行波管注波互作用时域理论与通用非线性模拟技术研究
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摘要
作为一类重要的微波电真空器件，行波管因具备宽频带及高功率的特点，已经成为国防和通信设备中不可或缺的关键组成部分。用于分析行波管电子注和电磁波相互作用过程的非线性理论也得到了快速的发展，对实际研制行波管起到了巨大的推动作用。当前的非线性理论主要是分析稳态注波互作用的频域理论，而缺乏对注波互作用瞬态过程的时域理论研究。同时，随着人们对微波器件更高频率和更高功率的需求，涌现出诸如折叠波导行波管等新型器件，需要采用新的模拟手段来仿真这些器件的注波互作用过程。因此，研究行波管注波互作用的非线性时域理论和通用模拟方法，具有重要的意义。
建立行波管注波互作用非线性理论体系至少需要三个基本方程组，即分析高频场与电子注能量交换过程的高频场方程、分析电子之间相互排斥力的空间电荷场方程以及描述电子注在电磁场作用下运动轨迹的电子运动方程。本论文围绕这三个方程组建立行波管注波互作用的非线性理论和模拟方法。论文首先在高频场方程和空间电荷场模型中引入时间变化因子，发展了行波管注波互作用非线性时域理论；然后利用数值方式建立广义高频场方程，得到了适用于各类行波管注波互作用的通用模拟模型。本论文工作的主要内容及创新点总结如下：
1.建立螺旋线行波管注波互作用的非线性时域理论。利用螺旋导电面模型推导螺旋线行波管的色散关系，然后根据该色散关系及高频电磁场表达式，建立时域高频场方程。利用空间电荷波理论求解空间电荷场，从而建立时域空间电荷场方程。将时域高频场方程、空间电荷场与相对论洛伦兹力方程描述的电子运动方程相结合，建立螺旋线行波管的非线性时域理论。
2.对实际的螺旋线行波管进行模拟以验证时域理论。首先给出模拟时域理论所需要的初始条件，包括空间网格划分方法、初始高频场在轴向网格上的分布和初始时刻电子的分布状态。同时介绍相应的数值模拟方法，其中主要推导能实现时间和位置同时步进的麦考马克方法。其次以一支C波段螺旋线行波管为例，编程求解色散方程并得到其色散曲线图。然后利用色散关系和初始条件，模拟该行波管的注波互作用并给出模拟结果，包括高频场信号的传播、高频场功率随轴向位置或时间变化的曲线、功率扫描等信息。通过对模拟结果进行分析，验证了非线性时域理论的可行性。
3.为实现对诸如谐波、交调互调等非线性现象的模拟，对螺旋线行波管时域理论进行改进。首先，利用从高频电磁仿真软件提取得到的耦合阻抗等参数来处理高频场方程，提高非线性时域模拟的适用性和精度；其次，将高频场方程和空间电荷场表达式中激励源对波长的积分替换为对时间的积分，从而可以利用不同的高频信号时间周期的倍数关系来简化时域模拟的网格划分并实现其对多频信号的模拟。
4.实现对折叠波导行波管注波互作用的非线性时域模拟。首先从折叠波导行波管慢波结构的周期性出发，利用高频电磁仿真软件和弗洛奎定理得到其互作用区的数值高频场表达式，进而利用该数值高频场求解折叠波导行波管的时域高频场方程。其次利用泊松方程与粒子模拟方法相结合的方式来处理空间电荷场，得到适用于折叠波导行波管的空间电荷场。编程实现该时域理论的一维数值仿真代码并模拟一支实际的折叠波导行波管。模拟结果与实测结果相一致，验证了该时域理论对折叠波导行波管注波互作用非线性模拟的可行性。
5.提出并实现适用于各类行波管注波互作用的通用模拟技术。首先利用注波互作用过程中电子注与高频场之间的能量守恒关系，推导通用高频场方程。其次利用傅里叶级数展开空间电荷波的方法得到通用空间电荷场模型。从电磁仿真软件中提取数值高频场来求解通用高频场方程，同时结合有限差分方法求解空间电荷场，从而建立适用于各类行波管的非线性通用模拟技术。编写基于该注波互作用通用理论的一维代码，并将其应用于对螺旋线行波管、耦合腔行波管和折叠波导行波管的非线性模拟。模拟结果表明该通用理论具备很好的适用性。
Being a branch of important microwave vacuum devices, traveling wave tubes(TWTs) become an indispensable key part in the defense and communicationequipments because of their compatibility with wide bandth and high powercharacteristics. Accordingly, nonlinear theories for simulating the beam and waveinteraction (BWI) of TWTs have been developed to improve their performances. Sincemost of the exsiting nonlinear theories are mainly in frequency domain to analyze theBWI in steady state, the time-dependent nonlinear theories are in lackage to study thetransient BWI situations in TWTs. Meanwhile, as the demand of devices with higherfrequency and higher power increases, new types of TWTs, such as folded waveguide(FWG) TWTs have been designed and manfactured. As a result, nonlinear theories forsimulating the BWI of these TWTs are needed. So it can be concluded that the study oftime-dependent theories and generalized nonlinear simulation techniques for the BWI ofTWTs is essentially important.
A nonlinear BWI theory in a TWT should include a system of at least three typesof basic equations. These include1) the radio frequency (RF) field equations describingthe energy transformation between the RF signals and the electron beam,2) the spacecharge (SC) fields describing the coulomb forces among electrons, and3) the dynamicelectron equations describing the motion of the electrons. To develop nonlinear BWItheories and models in TWTs, the main work of this dissertation is focused on thesethree types of equations as follows. Firstly, the variation of time is included in the radiofrequency (RF) and space charge (SC) field equations to develop the time-dependentnonlinear theory. Secondly, the digitized RF field profiles have been applied toconstruct the generalized nonlinear BWI simulation model for various types of TWTs.Therefore, the main work and innovations of this dissertation are concluded below.
1. The nonlinear time-dependent BWI theory for helix TWTs is presented. Thedispersion relationship of the helix TWTs is obtained based on the sheath helix model.Based on the dispersion relationship and the analytical RF field expressions, thetime-dependent RF field equations are developed. The SC fields are modeled by SC waves and the corresponding SC field equations are discussed. On combining the RFfield equations and the SC field models with the dynamic electron equations which aredescribed using the relativistic Lorentz equations, the nonlinear time-dependent BWItheory for helix TWTs is developed.
2. A practical helix TWT is modeled to validate the time-denpendent theory.Firstly, the initial conditions for simulation, including the grid settings, the initial RFfields along frids, as well as the initial distribution of electrons are given. Meanwhile,the MacCormack method, which can be used to simulaously step the time and position,is discussed and applied in the numerial model. Secondly, as an example, the dispersionrelationship of a C band helix TWT is obtained. The BWI of this helix TWT is thenmodeled within the dispersion relationship and the initial conditions. The simulationresults, including the propagation of RF signals, the RF power varied with axial positionor time, and the scan of power are shown and discussed to prove the validation of thistime-dependent BWI theory in helix TWTs.
3. To increase the simulation accuracy, as well to simulate the multisiganalnonlinear charactistics, such as harmonic generation and intermodulations, the nonlineartime-dependent BWI theory has been improved. Firstly, the parameters obtained fromhigh frequency electromagnetic simulation software (e.g. HFSS), such as the couplingimpedence and so on, are applied in the RF field expressions to improve the simulationpracticiticy and accutacy. Secondly for the stimulus sources of the RF and SC fieldequations, the axial average over RF wavelength is replaced by the average over thecommon time period among RF signals. Hence the BWI grids are simplified andmultifrequency signals can be simulated.
4. The nonlinear time-dependent BWI model for the FWG TWTs has beendeveloped. Firstly, with the digitized RF fields in a single period from HFSS, the RFfield profile in the whole BWI scale can obtained by means of the Floquet theorem tosolve the RF field equations. Secondly, the SC fields in the FWG TWTs are calculatedby the combination of the Possion’s equations with the Particle-In-Cell (PIC) method.The one-dimensional (1-D) code based on this time dependent BWI theory is compiledto simulate a practical FWG TWT. The consistency between the simulation and testresults proves the validation of the BWI theory in FWG TWTs.
5. The generalized nonlinear BWI simulation technique has been developed forvarious types of TWTs in a unified way. Firstly, the RF field equations are developedfrom the Law of Energy Conservation between the RF signals and the electron beam.Accordingly, the digitized RF fields obtained from HFSS can be applied to solve thegeneralized RF field equations. The Fourier series of the SC wave have been applied inthe generalized SC model where the SC fields in TWTs are solved by the finitedifference method. The1-D code has been constructed to simulate a helix TWT, a CCTWT and a FWG TWT. The consistency between the simulation and test results showsthe feasibility of this generalized BWI model.
建立行波管注波互作用非线性理论体系至少需要三个基本方程组，即分析高频场与电子注能量交换过程的高频场方程、分析电子之间相互排斥力的空间电荷场方程以及描述电子注在电磁场作用下运动轨迹的电子运动方程。本论文围绕这三个方程组建立行波管注波互作用的非线性理论和模拟方法。论文首先在高频场方程和空间电荷场模型中引入时间变化因子，发展了行波管注波互作用非线性时域理论；然后利用数值方式建立广义高频场方程，得到了适用于各类行波管注波互作用的通用模拟模型。本论文工作的主要内容及创新点总结如下：
1.建立螺旋线行波管注波互作用的非线性时域理论。利用螺旋导电面模型推导螺旋线行波管的色散关系，然后根据该色散关系及高频电磁场表达式，建立时域高频场方程。利用空间电荷波理论求解空间电荷场，从而建立时域空间电荷场方程。将时域高频场方程、空间电荷场与相对论洛伦兹力方程描述的电子运动方程相结合，建立螺旋线行波管的非线性时域理论。
2.对实际的螺旋线行波管进行模拟以验证时域理论。首先给出模拟时域理论所需要的初始条件，包括空间网格划分方法、初始高频场在轴向网格上的分布和初始时刻电子的分布状态。同时介绍相应的数值模拟方法，其中主要推导能实现时间和位置同时步进的麦考马克方法。其次以一支C波段螺旋线行波管为例，编程求解色散方程并得到其色散曲线图。然后利用色散关系和初始条件，模拟该行波管的注波互作用并给出模拟结果，包括高频场信号的传播、高频场功率随轴向位置或时间变化的曲线、功率扫描等信息。通过对模拟结果进行分析，验证了非线性时域理论的可行性。
3.为实现对诸如谐波、交调互调等非线性现象的模拟，对螺旋线行波管时域理论进行改进。首先，利用从高频电磁仿真软件提取得到的耦合阻抗等参数来处理高频场方程，提高非线性时域模拟的适用性和精度；其次，将高频场方程和空间电荷场表达式中激励源对波长的积分替换为对时间的积分，从而可以利用不同的高频信号时间周期的倍数关系来简化时域模拟的网格划分并实现其对多频信号的模拟。
4.实现对折叠波导行波管注波互作用的非线性时域模拟。首先从折叠波导行波管慢波结构的周期性出发，利用高频电磁仿真软件和弗洛奎定理得到其互作用区的数值高频场表达式，进而利用该数值高频场求解折叠波导行波管的时域高频场方程。其次利用泊松方程与粒子模拟方法相结合的方式来处理空间电荷场，得到适用于折叠波导行波管的空间电荷场。编程实现该时域理论的一维数值仿真代码并模拟一支实际的折叠波导行波管。模拟结果与实测结果相一致，验证了该时域理论对折叠波导行波管注波互作用非线性模拟的可行性。
5.提出并实现适用于各类行波管注波互作用的通用模拟技术。首先利用注波互作用过程中电子注与高频场之间的能量守恒关系，推导通用高频场方程。其次利用傅里叶级数展开空间电荷波的方法得到通用空间电荷场模型。从电磁仿真软件中提取数值高频场来求解通用高频场方程，同时结合有限差分方法求解空间电荷场，从而建立适用于各类行波管的非线性通用模拟技术。编写基于该注波互作用通用理论的一维代码，并将其应用于对螺旋线行波管、耦合腔行波管和折叠波导行波管的非线性模拟。模拟结果表明该通用理论具备很好的适用性。
Being a branch of important microwave vacuum devices, traveling wave tubes(TWTs) become an indispensable key part in the defense and communicationequipments because of their compatibility with wide bandth and high powercharacteristics. Accordingly, nonlinear theories for simulating the beam and waveinteraction (BWI) of TWTs have been developed to improve their performances. Sincemost of the exsiting nonlinear theories are mainly in frequency domain to analyze theBWI in steady state, the time-dependent nonlinear theories are in lackage to study thetransient BWI situations in TWTs. Meanwhile, as the demand of devices with higherfrequency and higher power increases, new types of TWTs, such as folded waveguide(FWG) TWTs have been designed and manfactured. As a result, nonlinear theories forsimulating the BWI of these TWTs are needed. So it can be concluded that the study oftime-dependent theories and generalized nonlinear simulation techniques for the BWI ofTWTs is essentially important.
A nonlinear BWI theory in a TWT should include a system of at least three typesof basic equations. These include1) the radio frequency (RF) field equations describingthe energy transformation between the RF signals and the electron beam,2) the spacecharge (SC) fields describing the coulomb forces among electrons, and3) the dynamicelectron equations describing the motion of the electrons. To develop nonlinear BWItheories and models in TWTs, the main work of this dissertation is focused on thesethree types of equations as follows. Firstly, the variation of time is included in the radiofrequency (RF) and space charge (SC) field equations to develop the time-dependentnonlinear theory. Secondly, the digitized RF field profiles have been applied toconstruct the generalized nonlinear BWI simulation model for various types of TWTs.Therefore, the main work and innovations of this dissertation are concluded below.
1. The nonlinear time-dependent BWI theory for helix TWTs is presented. Thedispersion relationship of the helix TWTs is obtained based on the sheath helix model.Based on the dispersion relationship and the analytical RF field expressions, thetime-dependent RF field equations are developed. The SC fields are modeled by SC waves and the corresponding SC field equations are discussed. On combining the RFfield equations and the SC field models with the dynamic electron equations which aredescribed using the relativistic Lorentz equations, the nonlinear time-dependent BWItheory for helix TWTs is developed.
2. A practical helix TWT is modeled to validate the time-denpendent theory.Firstly, the initial conditions for simulation, including the grid settings, the initial RFfields along frids, as well as the initial distribution of electrons are given. Meanwhile,the MacCormack method, which can be used to simulaously step the time and position,is discussed and applied in the numerial model. Secondly, as an example, the dispersionrelationship of a C band helix TWT is obtained. The BWI of this helix TWT is thenmodeled within the dispersion relationship and the initial conditions. The simulationresults, including the propagation of RF signals, the RF power varied with axial positionor time, and the scan of power are shown and discussed to prove the validation of thistime-dependent BWI theory in helix TWTs.
3. To increase the simulation accuracy, as well to simulate the multisiganalnonlinear charactistics, such as harmonic generation and intermodulations, the nonlineartime-dependent BWI theory has been improved. Firstly, the parameters obtained fromhigh frequency electromagnetic simulation software (e.g. HFSS), such as the couplingimpedence and so on, are applied in the RF field expressions to improve the simulationpracticiticy and accutacy. Secondly for the stimulus sources of the RF and SC fieldequations, the axial average over RF wavelength is replaced by the average over thecommon time period among RF signals. Hence the BWI grids are simplified andmultifrequency signals can be simulated.
4. The nonlinear time-dependent BWI model for the FWG TWTs has beendeveloped. Firstly, with the digitized RF fields in a single period from HFSS, the RFfield profile in the whole BWI scale can obtained by means of the Floquet theorem tosolve the RF field equations. Secondly, the SC fields in the FWG TWTs are calculatedby the combination of the Possion’s equations with the Particle-In-Cell (PIC) method.The one-dimensional (1-D) code based on this time dependent BWI theory is compiledto simulate a practical FWG TWT. The consistency between the simulation and testresults proves the validation of the BWI theory in FWG TWTs.
5. The generalized nonlinear BWI simulation technique has been developed forvarious types of TWTs in a unified way. Firstly, the RF field equations are developedfrom the Law of Energy Conservation between the RF signals and the electron beam.Accordingly, the digitized RF fields obtained from HFSS can be applied to solve thegeneralized RF field equations. The Fourier series of the SC wave have been applied inthe generalized SC model where the SC fields in TWTs are solved by the finitedifference method. The1-D code has been constructed to simulate a helix TWT, a CCTWT and a FWG TWT. The consistency between the simulation and test results showsthe feasibility of this generalized BWI model.
引文
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