Method for solving dispersion characteristic of helical corrugated waveguide in over-mode state

Abstract

The invention relates to a method for solving dispersion characteristics of a spiral corrugated waveguide in an over-mode state. The method comprises the following steps of: determining an associated mode which can be coupled with a working mode and is coupled with the working mode; quantitatively describing a coupling process between the working mode and the associated mode; constructing a multimode coupling dispersion equation based on the coupling process between the working mode and the associated mode; and carrying out numerical solution on the multimode coupling dispersion equation by adopting an iterative algorithm to obtain a dispersion curve of the helical corrugated waveguide. Based on a coupling wave equation in a vector form, a mode coupling problem under a spiral ripple boundary condition is converted into an eigenvalue problem, a dispersion equation describing multimode coupling generalized is finally derived, numerical solution is carried out on the dispersion equation by adopting a fast convergence algorithm, and therefore a multi-mode coupling model is obtained. And finally, accurate and efficient analysis of the dispersion characteristics of the helical corrugated waveguide in the over-mode state is realized.

Description

Technical Field

[0001] This invention relates to the fields of microwave technology and waveguide theory, and in particular to a method for solving the dispersion characteristics of a helical corrugated waveguide under overmode conditions. Background Technology

[0002] As an important waveguide structure in the field of microwave technology, the helical corrugated waveguide is based on a regular cylindrical waveguide or coaxial waveguide, and is achieved by etching helical corrugations with two dimensions—angular and axial periodicity—on the inner wall of the waveguide. When an electromagnetic signal propagates in the helical corrugated waveguide, the helical corrugations on the inner wall of the waveguide exert a specific constraint on the electromagnetic field, causing significant mode coupling of electromagnetic modes that satisfy the Bragg condition. This coupling effect directly changes the transmission characteristics of the electromagnetic modes, resulting in a dispersion curve (i.e., the correspondence between the longitudinal propagation constant and the operating frequency) that is significantly different from that of a regular waveguide.

[0003] This unique dispersive property makes helical corrugated waveguides a core dispersive element in high-power microwave systems, widely used in gyrotron devices (such as traveling wave tubes and backward wave tubes), particle accelerators, high-power microwave transmission systems, and high-power microwave pulse compressors. Their dispersive characteristics (the relationship between propagation constant and frequency) directly determine the key performance parameters of the device, including operating bandwidth, coupling efficiency, pulse compression efficiency, and mode stability. By adjusting the corrugation parameters to induce specific mode coupling, the desired dispersive relationship can be customized, further optimizing the overall device performance. Therefore, the precise analysis and research of the dispersion curves of helical corrugated waveguides has become a core focus of their technological development and engineering applications.

[0004] Currently, the methods for solving the dispersion characteristics of helical corrugated waveguides are mainly divided into two categories:

[0005] 1. Traditional full-wave numerical method:

[0006] The methods used include the Finite Element Method (FEM) (JM Jin, The finite element method inelectromagnetics. Piscataway, NJ, USA: Wiley-IEEE Press, 2014.), the Finite Integration Method (FIT) (T. Weiland, “Finite integration method and discrete electromagnetism,” In Computational Electromagnetics, P. Monk, C. Carstensen, S. Funken, W. Hackbusch, RHWL Hoppe, Eds. Berlin, Heidelberg, Germany: Springer-Verlag, 2003, pp. 183-198.), and the Finite Difference Method (FDM) (KS Kunz and RJ Luebbers, The finite difference time domain method for electromagnetics. Boca Raton, Florida, USA: CRC press, 2014.). Represented by [1993.], the core principle of this approach is to discretize the continuous electromagnetic field problem into a large system of algebraic equations, achieving high-precision solutions through numerical computation. This approach plays an irreplaceable role in the accurate verification of dispersion characteristics. However, this type of method has significant limitations: firstly, solving large systems of equations requires extremely high computational resources, especially when analyzing high-frequency or complex structures, where the computational cost often becomes prohibitively high; secondly, the results are essentially discrete data sets, failing to intuitively reveal the physical origin of dispersion behavior and providing clear physical mechanism support for structural design.

[0007] 2. Analysis method based on Coupled Mode Theory (CMT):

[0008] As an efficient and physically meaningful alternative, dispersion analysis based on Coupled Mode Theory (CMT) quantitatively describes the power exchange process between different modes by constructing coupled wave equations. The core advantage of this theory lies in its ability to clearly reveal the influence of geometric parameters such as ripple depth and period on dispersion relationships with relatively low computational overhead. Especially in shallow ripple scenarios, the predictions of CMT closely match actual characteristics, and the computational accuracy meets engineering requirements. Therefore, dispersion analysis based on CMT has become a rapid analysis and design tool in the early stages of helical ripple waveguide development, widely used for preliminary device structure selection and parameter optimization.

[0009] To date, all dispersion analysis methods for helical ripple waveguides based on coupled-mode theory (CMT) presuppose two-mode coupling. Their core assumption is that the operating mode couples with only a single associated mode via synchrotron spatial harmonics, and the dispersion equation is derived under this assumption. Early studies only considered coupling between two TE modes (G. Burt et al., “Dispersion of helically corrugated waveguides: Analytical, numerical, and experimental study,” Phys. Rev. E, vol. 70, no. 4, Oct. 2004, Art. no.046402.); subsequently, L. Zhang et al. (L. Zhang et al., “Multi-Mode Coupling Wave Theory for Helically Corrugated Waveguide,” IEEE Trans. Microw. Theory Techn., vol.60, no. 1, pp. 1-7, Jan. 2012.) extended the range of possible coupled mode pairs to two TM modes and TE-TM hybrid mode combinations, but the resulting dispersion equation still did not escape the limitations of the two-mode framework. In recent years, this dual-mode framework has been further applied to the dispersion characteristics analysis of coaxial helical waveguides (YX Lai, A. Yan, C. Chen, WCKuang, and SJ Wang, “Analysis of dispersion characteristics in helicallycorrugated coaxial waveguides: a theoretical and comparative study,” New J.Phys., vol. 27, no.1, Jan. 2025, Art. no. 013016.).

[0010] Currently, the rapid development of fields such as long-range early warning radar, remote sensing, and material structure research has driven the demand for high-power microwave systems at millimeter, sub-millimeter, and terahertz frequencies. As a key component of many high-power microwave systems, helical corrugated waveguides must meet the technical requirements of higher operating frequencies and greater power capacity. Therefore, large-lateral-size helical corrugated waveguides operating in higher-order modes are being increasingly adopted. With the increase in operating frequency, the longitudinal propagation constants of different modes in large-lateral-size helical corrugated waveguides will approach each other, leading to extreme congestion of the eigenmode spectrum, inevitably causing the helical corrugated waveguide to enter an overmode operating state. Currently, the dispersion characteristics of helical corrugated waveguides in the overmode state remain extremely challenging, and the two methods mentioned above both have significant shortcomings in this state. This is because: a large number of higher-order modes will be excited in the waveguide under overmode conditions, and the traditional coupled-mode theory based on the dual-mode coupling framework is difficult to accurately describe the multimode coupling effect; while existing full-wave numerical methods face problems such as a sharp increase in computational complexity, slow convergence speed, and insufficient ability to handle multimode coupling scenarios due to the surge in the number of higher-order modes, and cannot efficiently meet the dispersion analysis requirements of overmode spiral waveguides. Summary of the Invention

[0011] The purpose of this invention is to address the shortcomings of traditional analytical methods for two-mode coupling, which suffer from insufficient accuracy due to the large number of higher-order modes and complex multimode coupling in helical corrugated waveguides under overmode conditions, while full-wave numerical methods suffer from high computational cost and slow convergence. This invention aims to provide an efficient and high-precision method for solving dispersion characteristics. Based on the vector form of the coupled-wave equations, this method transforms the mode coupling problem under helical corrugated boundary conditions into an eigenvalue problem, ultimately deriving a generalized dispersion equation describing multimode coupling. By employing a fast-converging algorithm to numerically solve the dispersion equation, accurate and efficient analysis of the dispersion characteristics of helical corrugated waveguides under overmode conditions is achieved.

[0012] To achieve the above objectives, the present invention provides the following solution:

[0013] A method for solving the dispersion characteristics of a helical corrugated waveguide under overmode conditions includes:

[0014] Identify the associated modes that can be coupled with the operating mode;

[0015] Quantitatively describe the coupling process between the operating mode and the associated mode;

[0016] Based on the coupling process between the working mode and the associated mode, a multimode coupled dispersion equation is constructed.

[0017] An iterative algorithm is used to numerically solve the multimode coupled dispersion equation to obtain the dispersion curve of the helical waveguide.

[0018] Optionally, the associated modes that can be coupled with the operating mode include:

[0019] Given the known structural parameters and operating mode of the helical corrugated waveguide, the angular mode index of the associated mode k is determined based on the first preset condition.

[0020] Based on the second preset condition, the center frequency of phase synchronization between the working mode and the associated mode is determined, thereby obtaining the associated mode that can be coupled with the working mode.

[0021] Optionally, the first preset condition is:

[0022]

[0023] Where, m k m is the angular mode index of the associated mode k. i m is the angular mode index of the incident wave, i.e., the operating mode. b The number of angular folds in the spiral corrugations;

[0024] The second preset condition is:

[0025]

[0026] in, and The longitudinal propagation constants for operating mode i and associated mode k are respectively, k b The wave number is the spiral wave pattern.

[0027] Optionally, quantitatively describing the coupling process between the operating mode and the associated mode includes:

[0028] The coupling process of the two modes is characterized by selecting the 0th harmonic of the operating mode and the 1st harmonic of the associated mode.

[0029] The coupling process characterizing the two modes is expanded into 2N+1 coupled wave equations to obtain the final vector form of the coupling process between the operating mode and the associated mode.

[0030] Optionally, the coupling process representing the two modes is as follows:

[0031]

[0032]

[0033]

[0034] in, The complex amplitude of the incident wave, i.e., the 0th harmonic of the operating mode. and These are the complex amplitudes of the first harmonics of the forward and backward waves of the associated mode k, respectively. and Let represent the coupling coefficients between the forward and reverse waves of mode i and mode k, respectively. and The longitudinal propagation constants for operating mode i and associated mode k are respectively, k b The wave number of the spiral ripples. The imaginary unit, Let be the coupling coefficient between the forward wave of mode k and the incident mode i. Let be the coupling coefficient between the reverse wave of mode k and the incident wave mode i, satisfying z is the coordinate variable along the axis (i.e., the direction of mode propagation);

[0035] The final vector form is:

[0036] ;

[0037] ;

[0038] ;

[0039] in, denoted as a column vector consisting of the complex amplitudes of different mode harmonics, c is a coefficient matrix consisting of the propagation constants of different modes and the coupling coefficients between different modes, N is a positive integer, and k = 1, 2, 3...N.

[0040] Optionally, based on the coupling process between the operating mode and the associated mode, constructing the multimode coupled dispersion equation includes:

[0041] Substitute the preset particular solution into the final vector form to obtain the preset characteristic equation;

[0042] By utilizing the coupling coefficient relationship between the forward and reverse waves of operating mode i and associated mode k, and the second preset condition, the characteristic equation is simplified to obtain the multimode coupled dispersion equation.

[0043] Optionally, the preset particular solution is:

[0044]

[0045] in, It is an N+1 order column vector. Let be the longitudinal propagation constant of the new intrinsic mode formed by the coupling of working mode i with all associated modes k.

[0046] Optionally, the multimode coupled dispersion equation is:

[0047]

[0048]

[0049] in, Let i be the longitudinal propagation constant of the new intrinsic mode formed by the coupling of working mode i with all associated modes k. for The square of k, where s is an integer from 1 to N excluding k. for The square of.

[0050] Optionally, the numerical solution of the multimode coupled dispersion equation using an iterative algorithm includes:

[0051] The multimode coupling dispersion equation is numerically solved using an iterative algorithm. The in fact roots are the propagation constants of the eigenmodes generated by the coupling of the working mode i and N companion modes k.

[0052] Within different operating frequency ranges, the number of real roots of the multimode coupled dispersion equation is an odd number between 1 and 2N+1. When the calculation frequency is lower than the cutoff frequency of the operating mode and all associated modes, the multimode coupled dispersion equation has no real roots.

[0053] By selecting a sufficient number of frequency points within a preset frequency range, the corresponding frequency can be determined. This yields the dispersion curve of the helical waveguide.

[0054] The beneficial effects of this invention are as follows:

[0055] (1) Engineering application value: It provides efficient and accurate analysis tools for the research and development of high-power microwave devices;

[0056] 1) Supporting the optimization of key device performance: This invention can be directly applied to the dispersion characteristic analysis of high-power microwave devices (such as high-power pulse compressors, gyrotrons, and particle accelerators) in the millimeter-wave / terahertz band. By accurately calculating the dispersion curve (the relationship between propagation constant and frequency), it helps engineers optimize the core parameters of the device, such as the operating bandwidth, pulse compression efficiency, and mode stability.

[0057] 2) Shorten R&D cycle and cost: Traditional full-wave numerical methods are too time-consuming, resulting in device parameter iteration cycles of several weeks (e.g., simulation of 1000 frequency points requires more than 166 hours); this invention can compress the single analysis time to the second level and shorten the parameter iteration cycle to the hour level, significantly reducing the time cost and hardware resource consumption in the R&D process (no need to rely on high-performance servers, ordinary portable computers can meet the requirements).

[0058] (2) Significance of technology promotion: It is adaptable to multiple structures, easy to integrate, and has a wide range of application scenarios;

[0059] 1) Adaptable to various helical corrugated waveguide structures: The theoretical model of this invention can be applied to different types of helical corrugated waveguides, such as cylindrical and coaxial types, and supports different angular fold numbers and different working modes, adapting to diverse structural requirements in over-mode scenarios;

[0060] 2) Easy to integrate into existing design flow: The solution algorithm of this invention (Jenkins-Traub iterative algorithm) can be implemented through general engineering software such as Fortran and MATLAB. There is no need to develop a dedicated simulation platform. It can be directly integrated into the existing microwave device design flow (such as forming a "rapid initial screening + accurate verification" combination scheme with Ansys HFSS, that is, using this invention to quickly screen the optimal parameter range, and then using the full-wave numerical method to verify the key parameters, further improving R&D efficiency). Attached Figure Description

[0061] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0062] Figure 1 This is a schematic diagram of the dispersion curves of the intrinsic modes within a preset operating frequency, as shown in the dispersion characteristic analysis embodiment of the present invention.

[0063] Figure 2 This is a comparative schematic diagram of the Em3 dispersion curves obtained by various analysis methods in embodiments of the present invention;

[0064] Figure 3 This is a schematic diagram of a helical corrugated waveguide structure according to an embodiment of the present invention; wherein, (a) is a 3D view of the structure and (b) is a cross-sectional view;

[0065] Figure 4 This is a schematic flowchart of a method for solving the dispersion characteristics of a spiral corrugated waveguide under overmode conditions, according to an embodiment of the present invention. Detailed Implementation

[0066] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0067] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0068] like Figure 4 As shown in the figure, this embodiment proposes a method for solving the dispersion characteristics of a spiral corrugated waveguide under overmode conditions, including:

[0069] Step 1: Identify the associated modes that can be coupled with the operating mode;

[0070] Step 2: Quantitatively describe the coupling process between the working mode and the associated mode;

[0071] Step 3: Based on the coupling process between the working mode and the associated mode, construct the multimode coupled dispersion equation;

[0072] Step 4: Use an iterative algorithm to numerically solve the multimode coupled dispersion equation and obtain the dispersion curve of the helical waveguide.

[0073] Furthermore, the associated modes that can be coupled with the operating mode include:

[0074] Given the known structural parameters and operating mode of the helical corrugated waveguide, the angular mode index of the associated mode k is determined based on the first preset condition.

[0075] Based on the second preset condition, the center frequency of phase synchronization between the working mode and the associated mode is determined, thereby obtaining the associated mode that can be coupled with the working mode.

[0076] In this embodiment, step 1, determining the associated modes that can be coupled with the operating mode, specifically includes:

[0077] Under the influence of the corrugated boundary of a helical corrugated waveguide, the operating mode and associated modes can achieve phase synchronization through spatial harmonics, thus generating continuous coupling. For ease of description, assume that mode i is the incident wave mode (i.e., the operating mode) of the helical corrugated waveguide, and that N associated modes can couple with the operating mode within the frequency range of interest. According to the Bragg condition for periodic structures, the following conditions must be met for phase synchronization to be established between operating mode i and the spatial harmonic of a certain associated mode k:

[0078] (1);

[0079] (2);

[0080] Where, p b and m b These are the longitudinal period and angular fold number of the helical corrugations, respectively, k b (=2π / p)b () represents the wave number of the spiral ripples. and These are the longitudinal propagation constants for mode i and mode k, respectively; when mode i and mode k propagate in the same direction, in (2) Take the positive value, and take the negative value when they propagate in opposite directions. Under the condition that the structural parameters and operating modes of the helical waveguide are known, the angular mode index of the associated mode k can be determined by using equation (1), while the center frequency (i.e., the Bragg frequency) at which mode i and mode k establish phase synchronization can be determined by using equation (2).

[0081] Furthermore, a quantitative description of the coupling process between the working mode and the associated mode includes:

[0082] The coupling process of the two modes is characterized by selecting the 0th harmonic of the operating mode and the 1st harmonic of the associated mode.

[0083] The coupling process characterizing the two modes is extended to 2N+1 coupled wave equations to obtain the final vector form of the coupling process between the operating mode and the associated mode.

[0084] Specifically, in this embodiment, the quantitative description of the coupling process between the working mode and the accompanying mode in step 2 is as follows:

[0085] Under the constraint of the helical corrugated boundary, once the working mode i and the associated mode k satisfy the Bragg condition in equations (1) and (2), the nth spatial harmonic of mode i and the (n+1)th harmonic of mode k can achieve phase synchronization, that is, the harmonic orders at which the two modes achieve phase synchronization differ by 1. In principle, the coupling between working mode i and associated mode k can be described by the interaction between any harmonics that have already achieved phase synchronization. Considering that the 0th and 1st spatial harmonics have the largest amplitudes among all harmonic components, the 0th harmonic of working mode i and the 1st harmonic of associated mode k are selected to characterize the coupling process of the two modes. Under the condition of neglecting the waveguide wall loss of high conductivity materials, the amplitude change of the 0th harmonic of the forward wave of working mode i and the 1st harmonic of the forward and reverse waves of associated mode k during the coupling process can be described by the following set of differential equations:

[0086] (3);

[0087] (4);

[0088] (5);

[0089] in, It is the complex amplitude of the 0th harmonic of the incident wave (operating mode). and These are the complex amplitudes of the first harmonics of the forward and backward waves of the associated mode k, respectively. and Let represent the coupling coefficients between the forward and reverse waves of mode i and mode k, respectively, satisfying the following relationship:

[0090] (6);

[0091] According to the setting in step one, there are N associated modes that can couple with operating mode i within the frequency range of interest. Considering the coupling of all associated modes with the operating mode, the coupling process is expanded from the three coupled wave equations ((3)-(5)) describing the coupling of two modes to 2N+1 coupled wave equations, which can be expressed in vector form as follows:

[0092] (7);

[0093] in

[0094] (8);

[0095] (9);

[0096] In equation (8), the superscript T represents the transpose of the row vector to the column vector.

[0097] Furthermore, based on the coupling process between the working mode and the associated mode, the multimode coupled dispersion equation is constructed as follows:

[0098] Substitute the pre-defined particular solution into the final vector form to obtain the pre-defined characteristic equation;

[0099] By utilizing the coupling coefficient relationship between the forward and reverse waves of operating mode i and associated mode k, and the second preset condition, the characteristic equation is simplified to obtain the multimode coupled dispersion equation.

[0100] Specifically, in this embodiment, step 3, constructing the multimode coupled dispersion equation, involves:

[0101] The solution to equation (7) has the form:

[0102] (10);

[0103] The special solution, of which It is an N+1 order column vector. Let be the longitudinal propagation constant of the new eigenmode (i.e., the adaptive spiral corrugated boundary eigenmode) formed by the coupling of working mode i with all associated modes k. Substituting (10) into (7) yields:

[0104] (11);

[0105] in It is an N+1 order identity matrix. It is obvious that if and only if Coefficient matrix When the eigenvalues ​​are , the coupled wave equations (7) have a solution of the form (10). At this time, It is the coefficient matrix The eigenvector corresponding to the eigenvalue -jβ. The characteristic equation satisfied by the eigenvalue -jβ is:

[0106] (12);

[0107] coefficient matrix Except for the first row, the other rows contain only two non-zero elements. Using this characteristic, combined with (6) and the Bragg condition (2), the characteristic equation can be simplified, ultimately yielding the dispersive equation in a multimode coupled form, whose analytical expression is as follows:

[0108] (13);

[0109] It can be represented as:

[0110] (14);

[0111] in:

[0112] (15);

[0113] The analytical expression depends on the waveguide structure and the types of modes i and k.

[0114] Specifically, in this embodiment, step 4 involves the numerical solution of the multimode coupled dispersion equation.

[0115] The dispersion equation (14) is an algebraic polynomial of degree 2N+1. The roots of this polynomial can be numerically solved using the Jenkins-Traub iterative algorithm. The real roots are the propagation constants of the eigenmodes generated by the coupling of the operating mode i and N associated modes. Within different operating frequency ranges, the number of real roots of the dispersion equation (14) is an odd number between 1 and 2N+1. When the calculation frequency is lower than the cutoff frequency of the operating mode and all associated modes, the dispersion equation (14) has no real roots. By selecting a sufficient number of frequency points within a preset frequency range and calculating β at the corresponding frequencies, the dispersion curve (the relationship curve between frequency and propagation constant) of the helical waveguide can be obtained.

[0116] This invention overcomes the technical limitations of traditional methods in dispersion analysis of over-mode spiral waveguides, forming two core innovations, both of which are verified by quantitative data from specific embodiments, demonstrating both innovation and practicality.

[0117] (1) Breakthrough in computational efficiency: Significantly reduces computational resource consumption in over-modeling scenarios;

[0118] Compared to traditional full-wave numerical methods (such as the finite element method and the finite integral method), this invention achieves an order-of-magnitude improvement in computational efficiency in over-model scenarios. Its core advantages are reflected in three aspects: computation time, hardware dependence, and convergence speed.

[0119] 1) The computation time is significantly reduced. The dispersion analysis method proposed in this invention can be deployed on ordinary computers or even portable computers. Under the condition of sampling thousands of frequency points, the overall computation time can be reduced to the second level. In contrast, under the same computing hardware resources, Ansys HFSS (full-wave numerical method) requires first constructing a three-dimensional solid model of the helical ripple and then completing the meshing of tens of thousands of mesh elements. The simulation time for a single frequency point alone exceeds 10 minutes, with an efficiency difference of over 10%. 5 times.

[0120] 2) Avoiding complex mesh partitioning: Full-wave numerical methods require increasing mesh partitioning complexity as the number of higher-order modes increases (e.g., the number of mesh elements may exceed 100,000 when the number of higher-order modes increases), resulting in a sharp drop in convergence speed; This invention is based on coupled wave equations and eigenvalue solutions, which do not require mesh discretization, have a stable convergence speed, and are not affected by the number of higher-order modes in over-mode scenarios.

[0121] (2) Improved analysis accuracy: accurately captures the multimode aliasing coupling effect under over-mode conditions;

[0122] Compared to traditional coupled-mode dispersion analysis methods based on "two-mode coupling", this invention breaks through the framework limitation of "considering only one co-occurring mode" and achieves a leap in accuracy in multi-mode coupling scenarios:

[0123] 1) Covering more coupling modes: Traditional dual-mode coupling methods can only describe the coupling between the operating mode and one companion mode (e.g., in the embodiments, the traditional method only considers TE). -3,1 With TE 2,2 Coupling); This invention can simultaneously cover N associated modes (such as TE in the embodiment) according to the uncoupled intrinsic mode distribution within a preset calculation frequency range. 2,1 TM 2,1 TE 2,2 TM 2,2 (4 companion modes) to fully recreate the real coupling environment of "pattern spectrum crowding" in over-modeling scenarios.

[0124] 2) High agreement with measured and simulation results. Because the coupling between the operating frequency and all influential associated modes within the preset operating frequency range is fully considered, the multimode coupling dispersion analysis results proposed in this invention agree well with Ansys HFSS simulation results and experimental results. In contrast, the traditional two-mode coupling dispersion analysis method neglects the coupling effect between the operating mode and the adjacent modes of the preset associated modes, resulting in dispersion curves that deviate significantly from the measured results. This demonstrates that this invention can effectively avoid the calculation errors caused by "ignoring some associated modes."

[0125] Currently, there are numerous experimental research cases demonstrating the use of cylindrical helical corrugated waveguides as dispersive structures for high-power microwave pulse signal compression. In a collaborative study between the Institute of Applied Physics of the Russian Academy of Sciences and the University of Strathclyde in the UK, researchers employed a 5-fold (m... b A helical corrugated cylindrical waveguide (=5) is used as the dispersive structure for a high-power pulse compressor (L. Zhang et al., “Experimental Study of Microwave Pulse Compression Using a Five-Fold Helically Corrugated Waveguide,” IEEE Trans. Microw. Theory Techn., vol. 63, no. 3, pp. 1090-1096, Mar. 2015.), and its structural parameters are shown in Table 1. To improve the operating frequency under the condition of large transverse dimensions, this helical corrugated waveguide employs a higher-order TE. -3,1 The working mode is used as input, and TE is preset. 2,2 As a companion mode, the dispersion characteristics required for pulse compression are formed through the coupling of the two. However, TE 2,2 It is not that it can be compared with TE -3,1 The lowest-order mode in which coupling occurs has a cutoff frequency between TM and TM. 2,1 and TM 2,2 The dispersive characteristics of this structure are influenced by the coupling between the operating mode and adjacent associated modes, as the cutoff frequency is between [a certain range]. Given that this helical corrugated waveguide combines large size with aliasing mode coupling, this structure will be used as an example for dispersive characteristic analysis to illustrate the implementation process and beneficial effects of the method proposed in this invention.

[0126] Table 1. Parameters of the Dispersion Characteristic Analysis Example (5-fold Helical Corrugated Cylindrical Waveguide)

[0127]

[0128] 1. Determine the associated growth pattern based on step 1;

[0129] The incident wave mode of the example structure is TE. -3,1 According to Prague condition (1), at 50% (m b =5) Under the constraint of the helical corrugation, the angular mode index of the associated mode that can couple with the incident operating mode is 2. In order to cover the compressor's operating frequency band (X-band), the frequency range of the dispersion analysis is set to 6.5 GHz to 14 GHz. According to the Bragg condition (2), within the set frequency range, the operating mode TE -3,1 The associated mode TE with an angular mode index of 2 will be used. 2,1 TM 2,1 TE 2,2 and TM 2,2 Coupling occurs, and the corresponding Bragg frequencies for the combinations are shown in the operating parameters in Table 1.

[0130] 2. Based on step 2, quantitatively describe the coupling between the working mode and the four associated modes;

[0131] According to step 2, the working mode is TE. -3,1 With companion mode TE 2,1 TM 2,1 TE 2,2 and TM 2,2 The coupling can be described by nine coupled-wave equations, in vector form as follows:

[0132] ;

[0133] in:

[0134] ;

[0135] ;

[0136] In the formula, Indicates working mode TE -3,1 The 0th harmonic complex amplitude, , , , These represent the companion mode TE. 2,1 TM 2,1 TE 2,2 TM 2,2 The complex amplitude of the first harmonic of a positive wave. , , , These represent the associated mode TE respectively. 2,1 TM 2,1 TE 2,2 TM 2,2 The complex amplitude of the first harmonic of the reverse wave. This is the coupling coefficient between the working mode and the accompanying mode.

[0137] 3. Construct the dispersion equation for multimode coupling analysis based on step 3;

[0138] TE can be constructed according to the process described in step 3. -3,1 With 4 companion modes TE 2,1 TM 2,1 TE 2,2 TM 2,2 Multimode coupling dispersion equations under synchronous coupling framework:

[0139] ;

[0140] In the formula, , , , , TE -3,1 TE 2,1 TM 2,1 TE 2,2 TM 2,2 The longitudinal propagation constant amplitude, The longitudinal propagation constant of the new intrinsic modes formed by coupling.

[0141] 4. Solve the dispersion equation and plot the dispersion curve according to step 4;

[0142] Within a preset frequency range (6.5 GHz to 14 GHz), 1000 frequency samples are set (to ensure the dispersion curve is continuous and smooth, the number of frequency samples must be sufficient). Following the algorithm described in step 4, the dispersion equation for each frequency sample is numerically solved from the low-frequency end to the high-frequency end, thereby obtaining the longitudinal propagation constant of the intrinsic mode. The real roots. Using Origin software, the dispersion curves of the eigenmodes within a preset frequency range can be plotted, as shown in the figure. Figure 1 As shown.

[0143] By comparing the pulse compression operating region of this structure given in the literature "L. Zhang et al., “Multi-Mode Coupling Wave Theory for Helically Corrugated Waveguide,” IEEE Trans. Microw. Theory Techn., vol. 60, no. 1, pp. 1-7, Jan. 2012,” it can be seen that… Figure 1Em3 in the text is the intrinsic mode used in the structure pulse compression operation. This embodiment will focus on this mode for further comparative analysis. Figure 2 The theoretical analysis, software simulation, and experimental test results of the dispersion curve of this mode are presented, where the black solid line represents... Figure 2 The results of the multimode coupling analysis are shown in the figure. The dashed line represents the results based on two-mode coupling (TE). -3,1 -TE 2,2 The results of the dispersion theory analysis are shown. The dots represent the simulation results of Ansys HFSS (based on the full-wave numerical method) (obtained using the eigenmode solver of Ansys HFSS combined with master-slave boundary condition settings). The red solid line represents the measured dispersion curve of the structure in the pulse compression working region. This result is derived from the literature "L. Zhang et al., “Design and experiments of a five-foldhelically corrugated waveguide for microwave pulse compression,” In 2015 40thInt. Conf. on Infra., Millim., and Terah. waves (IRMMW-THz), Hong Kong, China, Aug. 23-28, 2015, Art. no. 7327459." Figure 2 It is worth mentioning that, due to the mode converter used in the experiment (used to convert TE...) 1,1 The incident wave TE converted to the compressor -3,1 Due to bandwidth limitations, experimental tests can only obtain dispersion curves within a local range. Figure 2 The abnormal data at the low-frequency and high-frequency ends of the measured dispersion curve also originate from this.

[0144] By comparing the dispersion curves obtained by different analytical methods and their acquisition process, it can be found that:

[0145] 1) Overall, the multimode coupling dispersion analysis results are highly consistent with the Ansys HFSS simulation results. Furthermore, in the longitudinal propagation constant range of 130–195 rad / m (corresponding to a frequency range of 8.75 GHz–9.65 GHz, covering the pulse compression operating region), the theoretical calculations, software simulations, and experimental results of multimode coupling are almost perfectly matched. However, in this region, the dispersion curve obtained from the theoretical analysis of two-mode coupling shows significant differences compared to results obtained through other methods, and these differences become increasingly pronounced as the frequency decreases. This indicates that the multimode coupling dispersion analysis method proposed in this invention can effectively capture the complex effects of multimode aliasing coupling under overmode conditions, avoiding the calculation deviations caused by neglecting some associated mode coupling effects in traditional two-mode coupling methods, and significantly improving the accuracy of dispersion characteristic analysis of overmode spiral waveguides.

[0146] 2) Regarding computational resources, the multimode coupled dispersion analysis model proposed in this invention needs to solve 1000 frequency points within the 6.5 GHz to 14 GHz frequency range. On a typical portable computer configured with an Intel Core i7-1165G7 processor and 40GB DDR4 memory, using Fortran software to implement the Jenkins-Traub iterative algorithm, the total computation time for all frequency points is less than 1 second. However, when using Ansys HFSS for full-wave numerical simulation, under the same hardware configuration, frequency range, and number of frequency points, a 3D solid model containing helical corrugation details must first be constructed, followed by mesh generation (approximately 80,000 mesh elements), and then the intrinsic mode solver must be started. The total simulation time for a single frequency point is approximately 10 minutes. Furthermore, as the number of higher-order modes within the waveguide increases, the mesh generation complexity further increases, significantly extending the simulation time. Therefore, the method of this invention significantly reduces computational resource consumption while maintaining computational accuracy, significantly improving the analysis efficiency of dispersion characteristics of overmode helical corrugated waveguides.

[0147] In summary, through the analysis and comparison of the dispersion characteristics of the above embodiments, the stability and reliability of the method proposed in this invention in overmode scenarios are fully demonstrated. This provides an efficient and accurate analysis tool for the design and optimization of overmode spiral waveguide devices in the millimeter-wave and terahertz bands, effectively shortening the device development cycle and reducing engineering design costs.

[0148] Figure 1 The dispersion characteristics analysis of the embodiment are shown, including the dispersion curves of the eigenmodes within a preset operating frequency range (6.5 GHz to 14 GHz). The solid lines represent the five coupled eigenmodes (Em1 to Em5) obtained from multimode analysis, while the dashed lines represent the uncoupled operating modes TE. -3,1 0th harmonic and associated mode TE 2,1 TM2,1 TE 2,2 TM 2,2 The dispersion curve of the first harmonic.

[0149] Figure 2 This paper presents a comparison of Em3 dispersion curves obtained by various analysis methods: the multimode coupling dispersion analysis results proposed in this invention (blue solid line), and the traditional two-mode coupling (TE) method. -3,1 -TE 2,2 Dispersion analysis results (yellow dashed line), AnsysHFSS (full-wave numerical analysis) simulation results (black dots), and experimental measurement results (red solid line).

[0150] Figure 3 A schematic diagram of a helical corrugated waveguide structure is shown (in five folds (m)). b =5) Taking a helical corrugated coaxial waveguide as an example); where... Figure 3 (a) is a 3D view of the structure. Figure 3 (b) is a cross-sectional view, where a0 and b0 are the average radii of the outer and inner conductors of the helical waveguide, respectively. o and l i p is the average radius of the helical ripples on the surfaces of the outer and inner conductors. b and m b These represent the axial period length and the number of angular folds of the helical corrugations, respectively.

[0151] The beneficial effects of this invention revolve around "engineering application implementation" and "technology promotion and adaptation", directly solving the core pain points in the research and development of millimeter-wave and terahertz overmode waveguide devices.

[0152] (1) Engineering application value: It provides efficient and accurate analysis tools for the research and development of high-power microwave devices;

[0153] 1) Supporting the optimization of key device performance: This invention can be directly applied to the analysis of dispersion characteristics of high-power microwave devices (such as high-power pulse compressors, gyrotrons, and particle accelerators) in the millimeter-wave / terahertz band. By accurately calculating the dispersion curve (the relationship between propagation constant and frequency), it helps engineers optimize the core parameters of the device, such as operating bandwidth, pulse compression efficiency, and mode stability.

[0154] 2) Shorten the R&D cycle and cost: Traditional full-wave numerical methods are too time-consuming, resulting in a device parameter iteration cycle of several weeks (e.g., simulation of 1000 frequency points requires more than 166 hours); this invention can compress the single analysis time to the second level and shorten the parameter iteration cycle to the hour level, significantly reducing the time cost and hardware resource consumption in the R&D process (no need to rely on high-performance servers, ordinary portable computers can meet the requirements).

[0155] (2) Significance of technology promotion: It is adaptable to multiple structures, easy to integrate, and has a wide range of application scenarios;

[0156] 1) Adaptable to various helical corrugated waveguide structures: The theoretical model of this invention can be applied to different types of helical corrugated waveguides, such as cylindrical and coaxial types, and supports different angular fold numbers and different working modes, adapting to diverse structural requirements in over-mode scenarios;

[0157] Easy to integrate into existing design flow: The solution algorithm of this invention (Jenkins-Traub iterative algorithm) can be implemented through general engineering software such as Fortran and MATLAB. There is no need to develop a dedicated simulation platform. It can be directly integrated into the existing microwave device design flow (such as forming a "rapid initial screening + accurate verification" combination scheme with Ansys HFSS, that is, using this invention to quickly screen the optimal parameter range, and then using the full-wave numerical method to verify the key parameters, further improving R&D efficiency).

[0158] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for solving the dispersion characteristics of a helical corrugated waveguide under overmode conditions, characterized in that, include: Identify the associated modes that can be coupled with the operating mode; Quantitatively describe the coupling process between the operating mode and the associated mode; Based on the coupling process between the working mode and the associated mode, a multimode coupled dispersion equation is constructed. An iterative algorithm is used to numerically solve the multimode coupled dispersion equation to obtain the dispersion curve of the helical waveguide.

2. The method for solving the dispersion characteristics of a spiral corrugated waveguide under overmode conditions according to claim 1, characterized in that, The associated modes that can be coupled with the operating mode include: Given the known structural parameters and operating mode of the helical corrugated waveguide, the angular mode index of the associated mode k is determined based on the first preset condition. Based on the second preset condition, the center frequency of phase synchronization between the working mode and the associated mode is determined, thereby obtaining the associated mode that can be coupled with the working mode.

3. The method for solving the dispersion characteristics of a spiral corrugated waveguide under overmode conditions according to claim 2, characterized in that, The first preset condition is: Where, m k m is the angular mode index of the associated mode k. i m is the angular mode index of the incident wave, i.e., the operating mode. b The number of angular folds in the spiral corrugations; The second preset condition is: in, and The longitudinal propagation constants for operating mode i and associated mode k are respectively, k b The wave number is the spiral wave pattern.

4. The method for solving the dispersion characteristics of a spiral corrugated waveguide under overmode conditions according to claim 3, characterized in that, A quantitative description of the coupling process between the operating mode and the associated mode includes: The coupling process of the two modes is characterized by selecting the 0th harmonic of the operating mode and the 1st harmonic of the associated mode. The coupling process characterizing the two modes is expanded into 2N+1 coupled wave equations to obtain the final vector form of the coupling process between the operating mode and the associated mode.

5. The method for solving the dispersion characteristics of a spiral corrugated waveguide under overmode conditions according to claim 4, characterized in that, The coupling process representing the two modes is as follows: in, The complex amplitude of the incident wave, i.e., the 0th harmonic of the operating mode. and These are the complex amplitudes of the first harmonics of the forward and backward waves of the associated mode k, respectively. and Let represent the coupling coefficients between the forward and reverse waves of mode i and mode k, respectively. and The longitudinal propagation constants for operating mode i and associated mode k are respectively, k b The wave number of the spiral ripples. The imaginary unit, Let be the coupling coefficient between the forward wave of mode k and the incident mode i. Let be the coupling coefficient between the reverse wave of mode k and the incident wave mode i, satisfying z is the axis, i.e., the coordinate variable in the direction of mode propagation; The final vector form is: ； ； ； in, is a column vector composed of complex amplitudes of different mode harmonics, c is the coefficient matrix, N is a positive integer, and k = 1, 2, 3...N.

6. The method for solving the dispersion characteristics of a spiral corrugated waveguide under overmode conditions according to claim 5, characterized in that, Based on the coupling process between the operating mode and the associated mode, the multimode coupled dispersion equation is constructed as follows: Substitute the preset particular solution into the final vector form to obtain the preset characteristic equation; By utilizing the coupling coefficient relationship between the forward and reverse waves of operating mode i and associated mode k, and the second preset condition, the characteristic equation is simplified to obtain the multimode coupled dispersion equation.

7. The method for solving the dispersion characteristics of a spiral corrugated waveguide under overmode conditions according to claim 6, characterized in that, The preset particular solution is: in, It is an N+1 order column vector. Let be the longitudinal propagation constant of the new intrinsic mode formed by the coupling of working mode i with all associated modes k.

8. The method for solving the dispersion characteristics of a helical corrugated waveguide under overmode conditions according to claim 1, characterized in that, The multimode coupled dispersion equation is: in, Let i be the longitudinal propagation constant of the new intrinsic mode formed by the coupling of working mode i with all associated modes k. for The square of k, where s is an integer from 1 to N excluding k. for The square of.

9. The method for solving the dispersion characteristics of a spiral corrugated waveguide under overmode conditions according to claim 1, characterized in that, The numerical solution of the multimode coupled dispersion equation using an iterative algorithm includes: The multimode coupling dispersion equation is numerically solved using an iterative algorithm. The in fact roots are the propagation constants of the eigenmodes generated by the coupling of the working mode i and N companion modes k. Within different operating frequency ranges, the number of real roots of the multimode coupled dispersion equation is an odd number between 1 and 2N+1. When the calculation frequency is lower than the cutoff frequency of the operating mode and all associated modes, the multimode coupled dispersion equation has no real roots. By selecting a sufficient number of frequency points within a preset frequency range, the corresponding frequency can be determined. This yields the dispersion curve of the helical waveguide.

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