudinal transmission component in the grating, indicating that there is a standing wave inside. Figure 9 (d) captures the last few periods of Fig. 9 (b). It can be seen that the signal is amplified. Figure 9 (e) is the vacuum model of TWA. The standard waveguide WR-4 is used at the input and output ports. There is an integral surface set at the junction of coupled waveguide and SGS, marked by the dotted line. The surface integral of the Poynting vector is calculated. The normal vectors of all integral surfaces are in the y direction. The power change relationship as a function of time is in Fig. 9 (f). The green line represents the result of integration from the S1 (the 56th period), the red represents the result of integration from the S2 (the last period), and the bule represents the sum of integration Stotal of all faces. It can be seen from the Fig. 9 (f) that the power at S2 is greater than that at S1, indicating that the energy change trend in the symmetrical grating is consistent with that in the coupled waveguide. And, the average value of Stotal is equal to the output signal. It is verified that the power is exchanged along the y-axis. That is to say, the coupled signal in the symmetric grating interacts with the electron beam and excites a high frequency field, continuously feeding the coupled waveguide for superposition. 4 Conclusion A method for expanding the bandwidth of SGS to develop millimeter wave and terahertz TWAs is proposed in this paper, which is verified by experiments. The SGS connected in parallel with the coupled waveguide realize the traveling wave amplification, which shows good performance application in G-band TWA. PIC simulation results demonstrate that the advantages of the modelled device are as follows. Firstly, the cross-sectional area of the proposed structure (0.92×1.88 (i.e. a*(ga + b))) has been increased by a factor of 4.67, compared with the standard WR-3 waveguide (0.86×0.43mm). The thickness of the grating with the same length of single period in the SGS is 2–3 times that of staggered double slow wave structure. It improves the mechanical strength of the structure in terahertz TWA. Secondly, because it is extended on the basis of rectangular waveguide, it does not need any complicated input and output structures for ultra-wideband traveling wave signal high-frequency system. Finally, the linear/sheet beam tolerates slight changes in size and position of the electron beam tunnel reducing any effect on the transmission characteristics for operating mode, thereby largely mitigating any impacts of machining errors on transmission performance. Declarations Authors contributions. Qinwen Xue: Data curation (equal); Investigation (equal); Writing -original draft (equal). Xuesong Yuan: Conceptualization (equal); Funding acquisition (equal); Investigation (equal); Writing - review &editing (equal). Zhongtao Cui: Investigation (equal). Yunze Zhu: Data curation (equal). Investigation (equal). Matthew Thomas Cole: Writing-review & editing (equal). Yanyu Wei: Investigation (equal). Yang Yan: Investigation (lead). Acknowledgments. This work was supported by the Natural Science Foundation of Sichuan Province under Grant 2024NSFSC0467 and National Natural Science Foundation of China under Grant 61771096. Competing Interests. The authors declare no competing interests. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6519536","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":450102588,"identity":"b74a88e0-54b4-47d4-b01b-f9c46ecac161","order_by":0,"name":"Qinwen Xue","email":"","orcid":"","institution":"University of Electronic Science and Technology of China","correspondingAuthor":false,"prefix":"","firstName":"Qinwen","middleName":"","lastName":"Xue","suffix":""},{"id":450102589,"identity":"6610bc26-0e29-4acf-9c84-b06e718ef964","order_by":1,"name":"Xuesong Yuan","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAzUlEQVRIiWNgGAWjYPACGxiDmWgtaTDVxGs5TIIWgxvJzx7z/Dmf2M9//uAHhgrrxAb2swcIaEkzN5zZdjtx5oxkZgmGM+mJDTx5CQS0JJhJfGy4nbjhBjMbA2Pb4cQGCR4DAlrSv0kk/DmXuP/8YaCWf0RpyTGT+MB2IHEDQzJQSwMRWiTPvCmTnNmWbDzjRrKxRMKxdOM2nhz8WviOp2+T5vljJ9vff/Dhhw811rL97Gfwa1E4gMxLAGI2vOqBQL6BkIpRMApGwSgYBQCiUkWlJ9toqwAAAABJRU5ErkJggg==","orcid":"","institution":"University of Electronic Science and Technology of China","correspondingAuthor":true,"prefix":"","firstName":"Xuesong","middleName":"","lastName":"Yuan","suffix":""},{"id":450102590,"identity":"3b732f85-4de4-4bed-bdeb-442df9b62a8d","order_by":2,"name":"Zhongtao Cui","email":"","orcid":"","institution":"University of Electronic Science and Technology of China","correspondingAuthor":false,"prefix":"","firstName":"Zhongtao","middleName":"","lastName":"Cui","suffix":""},{"id":450102591,"identity":"3c248a67-d349-43de-89e6-fa8e11bcf8d5","order_by":3,"name":"Yunze Zhu","email":"","orcid":"","institution":"University of Electronic Science and Technology of China","correspondingAuthor":false,"prefix":"","firstName":"Yunze","middleName":"","lastName":"Zhu","suffix":""},{"id":450102592,"identity":"260d7435-6b3e-48a0-bee2-18c5809159ca","order_by":4,"name":"Matthew Thomas Cole","email":"","orcid":"","institution":"University of Bath","correspondingAuthor":false,"prefix":"","firstName":"Matthew","middleName":"Thomas","lastName":"Cole","suffix":""},{"id":450102594,"identity":"b1e37cd6-f4e7-4efe-a0a1-38c2da0d787a","order_by":5,"name":"Yanyu Wei","email":"","orcid":"","institution":"University of Electronic Science and Technology of China","correspondingAuthor":false,"prefix":"","firstName":"Yanyu","middleName":"","lastName":"Wei","suffix":""},{"id":450102595,"identity":"4456e05b-6bfc-446c-97ee-b7b13ff270cc","order_by":6,"name":"Yang Yan","email":"","orcid":"","institution":"University of Electronic Science and Technology of China","correspondingAuthor":false,"prefix":"","firstName":"Yang","middleName":"","lastName":"Yan","suffix":""}],"badges":[],"createdAt":"2025-04-24 09:53:27","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6519536/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6519536/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":81959438,"identity":"d0ac72ef-1a36-40aa-8b63-ef6ff15730b7","added_by":"auto","created_at":"2025-05-05 10:27:35","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":233205,"visible":true,"origin":"","legend":"\u003cp\u003eThe design idea diagram of the operating mode for the proposed traveling wave amplifier.\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-6519536/v1/4d8d0d5118325ca085ee47f2.png"},{"id":81959437,"identity":"61f7f7d2-4e27-449b-ab99-90f890216230","added_by":"auto","created_at":"2025-05-05 10:27:35","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":108691,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic of the traveling wave amplifier.\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-6519536/v1/3173d68cd876067529112a86.png"},{"id":81959447,"identity":"1f7e3c0e-616d-46d0-b323-6cd21f9df7ec","added_by":"auto","created_at":"2025-05-05 10:27:36","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":88092,"visible":true,"origin":"","legend":"\u003cp\u003eDispersion characteristics. (a) SGS in detail. Insert: Electric field distribution and single period model. (b) The slow wave structure in this paper. Insert: Electric field distribution and single period model.\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-6519536/v1/84cf31721f63d8c635d9951e.png"},{"id":81959445,"identity":"fc87e833-9392-40d3-a7b8-06157b2195c0","added_by":"auto","created_at":"2025-05-05 10:27:36","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":309825,"visible":true,"origin":"","legend":"\u003cp\u003eExperimental verification. (a) Photograph of fabricated components. (b) Assembly. (c) S\u003csub\u003e11\u003c/sub\u003e. (d) S\u003csub\u003e21\u003c/sub\u003e.\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-6519536/v1/5760bfb8349382c17a74b282.png"},{"id":81959441,"identity":"78a12d71-aca9-4ad8-b032-44d9b7390743","added_by":"auto","created_at":"2025-05-05 10:27:36","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":75962,"visible":true,"origin":"","legend":"\u003cp\u003eCross-sectional schematic diagram. (a)\u003cem\u003e x-y\u003c/em\u003e plane. (b) \u003cem\u003ey-z\u003c/em\u003e plane.\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-6519536/v1/3c8400931fee3e7a5b4c3ffa.png"},{"id":81959439,"identity":"b46266a0-f87c-40b1-8b25-94e29ff40389","added_by":"auto","created_at":"2025-05-05 10:27:35","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":68003,"visible":true,"origin":"","legend":"\u003cp\u003eSingle period characteristic. (a) Dispersion diagrams. (b) Coupling impedance\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-6519536/v1/e582f592b1c21df05b088442.png"},{"id":81960440,"identity":"c8609709-7f2b-4bc0-bc68-62ae68a6948f","added_by":"auto","created_at":"2025-05-05 10:43:36","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":95473,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic diagram of S-parameter. (a)S\u003csub\u003e11\u003c/sub\u003e and S\u003csub\u003e21\u003c/sub\u003e. (b)S\u003csub\u003e31\u003c/sub\u003e and S\u003csub\u003e41\u003c/sub\u003e.\u003c/p\u003e","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-6519536/v1/6a9ea0670280302516a08d30.png"},{"id":81959450,"identity":"c38ad833-82a5-4dea-ac3f-1151fb9a8e40","added_by":"auto","created_at":"2025-05-05 10:27:36","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":125942,"visible":true,"origin":"","legend":"\u003cp\u003eTWA performance. (a) Input and Output signal at 219 GHz. Inset: Spectrum diagram. (b) Output power and gain. Inset: Beam bunching\u003c/p\u003e","description":"","filename":"floatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-6519536/v1/7d7a143ea9ec64509d14c974.png"},{"id":81959707,"identity":"edbabff7-c430-44d5-864e-b2351521a0a8","added_by":"auto","created_at":"2025-05-05 10:35:36","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":290818,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic diagram of power flow at 219 GHz. (a) Cold characteristic. (b) Hot characteristic. (c) Cold characteristic in detail. (d) Hot characteristic in detail. (e) Vacuum model of TWA. (f) Poynting vector integrated over S\u003csub\u003etotal\u003c/sub\u003e, S\u003csub\u003e1\u003c/sub\u003e and S\u003csub\u003e2\u003c/sub\u003e.\u0026nbsp;\u003c/p\u003e","description":"","filename":"floatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-6519536/v1/cc758de483a6069d2f510a6e.png"},{"id":93697244,"identity":"bc25112c-e6eb-43d8-ac36-d70f60cc7d57","added_by":"auto","created_at":"2025-10-16 14:53:54","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1800733,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6519536/v1/c7b90b67-3a10-4d56-8349-4cc676e1a2d4.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Design and Method of Symmetric Grating Structure for Traveling Wave Amplifier","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eMillimeter and terahertz radiation sources have proven themselves essential in high speed communications, and phased array radar applications [1], [2], [3]. When developing higher frequency radiation sources, the size of high-frequency structures is limited due to the decreased transversal dimension, which brings difficulties in designing the electron optical systems as well as in the manufacturing and processing of the high-frequency structures [4]. Folded waveguides [5], sine waveguides [6], helix [7], microstrip meander lines [8] and staggered double corrugated waveguides [9] and other structures show good performance in traveling wave amplifiers (TWAs). As a kind of classical slow wave structure, rectangular grating slow wave structure has many advantages, such as simple structure, large lateral size, and compatibility with planar micromachining technology, which is widely used in backward wave oscillator [10], extended interaction device [11], [12], traveling wave tube [13], diffraction radiation oscillator [14] and so on [15].\u003c/p\u003e \u003cp\u003eRectangular grating slow wave structures are generally divided into double grating structures (symmetrical [16] and staggered) and single grating structures [17]. This paper mainly discusses the symmetric double grating structure. The common symmetric grating structure (SGS) is presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(a). There are two modes in the SGS, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e (b) and (c), which respectively regarded as TE\u003csub\u003e10\u003c/sub\u003e mode and TM\u003csub\u003e11\u003c/sub\u003e mode. In Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e (b), TE\u003csub\u003e10\u003c/sub\u003e mode has a large bandwidth. However, the axial electric field is distributed asymmetrically about the plane x\u0026thinsp;=\u0026thinsp;0 [18], [19], which leads to the very low coupling impedance at the gap. It is not conducive to the beam wave interaction between electrons and electromagnetic fields. In Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e (c), the axial electric field is symmetrically distributed about the plane x\u0026thinsp;=\u0026thinsp;0, and it has a very strong coupling impedance, which is beneficial to the beam wave interaction between electrons and electromagnetic fields. However, its bandwidth is very narrow, and there are few works to apply this mode to TWA at present. The researchers found that the staggered grating structure can be obtained by moving the symmetric grating in the z-axis direction for a certain distance [20], as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e (d). Therefore, the electric field distribution can also change, as displayed in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e (e) and (f), that Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e (e) corresponds to Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e (b), Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e (f) corresponds to Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e (c). A lot of research has been done on this structure. When the high-frequency structure works in the mode of Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e (e) [21], [22], [23], the cutoff frequency of this mode depends on the lateral width. Hence, affected by the size coordination effect, the device will be similar to the wavelength at high frequency. Besides, there is also leakage in the electron beam tunnel, which needs to be suppressed by the Bragg reflector. Moreover, when the high frequency structure works in the mode of Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e (f), inevitably, the backward wave oscillation of the fundamental mode and the self-excited oscillation of the 3π point will be produced [24], [25], [26].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFor the SGS in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e (c), increasing the thickness of the grating and changing the transverse dimension of beam tunnel, the electric field distribution will not be changed. It reduces the pressure of processing technology and ensures the efficiency of beam wave interaction. Then rotate it 90 degrees along the z-axis and increase the number of periods to get Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(h). We use the coupling waveguide shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e (g) to connect in parallel with the SGS depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e (h). Finally, the electric field distribution of the proposed high frequency structure is acquired, as described in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e (i). Therefore, the vacuum model of a single cycle for proposed TWA is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e (j).\u003c/p\u003e"},{"header":"2 Beam Wave Interaction Model and Experiment Verification","content":"\u003cp\u003eAccording to the design idea of the slow wave structure mentioned above, the ideal mode diagram of the whole high frequency system of the proposed TWA is given below, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. The whole circuit is mainly divided into two parts, the coupled waveguide and SGS.\u003c/p\u003e \u003cp\u003eThe specific principle is described as follows. The signal is injected into the standard waveguide from port 1, entering coupled waveguide through the transition section. When the partial signal arrives at the coupling hole, it couples into the symmetric grating continuously. The coupled signals interact with the electron beam to obtain an amplified high frequency signal. In particular, the electron beam interacts with the RF field indirectly by gratings. Then the amplified signal is diverted to the coupled waveguide. Finally, the combined power goes out from the standard waveguide port 2.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo demonstrate the bandwidth enhancement intuitively, the dispersion of single period is calculated by eigenmode solver firstly in Ka-band. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e (a), the dispersion of SGS is almost a straight line with an absolute bandwidth of 101 MHz. Furthermore, the absolute bandwidth of the single period dispersion curve obtained by expanding the coupled waveguide based on the SGS as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e (b) reaches 2.76 GHz. It can be calculated that the relative bandwidth based on the extension of coupled waveguide has increased from 0.03\u0026ndash;8.3%. At the same time, comparing the electric field distribution of the two structures inserted in the figure, we can find that they are both TM\u003csub\u003e11\u003c/sub\u003e mode, which is proved that this method can effectively broaden the bandwidth of SGS.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThen, to verify the feasibility of the slow wave structure in TWA, we have carried out experimental research. The fabricated models are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e (a). It has two parts. One is coupled waveguide, which digs out a part component in standard waveguide WR-28 due to its high pass characteristics. The other is SGS. It consists of two pieces of metal periodic grating, which is etched by machining and milling technology. Then two halves are bonded and assembled with coupled waveguide, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e (b).\u003c/p\u003e \u003cp\u003eWe use a vector network analyzer (VNA, Model: AV3672C) to test the S-parameters, and the experiment results and simulation results of TWA are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. By comparison, the resonance characteristics of S\u003csub\u003e11\u003c/sub\u003e and the passband characteristics of S\u003csub\u003e21\u003c/sub\u003e are in good agreement. The experimental findings demonstrate that S\u003csub\u003e11\u003c/sub\u003e\u0026lt;-5 dB in the range of 32-34.6 GHz is detailed in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e(c). And, S\u003csub\u003e21\u003c/sub\u003e of \u0026gt;-3dB in the range of 32.5\u0026ndash;34.4 GHz as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e (d). For S\u003csub\u003e21\u003c/sub\u003e, it can be found that the measured results are a little lower than the simulation results. It is possible to the leakage of waves without welding and surface loss. Therefore, it is proved that the bandwidth of SGS can be expanded by coupling waveguide through the verification experiments of processing and assembly.\u003c/p\u003e"},{"header":"3 Application in G-band TWA","content":"\u003cp\u003eNext, to illustrate the hot characteristics of the proposed high frequency structure, a G-band TWA is designed by PIC simulation. Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e shows a cross-sectional view of the proposed circuit. Considering the conductor loss and surface roughness in the G-band, the conductivity is set to 2.2\u0026times;107 S/m, which is made of copper. A summary of the geometry parameters is listed in the table I. Figure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(a) depicts the dispersion relationship of a single period structure. The dotted line is drawn according to the beam wave interaction theory, which is synchronism voltage, providing effective modulation with the electron beam. Figure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(b) describes the coupling impedance at point A, the centre of the beam tunnel, which is marked in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(a).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e shows the S-parameter of the TWA. Port1 is input and port 2 is output. Port 3 is set at the emission end of the electron beam tunnel, and port 4 is set at the end. S\u003csub\u003e11\u003c/sub\u003e is lower than \u0026minus;\u0026thinsp;15 dB from 214 GHz to 230 GHz. S\u003csub\u003e31\u003c/sub\u003e, and S\u003csub\u003e41\u003c/sub\u003e are both below \u0026minus;\u0026thinsp;155dB.\u003c/p\u003e \u003cp\u003eThe circuit operates at the forward\u0026thinsp;+\u0026thinsp;1st spatial harmonic. To test the amplifier in high current density, a sheet beam is adopted. The hot performance of the TWA is simulated. The operating voltage was set to 26.8 kV, the current is 0.3 A, the cross-sectional area of beam is 0.7 \u0026times; 0.1 mm, the current density is 428 A/cm2, the number of pitches is 62, and the total length of the beam tunnel is 32.9 mm, and the longitudinal magnetic field is 0.55 T. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e(a), when the input signal is 0.32 W, the maximum power obtained at the frequency of 219 GHz is 169 W. The illustration in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e(a) shows the Fourier transform of the frequency spectrum at 219 GHz. Note the absence of any parasitic components. The gain of the output signal is 27.2dB and the gain per unit length of the beam tunnel translates to 8.45dB/cm. Figure\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e(b) describes the variation of the gain and output power with frequency, where the particle bunching effect as an illustration is seen. The \u0026minus;\u0026thinsp;3dB bandwidth is 10.5 GHz.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eParameters of structure.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSymbol\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDescription\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eValue(mm)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ea\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLong side of coupled waveguide\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.92\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eb\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNarrow side of coupled waveguide\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.34\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ega\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLong side of grating\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.54\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003egb\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNarrow side of grating\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.78\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eta\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBroad side of beam tunnel\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.04\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003etb\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNarrow side of beam tunnel\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.16\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ep\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePeriod\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.52\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eh\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eThickness of the vane\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAccording to the maximum output power at 219 GHz, the characteristic is discussed in detail further. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e, the power flow distribution (i.e. Poynting vector) of the proposed TWA is conducted from the perspective of microwave transmission. Figure\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e (a) describes the cold characteristic, it is obvious that the transmission signal of the waveguide is attenuated along the longitudinal direction, and the energy in the grating is also reduced because of ohmic loss. Figure\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e (b) shows the hot characteristic. After the electron beam interacts with the modes in the grating, the amplified signal is continuously coupled into the waveguide through the coupling hole and superimposed, and finally output from the waveguide. Figure\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e (c) captures the last few periods of Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e (a). It can be seen that there is no longitudinal transmission component in the grating, indicating that there is a standing wave inside. Figure\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e (d) captures the last few periods of Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e (b). It can be seen that the signal is amplified. Figure\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e (e) is the vacuum model of TWA. The standard waveguide WR-4 is used at the input and output ports. There is an integral surface set at the junction of coupled waveguide and SGS, marked by the dotted line. The surface integral of the Poynting vector is calculated. The normal vectors of all integral surfaces are in the y direction. The power change relationship as a function of time is in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e(f). The green line represents the result of integration from the S1 (the 56th period), the red represents the result of integration from the S2 (the last period), and the bule represents the sum of integration Stotal of all faces. It can be seen from the Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e(f) that the power at S2 is greater than that at S1, indicating that the energy change trend in the symmetrical grating is consistent with that in the coupled waveguide. And, the average value of Stotal is equal to the output signal. It is verified that the power is exchanged along the y-axis. That is to say, the coupled signal in the symmetric grating interacts with the electron beam and excites a high frequency field, continuously feeding the coupled waveguide for superposition.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"4 Conclusion","content":"\u003cp\u003eA method for expanding the bandwidth of SGS to develop millimeter wave and terahertz TWAs is proposed in this paper, which is verified by experiments. The SGS connected in parallel with the coupled waveguide realize the traveling wave amplification, which shows good performance application in G-band TWA. PIC simulation results demonstrate that the advantages of the modelled device are as follows. Firstly, the cross-sectional area of the proposed structure (0.92\u0026times;1.88 (i.e. a*(ga\u0026thinsp;+\u0026thinsp;b))) has been increased by a factor of 4.67, compared with the standard WR-3 waveguide (0.86\u0026times;0.43mm). The thickness of the grating with the same length of single period in the SGS is 2\u0026ndash;3 times that of staggered double slow wave structure. It improves the mechanical strength of the structure in terahertz TWA. Secondly, because it is extended on the basis of rectangular waveguide, it does not need any complicated input and output structures for ultra-wideband traveling wave signal high-frequency system. Finally, the linear/sheet beam tolerates slight changes in size and position of the electron beam tunnel reducing any effect on the transmission characteristics for operating mode, thereby largely mitigating any impacts of machining errors on transmission performance.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003eAuthors contributions. Qinwen Xue: Data curation (equal); Investigation (equal); Writing -original draft (equal). Xuesong Yuan: Conceptualization (equal); Funding acquisition (equal); Investigation (equal); Writing - review \u0026amp;editing (equal). Zhongtao Cui: Investigation (equal). Yunze Zhu:\u0026nbsp;Data curation\u0026nbsp;(equal).\u0026nbsp;Investigation (equal). Matthew Thomas Cole: Writing-review \u0026amp; editing (equal).\u0026nbsp;Yanyu Wei: Investigation (equal). Yang Yan: Investigation (lead).\u003c/p\u003e\n\u003cp\u003eAcknowledgments.\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003eThis work was supported by the Natural Science Foundation of Sichuan Province under Grant 2024NSFSC0467 and National Natural Science Foundation of China under Grant 61771096.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eCompeting Interests.\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003eThe authors declare no competing interests.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eEthical Approval. Not applicable.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eQu B, Li Z, Zhao S, et al.: Design and Experimental Study of an E-Band CW Space TWT. IEEE Trans. on Plasma Science \u003cstrong\u003e51\u003c/strong\u003e(4), 1059-1064 (2023)\u003c/li\u003e\n\u003cli\u003eHuang Y, Shen Y, Wang J.: From terahertz imaging to terahertz wireless communications. Engineering \u003cstrong\u003e22\u003c/strong\u003e(3), 106-124 (2023)\u003c/li\u003e\n\u003cli\u003eC. Paoloni et. al.: Horizon 2020 TWEETHER project for W-band high data rate wireless communications. In: Proc.\u003cem\u003e \u003c/em\u003eIEEE Int. Vac. Electron. Conf. (IVEC), pp. 1\u0026ndash;2. Beijing, China, (2015)\u003c/li\u003e\n\u003cli\u003eJ. H. Booske. : Vacuum electronic high power terahertz sources. IEEE Trans. Terahertz Sci. Technol. \u003cstrong\u003e1\u003c/strong\u003e(1), 54-75 (2011)\u003c/li\u003e\n\u003cli\u003eLi F, Xiao L, Ma T, et al. 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Plasmas \u003cstrong\u003e31\u003c/strong\u003e(12), 1059-1064 (2024)\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Symmetric grating structure, High frequency structure, Traveling wave tube, Vacuum electronics","lastPublishedDoi":"10.21203/rs.3.rs-6519536/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6519536/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eExcellent performance high frequency structures are critical to the development of millimeter wave and terahertz traveling wave amplifiers (TWAs). The plane symmetric grating structure (SGS) has the advantages of large transverse dimension, simple structure and easy to manufacture with one-dimensional processing. The TM\u003csub\u003e11\u003c/sub\u003e mode in SGS has characteristics of high coupling impedance and strong resonance, but its bandwidth is narrow, which limits its application in sheet beam traveling wave tube. It is found that the bandwidth of SGS can be effectively expanded by loading the coupled waveguide (operating in TE\u003csub\u003e10\u003c/sub\u003e mode) in parallel with the symmetric grating in this paper. The experiment of expand the bandwidth of SGS has been done in the Ka-band. The results show that the relative bandwidth of SGS can be widened from 0.03\u0026ndash;8.3%. Besides, a G-band TWA is designed, and the cross-sectional area of its slow wave structure is more than twice that of the traditional high frequency structure. The PIC simulation results demonstrate that the maximum power is 169 W at 219 GHz, corresponding to a gain of 27.2 dB, and the \u0026minus;\u0026thinsp;3dB bandwidth is 10.5 GHz.\u003c/p\u003e","manuscriptTitle":"Design and Method of Symmetric Grating Structure for Traveling Wave Amplifier","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-05-05 10:27:31","doi":"10.21203/rs.3.rs-6519536/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"4d58951f-cf16-4c58-9f31-53cc0436d6f5","owner":[],"postedDate":"May 5th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-10-16T14:53:40+00:00","versionOfRecord":[],"versionCreatedAt":"2025-05-05 10:27:31","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6519536","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6519536","identity":"rs-6519536","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}