| Helical traveling-wave tube is one of the most important types of the microwave /millimeter wave vacuum electronic devices. For its high power, high gain, high efficiency and broad bandwidth, it is widely uesed in modern military electronic equipments, including communication systems, radars, electronic warfares, etc. The performance of helical slow-wave system has critical effects on the bandwidth, gain, output power, efficiency and any other targets of helical traveling wave tubes. How to improve the analysis accuracy and reliability and figure out a helical slow-wave system with better performance, is always a focus of attention. Consequently, scholars and engineers have devoted to develop new-style helical slow-wave structures to better the performance, and continued to explore theoretical analysis and numerical computation methods with better accuracy as well.In this doctoral dissertation, based on the frame of project 'research on CAD technology of wide-band high-power traveling-wave tubes', much work about theoretical analysis and computation methods of helical slow-wave circuits have been carried out deeply and detailedly and the results, including the theory and the developed software, has been applied in the high-frequency computation model of 'the CAD integrated environment of wide-band high-power traveling-wave tubes'. Several important and valuable results are listed as below:1. For the analysis of no-vane or infinite-vane loaded helical slow-wave circuits, the tape helix model is set up, in which helix thickness, helix width, surface current along the helix, support rods of arbitrary number and arbitrary shape, as well metal envelop are considered. Based on the filed-match theory, the equations of dispersion, interaction impedance and attenuation constant are derived and a modified theory model is put forward according to the effects of the helix thickness on the characteristics of helical slow-wave circuits. Using the modified theory model, the effects of metal envelop, vane, supports and tape helix are analyzed and two actual circuits are computed whose results are consistent with those of MAFIA simulation. In the end, founded on the effects of helix pitch, the linear interposition method is suggested to get the cold-test characteristics of helical slow-wave structures with tapered pitches.2. For the analysis of sector-vane loaded helical slow-wave system, the finite-size vane sheath-helix model is set up, in which helix thickness and the shape and the size of the sector vane are taken into account. The filed-match theory is used to get the equations of dispersion, interaction impedance and the attenuation constant step by step. Using this model, the effects of vane radius and vane angle are analyzed and also the computation accurary is tested and the error analysis is carried through.3. For the analysis of T-shaped vane loaded helical slow-wave system, the corresponding finite-size vane sheath-helix model is set up, in which helix thickness and the shape and the size of the T-shaped vane are taken into account. The filed-match theory is used to get the equations of dispersion, interaction impedance and the attenuation constant. Using this model, the effects of vane radius and vane width of the thick part of the T-shaped vane are analyzed and also the computation accurary is tested and the error analysis is carried through.4. The finite integration theory, one of the most successful three-dimensional electro-magnetic numerical methods, is deeply studied. From the Maxwell's equations in integral form directly, the Maxwell Grid Equations are derived through discretization of the solution space and the equations, and thereout the common equation of arbitary structures. Secondly, the solution uncertainty of a common electro-magnetic equation is proved and a strategy is advised to get the unique solution of the finite integration equation. Finally, to get the exclusive solution of a certain structure, the realization technology of electric and magnetic boundary conditions, as well as the quasi-periodic boundary condition is studied.5. Several key technologies concerning the property, formation and solution of the finite integration equation are studied. The "compressed sparse row data format" is adopted to save storage and the "mode multiplication" is used to improve the computation efficiency, so that the finite integration equation is obtained with low storage and high efficiency. To solve the finite integration equation, which is a large-scale sparse algebraic eigenvalue problem under the condition specified, the Krylov subspace iteration method is introduced and the shift-invert Arnoldi method is proposed to exclude the unphysical static electro-magnetic solution and get the needed eigensolution around the specified eigenvalue. Ultimately, a numerical program based on the shift-invert Arnoldi method is explored on the platform of ARPACK, which is a large-scale sparse matrix eigensolver package with open source codes.In the self-made program, the maximum mesh number reaches one million for the high-frequency structures with simple electro/magnetic boundary conditions whose eigenvalue matrix is real, and the maximum mesh number reaches five hundred and sixty thousand for the structures with qusi-periodic boundary conditions whose coeffiecient matrix is complex. The mesh number can meet the need of numerical analysis for high-frequency structures.6. Using the finite integration theory and the self-made program, the resonant frequency and the dispersion characteristics of the dominant wave of rectangular resonator, rectangular waveguide and cylinder waveguide are calculated, and also the convergence of the results with increasing mesh numbers are studied. The computation results are further compared with those of MAFIA simulation and the theoretical values. Good consistency has been discovered, which demonstrated the correctness of the theory analysis and the reliability of the numerical computation.7. Using the finite integration theory and the self-made program, the cold-test characteristics of two actual helical slow-wave systems are obtained. The convergence of the results with increasing mesh numbers are studied and the dispersion and impedance are compared with those of MAFIA simulation which have shown good consistence between each other.
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