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CN-122016241-A - Method for solving dispersion characteristics of spiral corrugated waveguide in overmode state

CN122016241ACN 122016241 ACN122016241 ACN 122016241ACN-122016241-A

Abstract

The invention relates to a method for solving dispersion characteristics of a spiral corrugated waveguide in an overmode state, which comprises the steps of determining an associated mode capable of being coupled with a 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 spiral corrugated waveguide. The invention converts the mode coupling problem under the spiral ripple boundary condition into the eigenvalue problem based on the vector form coupled wave equation, finally derives the dispersion equation describing multimode coupling generalized, and carries out numerical solution on the dispersion equation by adopting a fast convergence algorithm, thereby finally realizing the accurate and efficient analysis of the spiral ripple waveguide dispersion characteristic under the overmode state.

Inventors

  • LAI YINGXIN
  • WEI XILIN
  • KUANG WEICHAO
  • GUO ZHENGHAO

Assignees

  • 东莞理工学院

Dates

Publication Date
20260512
Application Date
20260129

Claims (9)

  1. 1. A method for solving dispersion characteristics of a helical waveguiding in an overmode state, comprising: Determining an associated mode which can be coupled with the working mode and is coupled with the working mode; quantitatively describing the coupling process between the working mode and the accompanying 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.
  2. 2. The method of solving for dispersion characteristics of a helical waveguiding in an overmode state of claim 1, wherein determining a coupled companion mode capable of coupling with an operating mode comprises: Under the condition that the structural parameters and the working modes of the helical corrugated waveguide are known, determining an angular mode index of an associated mode k based on a first preset condition; and determining the center frequency of phase synchronization between the working mode and the accompanying mode based on a second preset condition, so as to obtain the accompanying mode which can be coupled with the working mode and is coupled with the working mode.
  3. 3. The method for solving the dispersion characteristics of the helical waveguiding in the overmode state according to claim 2, wherein the first preset condition is: Wherein, m k is the angular mode index of the associated mode k, m i is the angular mode index of the incident wave, namely the working mode, and m b is the number of helical corrugation angular folds; the second preset condition is: Wherein, the And The longitudinal propagation constants of the working mode i and the accompanying mode k, respectively, k b are the wave numbers of the helical corrugations.
  4. 4. A method of solving for dispersion characteristics of a helical-corrugated waveguide in an overmode state as claimed in claim 3, wherein quantitatively describing the coupling process between the operating mode and the accompanying mode comprises: Selecting the 0 th harmonic of the working mode and the 1 st harmonic of the associated mode to represent the coupling process of the two modes; and expanding the coupling process for representing the two modes into 2N+1 coupled wave equations, and obtaining the final vector form of the coupling process between the working mode and the associated mode.
  5. 5. The method for solving the dispersion characteristics of the helical waveguiding in the overmode state according to claim 4, wherein the coupling process for characterizing the two modes is: Wherein, the For the complex amplitude of the incident wave i.e. the 0 th harmonic of the operating mode, And Complex amplitudes of the forward and backward wave 1 st harmonic of the associated mode k, And Representing the coupling coefficients between the forward and backward waves of mode i and mode k respectively, And Longitudinal propagation constants of the working mode i and the accompanying mode k, respectively, k b is the wave number of the helical corrugation, In units of imaginary numbers, Is the coupling coefficient of the forward wave of mode k with the incident mode i, Is the coupling coefficient of the reverse wave of the mode k and the incident wave mode i, meets the following requirements Z is the axial, i.e. the coordinate variable of the direction of propagation of the mode; the final vector form is: ; ; ; Wherein, the Column vectors composed of complex amplitudes for different mode harmonics, c being a coefficient matrix, N being an integer greater than zero, k=1, 2,3.
  6. 6. The method of solving the dispersion characteristics of the helical waveguiding in the overmode state of claim 5, wherein constructing a multimode coupling dispersion equation based on the coupling process between the operating mode and the accompanying mode comprises: substituting a preset special solution into the final vector form to obtain a preset characteristic equation; and simplifying the characteristic equation by utilizing the coupling coefficient relation between the forward wave and the backward wave of the working mode i and the associated mode k and the second preset condition, and obtaining a multimode coupling dispersion equation.
  7. 7. The method for solving the dispersion characteristics of the helical waveguiding in the overmode state according to claim 6, wherein the preset special solution is: Wherein, the Is a column vector of order N +1, Longitudinal propagation constants for the new eigenmodes formed by the coupling of the operating mode i with all the associated modes k.
  8. 8. The method for solving the dispersion characteristics of a helical corrugated waveguide in an overmode state according to claim 1, the multimode coupling dispersion equation is characterized in that: Wherein, the The longitudinal propagation constant of the new eigenmodes formed for the coupling of the operating mode i with all the associated modes k, Is that S is an integer from 1 to N not equal to k, Is that Square of (d).
  9. 9. The method of claim 1, wherein numerically solving the multimode coupling dispersion equation using an iterative algorithm comprises: Carrying out numerical solution on the multimode coupling dispersion equation by adopting an iterative algorithm, wherein a real root is a propagation constant of an eigenmode generated by coupling the working mode i and N companion modes k; In different working frequency ranges, the real root number of the multimode coupling dispersion equation is an odd number between 1 and 2N+1, and when the calculated frequency is lower than the cut-off frequency of the working mode and all the associated modes, the multimode coupling dispersion equation has no real root; by selecting enough frequency points in a preset frequency range, the corresponding frequency is obtained And obtaining the dispersion curve of the spiral corrugated waveguide.

Description

Method for solving dispersion characteristics of spiral corrugated waveguide in overmode state Technical Field The invention relates to the technical field of microwave technology and waveguide theory, in particular to a method for solving the dispersion characteristic of a spiral corrugated waveguide in an overmode state. Background The spiral ripple waveguide is an important guided wave structure in the technical field of microwaves, and is realized by etching spiral ripples with two dimensions, namely angular periodicity and axial periodicity on the inner wall of the waveguide on the basis of a regular cylindrical waveguide or a coaxial waveguide. When electromagnetic signals are transmitted in the spiral corrugated waveguide, the spiral corrugations of the inner wall of the waveguide can form specific constraint on the electromagnetic field, so that the electromagnetic modes meeting the Bragg condition are subjected to remarkable mode coupling. This coupling effect directly changes the transmission characteristics of the electromagnetic modes, so that the helical corrugated waveguide forms a dispersion curve (i.e., the correspondence between the longitudinal propagation constant and the operating frequency) that is significantly different from that of the regular waveguide. The unique dispersion property makes the spiral corrugated waveguide become a core dispersion element of a high-power microwave system, and is widely applied to the fields of gyrotron devices (such as a traveling wave tube and a return wave tube), particle accelerators, high-power microwave transmission systems, high-power microwave pulse compressors and the like. The dispersion characteristic (relation between propagation constant and frequency) directly determines key performance parameters of the device, including working bandwidth, coupling efficiency, pulse compression efficiency and mode stability, and the required dispersion relation can be customized by regulating and controlling ripple parameters to induce specific mode coupling, so that the overall performance of the device is further optimized. Therefore, the accurate analysis and research of the dispersion curve of the spiral corrugated waveguide has become the core emphasis of the technical development and engineering application. At present, the solving methods of the dispersion characteristics of the spiral corrugated waveguide are mainly divided into two types: 1. Traditional full wave numerical method: Represented by a finite element method （FEM）（J. M. Jin, The finite element method in electromagnetics. Piscataway, NJ, USA: Wiley-IEEE Press, 2014.）、 and a finite integral method （FIT）（T. Weiland, "Finite integration method and discrete electromagnetism," In Computational Electromagnetics, P. Monk, C. Carstensen, S. Funken, W. Hackbusch, R. H. W. L. Hoppe, Eds. Berlin, Heidelberg, Germany: Springer-Verlag, 2003, pp. 183-198.）、 and a finite difference method （FDM）（K. S. Kunz and R. J. Luebbers, The finite difference time domain method for electromagnetics. Boca Raton, Florida, USA: CRC press, 1993.）, the core principle is that the continuous electromagnetic field problem is discretized into a large algebraic equation set, high-precision solution is realized through numerical calculation, and the method has an irreplaceable effect in a precise verification scene of dispersion characteristics. The method has the remarkable limitations that on one hand, the solving of a large equation set consumes extremely high computational resources, and particularly when a high-frequency or complex structure is analyzed, the computational cost often reaches an intolerable degree, and on the other hand, the result is essentially a discrete data set, the physical origin of dispersion behaviors cannot be intuitively revealed, and clear physical mechanism support is difficult to provide for structural design. 2. Analytical method based on Coupled Mode Theory (CMT): As an alternative scheme with both definite efficiency and physical meaning, a dispersion analysis method based on a Coupled Mode Theory (CMT) quantitatively describes the power exchange process between different modes by constructing a coupled wave equation. The theory has the core advantage that the regulation and control rule of geometric parameters such as ripple depth, period and the like on the dispersion relation can be clearly revealed only by lower calculation cost. In a shallow ripple scene, in particular, the prediction result of the coupling mode theory is highly consistent with the actual characteristic, and the calculation precision can meet the engineering requirement. Therefore, the dispersion analysis method based on the coupling mode theory is a rapid analysis design tool for the early development stage of the spiral corrugated waveguide, and is widely applied to the primary model selection and parameter optimization of the device structure. Up to now, the spiral ripple waveguide dispersion analysis method base