回旋管注波互作用非线性理论与模拟研究
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摘要
回旋管是一类具有重要发展前景的毫米波器件,能在毫米波及亚毫米波波段产生高功率、高效率和高增益,性能稳定,有一定的带宽,广泛应用在高功率雷达、电子对抗、微波武器、通信等领域,是目前电真空器件的热点研究对象之一。
回旋管的注波互作用情况决定了回旋类器件的电子效率和主要的工作性能。是回旋类器件研究的关键内容,也是目前研究最为广泛的课题之一。各国学者开发了一系列可用于回旋管注波互作用的模拟与优化设计程序。本论文在深入了解回旋管的研究现状、发展方向及应用前景的基础上,对回旋管的注波互作用非线性理论进行了研究。主要工作和创新点如下：
1.从基本的电磁场理论出发,推导出回旋管中电子注与高频场相互作用的自洽非线性方程组,建立了回旋振荡管、回旋速调管以及回旋行波管均适用的注波互作用自洽非线性理论模型。该模型采用简化的电磁场描述方法,用波导中横向电磁场的本征模式的叠加表示电磁场。相应地,将麦克斯韦方程组简化为各模式电压复振幅与电流复振幅关于时间和轴向坐标的耦合偏微分方程组(即广义电报方程),从而将电磁场的求解转化为广义电报方程的求解。各模式的场幅值随时间缓慢变化,更新电磁场的基本时间量程仅与谐振腔的填充时间相联系,因而允许比较长的时间间隔更新场。在此基础上,为了能够求解含有有限表面阻抗的电磁场,对广义电报方程进行了扩展,给出了损耗边界积分的处理方法,使广义电报方程能够计算损耗结构中的场。
2.电子运动方程采用引导中心近似。在引导中心坐标系下,引入两种假设,其一是假设粒子穿过腔体的时间比电磁场演变时间要短。根据这种假设,粒子在腔内电磁场的辐射包络发生大的改变之前离开腔体。这就允许我们在描述电子运动方程时,将轴向坐标作为独立变量。而无需向PIC粒子模拟方法那样执行耗时的粒子位置沿轴向网格的插值运算,从而减少计算时间。其二是假设轴向磁场很强。在这种假设下,拉莫尔半径小于腔体特性长度,粒子沿磁场线运动。这两种假设的引入可以对电子运动方程进行简化,从而降低计算量。对激发电磁场的电流源,采用所有电子轨迹求和表示电流密度,根据电流源的定义得到电流源方程。从回旋管电子注横向速度满足高斯分布出发,建立了速度零散的分布模型。该模型更准确的反映粒子的分布情况,使非线性理论的计算结果更有意义。
3.利用回旋管注波互作用自洽非线性理论模型,本文对一支Ka波段两腔回旋速调管放大器的非线性特性进行了深入研究。分析了注波互作用中的能量变化,研究了输入功率、电子注电压、电流、工作磁场、横纵速度比等工作参量对效率的影响。同时,应用粒子模拟软件MAGIC对设计的Ka波段两腔回旋速调管放大器进行了模拟验证,并对两种方法计算的结果进行了对比分析。MAGIC粒子模拟结果与自洽非线性理论程序结果基本一致,从而验证了回旋管注波互作用自洽非线性理论的正确性。在此基础上,利用所建立的理论模型设计了一支Ka波段二次谐波三腔回旋速调管放大器,研究了该回旋速调管放大器的非线性过程及特点。通过分析其非线性特性,确定了该回旋速调管放大器的最佳工作参数。同时,利用粒子模拟软件MAGIC进行大量的计算模拟,对设计的Ka波段二次谐波三腔回旋速调管放大器进行了对比验证。
4.利用回旋管注波互作用自洽非线性理论模型,针对复合腔回旋管的特性,研究了94GHz二次谐波复合腔回旋管。分析了不同工作参数对复合腔回旋管非线性特性的影响,并总结模拟结果给出一组最优的参数。将优化参数代入粒子模拟软件MAGIC,对设计的复合腔回旋管进行了模拟验证。
5.利用高频软件HFSS、粒子模拟软件MAGIC和广义电报方程,讨论了漂移段内和谐振腔内损耗结构对回旋速调管和回旋行波管性能的影响。同时,基于回旋管注波互作用自洽非线性理论模型,对含有损耗结构的回旋行波管进行了研究,分析了损耗介质层厚度、介电常数等对回旋行波管性能的影响,并进一步研究了回旋行波管的非线性特性。同时,利用粒子模拟软件MAGIC对该回旋行波管进行了对比模拟验证。
Gyrotron is one of the most promising novel millimeter wave devices. In the millimeter wave and submillimeter wave bands, it is able to produce high power, high efficiency and high gain. The Gyrotron has a certain bandwidth, and the performance is stable. It has great value in the millimeter wave high power radar, electronic warfare, microwave weapons, communications and other aspects of a very wide range of applications. The Gyrotron is currently one of the hot research object of the electric vacuum devices.
Beam wave interaction in the gyrotron directly determines the efficiency and the working performance of electronic devices. Therefore, the study of gyrotron device of beam-wave interaction is the most widely studied topic, also is the most important and key device research content. Scholars at home and abroad spent a lot of time and energy to develop the program used for the gyrotron device simulation and optimization. In this dissertation, based on the depth analysis of gyrotron device development, application prospect and research status, the nonlinear self-consistent beam wave interaction theory and computer aided design are studied. The main work and innovation are as follows:
1. From the basic theory of electromagnetic field, this dissertation derived the gyrotron of electron beam and the high frequency field interaction nonlinear self-consistent equations, established nonlinear self-consistent beam wave interaction theory model, which is applicable for Gyrotron oscillators, Gyroklystron amplifier and Gyro-travelling wave tude. This model uses a simplified description of the fields as a superposition of transverse electric and transverse magnetic eigenmodes of the waveguide. Accordingly, the Maxwell equation is simplified as the mode of voltage and current of complex amplitude on time and axial coordinates of the partial differential equations (i.e. generalized telegrapher's equations). Therefore, the solving electromagnetic field problem is transformed into solving the generalized telegrapher's equations.The complex amplitudes of the modes vary slowly with time. The basic time scale for updating the radiation field is a fraction of the cavity fill time, rather than a fraction of the high frequency period. On this basis, the loss of boundary integral in the generalized telegrapher's equations is processed, making these equations to calculate the fields in the loss of structure.
2. Electronic equations of motion use the guiding center approximation. In the guiding center coordinate system, this dissertation introduces two kinds of hypothesis. One hypothesis is that the particles traverse the cavity in a time shorter than evolution time of the electromagnetic fields. Based on the hypothesis, particles transit the device before the envelope of the the radiation changes significantly. This allows us to describe the electron motion equations, the axial coordinates as independent variables. There is then no need to perform the usual interpolations on the axial grid of a particle location and the numercial operations of "gather" and "scatter", which is time consuming. The other hypothesis is that the axial magnetic field is strong. In this assumption, the Larmor radius is smaller than the cavity characteristic length and the particles essentially follow the magnetic-field lines.The introduction of the two hypotheses can be simplified equations of electron motion, thereby, reducing the amount of computation.With all electronic trajectories, it can calculate the current source. Then, the particles initial conditions are given. Transverse velocity of the electrons from the gyrotron satisfies the Gaussian distribution, distribution model of the velocity spread in the gyroklystron amplifier beam-wave interaction is established. In addition, we solved numerically the theory model of generalized telegrapher's equations and the electron motion equations. Using the unconditionally stable classical implicit format to difference combined with the boundary conditions, a numerical model of generalized telegrapher's equations is established.
3. Using the beam wave interaction self-consistent nonlinear theory model, a Ka band two cavities gyroklystron amplifier is numerically studied. The beam-wave interaction energy changes is discussed, and the input power, electron beam voltage, magnetic field, horizontal and vertical velocity ratio effects on efficiency and output power are analyzed. This dissertation use particle simulation software MAGIC to optimize and simulate the designed Ka band two cavities gyroklystron amplifier. The calculated results of the two methods were compared and analyzed. MAGIC simulation results and the self-consistent nonlinear theory program results are basically consistent, which verifies the self-consistent nonlinear theory. The program can be used as a gyrotron device preliminary design tool, which can greatly shorten the gyrotron device simulation time, accelerate device design process, and also deepen understanding of the amplifier of electron beam and wave interaction mechanisms and the physical process. Therefore, the work on gyrotron device development has important guiding significance. On this basis, the design and simulation of a Ka-band two harmonics three cavities of the gyroklystron amplifier is presented. The dissertation studied the gyrotron device nonlinear process and characteristic, and discussed electronic injection voltage, current and magnetic field, frequency and other working parameters on the device. Through the analysis of nonlinear characteristics, we determined the gyrotron optimum working parameters, and achieved the design goals.This dissertation also use particle simulation software MAGIC to optimize and simulate the designed Ka-band two harmonics of the three cavities gyroklystron amplifier.
4. Using the beam wave interaction self-consistent nonlinear theory simplified model, this dissertation study a94GHz second harmonics complex cavity gyrotron. By continuously adjusting the the complex cavity of dimension, it get a set of optimized parameters and give the impact of the changes in different parameters of the complex cavity gyrotron characteristics. Then, this dissertation use MAGIC to optimize and simulate the94GHz two harmonics complex cavity gyrotron.
5. Using the high frequency software HFSS, particle in cell simulation software MAGIC and the generalized telegrapher's equations, this dissertation discusses two kinds of loss structures on the gyrotrons. At the same time, the analysis of the loss of the structure and its application is given. Based on the theory model, this dissertation studied the Gyro-travelling wave tude with loss structure. The loss of the thickness of the dielectric layer, the dielectric constant of the gyrotron traveling wave tube on output power is analyzed, and further the nonlinear characteristics of the Gyro-travelling wave tude is studied in detail. Then, we use simulation software MAGIC to compare and validate the Gyro-travelling wave tude.
回旋管的注波互作用情况决定了回旋类器件的电子效率和主要的工作性能。是回旋类器件研究的关键内容,也是目前研究最为广泛的课题之一。各国学者开发了一系列可用于回旋管注波互作用的模拟与优化设计程序。本论文在深入了解回旋管的研究现状、发展方向及应用前景的基础上,对回旋管的注波互作用非线性理论进行了研究。主要工作和创新点如下：
1.从基本的电磁场理论出发,推导出回旋管中电子注与高频场相互作用的自洽非线性方程组,建立了回旋振荡管、回旋速调管以及回旋行波管均适用的注波互作用自洽非线性理论模型。该模型采用简化的电磁场描述方法,用波导中横向电磁场的本征模式的叠加表示电磁场。相应地,将麦克斯韦方程组简化为各模式电压复振幅与电流复振幅关于时间和轴向坐标的耦合偏微分方程组(即广义电报方程),从而将电磁场的求解转化为广义电报方程的求解。各模式的场幅值随时间缓慢变化,更新电磁场的基本时间量程仅与谐振腔的填充时间相联系,因而允许比较长的时间间隔更新场。在此基础上,为了能够求解含有有限表面阻抗的电磁场,对广义电报方程进行了扩展,给出了损耗边界积分的处理方法,使广义电报方程能够计算损耗结构中的场。
2.电子运动方程采用引导中心近似。在引导中心坐标系下,引入两种假设,其一是假设粒子穿过腔体的时间比电磁场演变时间要短。根据这种假设,粒子在腔内电磁场的辐射包络发生大的改变之前离开腔体。这就允许我们在描述电子运动方程时,将轴向坐标作为独立变量。而无需向PIC粒子模拟方法那样执行耗时的粒子位置沿轴向网格的插值运算,从而减少计算时间。其二是假设轴向磁场很强。在这种假设下,拉莫尔半径小于腔体特性长度,粒子沿磁场线运动。这两种假设的引入可以对电子运动方程进行简化,从而降低计算量。对激发电磁场的电流源,采用所有电子轨迹求和表示电流密度,根据电流源的定义得到电流源方程。从回旋管电子注横向速度满足高斯分布出发,建立了速度零散的分布模型。该模型更准确的反映粒子的分布情况,使非线性理论的计算结果更有意义。
3.利用回旋管注波互作用自洽非线性理论模型,本文对一支Ka波段两腔回旋速调管放大器的非线性特性进行了深入研究。分析了注波互作用中的能量变化,研究了输入功率、电子注电压、电流、工作磁场、横纵速度比等工作参量对效率的影响。同时,应用粒子模拟软件MAGIC对设计的Ka波段两腔回旋速调管放大器进行了模拟验证,并对两种方法计算的结果进行了对比分析。MAGIC粒子模拟结果与自洽非线性理论程序结果基本一致,从而验证了回旋管注波互作用自洽非线性理论的正确性。在此基础上,利用所建立的理论模型设计了一支Ka波段二次谐波三腔回旋速调管放大器,研究了该回旋速调管放大器的非线性过程及特点。通过分析其非线性特性,确定了该回旋速调管放大器的最佳工作参数。同时,利用粒子模拟软件MAGIC进行大量的计算模拟,对设计的Ka波段二次谐波三腔回旋速调管放大器进行了对比验证。
4.利用回旋管注波互作用自洽非线性理论模型,针对复合腔回旋管的特性,研究了94GHz二次谐波复合腔回旋管。分析了不同工作参数对复合腔回旋管非线性特性的影响,并总结模拟结果给出一组最优的参数。将优化参数代入粒子模拟软件MAGIC,对设计的复合腔回旋管进行了模拟验证。
5.利用高频软件HFSS、粒子模拟软件MAGIC和广义电报方程,讨论了漂移段内和谐振腔内损耗结构对回旋速调管和回旋行波管性能的影响。同时,基于回旋管注波互作用自洽非线性理论模型,对含有损耗结构的回旋行波管进行了研究,分析了损耗介质层厚度、介电常数等对回旋行波管性能的影响,并进一步研究了回旋行波管的非线性特性。同时,利用粒子模拟软件MAGIC对该回旋行波管进行了对比模拟验证。
Gyrotron is one of the most promising novel millimeter wave devices. In the millimeter wave and submillimeter wave bands, it is able to produce high power, high efficiency and high gain. The Gyrotron has a certain bandwidth, and the performance is stable. It has great value in the millimeter wave high power radar, electronic warfare, microwave weapons, communications and other aspects of a very wide range of applications. The Gyrotron is currently one of the hot research object of the electric vacuum devices.
Beam wave interaction in the gyrotron directly determines the efficiency and the working performance of electronic devices. Therefore, the study of gyrotron device of beam-wave interaction is the most widely studied topic, also is the most important and key device research content. Scholars at home and abroad spent a lot of time and energy to develop the program used for the gyrotron device simulation and optimization. In this dissertation, based on the depth analysis of gyrotron device development, application prospect and research status, the nonlinear self-consistent beam wave interaction theory and computer aided design are studied. The main work and innovation are as follows:
1. From the basic theory of electromagnetic field, this dissertation derived the gyrotron of electron beam and the high frequency field interaction nonlinear self-consistent equations, established nonlinear self-consistent beam wave interaction theory model, which is applicable for Gyrotron oscillators, Gyroklystron amplifier and Gyro-travelling wave tude. This model uses a simplified description of the fields as a superposition of transverse electric and transverse magnetic eigenmodes of the waveguide. Accordingly, the Maxwell equation is simplified as the mode of voltage and current of complex amplitude on time and axial coordinates of the partial differential equations (i.e. generalized telegrapher's equations). Therefore, the solving electromagnetic field problem is transformed into solving the generalized telegrapher's equations.The complex amplitudes of the modes vary slowly with time. The basic time scale for updating the radiation field is a fraction of the cavity fill time, rather than a fraction of the high frequency period. On this basis, the loss of boundary integral in the generalized telegrapher's equations is processed, making these equations to calculate the fields in the loss of structure.
2. Electronic equations of motion use the guiding center approximation. In the guiding center coordinate system, this dissertation introduces two kinds of hypothesis. One hypothesis is that the particles traverse the cavity in a time shorter than evolution time of the electromagnetic fields. Based on the hypothesis, particles transit the device before the envelope of the the radiation changes significantly. This allows us to describe the electron motion equations, the axial coordinates as independent variables. There is then no need to perform the usual interpolations on the axial grid of a particle location and the numercial operations of "gather" and "scatter", which is time consuming. The other hypothesis is that the axial magnetic field is strong. In this assumption, the Larmor radius is smaller than the cavity characteristic length and the particles essentially follow the magnetic-field lines.The introduction of the two hypotheses can be simplified equations of electron motion, thereby, reducing the amount of computation.With all electronic trajectories, it can calculate the current source. Then, the particles initial conditions are given. Transverse velocity of the electrons from the gyrotron satisfies the Gaussian distribution, distribution model of the velocity spread in the gyroklystron amplifier beam-wave interaction is established. In addition, we solved numerically the theory model of generalized telegrapher's equations and the electron motion equations. Using the unconditionally stable classical implicit format to difference combined with the boundary conditions, a numerical model of generalized telegrapher's equations is established.
3. Using the beam wave interaction self-consistent nonlinear theory model, a Ka band two cavities gyroklystron amplifier is numerically studied. The beam-wave interaction energy changes is discussed, and the input power, electron beam voltage, magnetic field, horizontal and vertical velocity ratio effects on efficiency and output power are analyzed. This dissertation use particle simulation software MAGIC to optimize and simulate the designed Ka band two cavities gyroklystron amplifier. The calculated results of the two methods were compared and analyzed. MAGIC simulation results and the self-consistent nonlinear theory program results are basically consistent, which verifies the self-consistent nonlinear theory. The program can be used as a gyrotron device preliminary design tool, which can greatly shorten the gyrotron device simulation time, accelerate device design process, and also deepen understanding of the amplifier of electron beam and wave interaction mechanisms and the physical process. Therefore, the work on gyrotron device development has important guiding significance. On this basis, the design and simulation of a Ka-band two harmonics three cavities of the gyroklystron amplifier is presented. The dissertation studied the gyrotron device nonlinear process and characteristic, and discussed electronic injection voltage, current and magnetic field, frequency and other working parameters on the device. Through the analysis of nonlinear characteristics, we determined the gyrotron optimum working parameters, and achieved the design goals.This dissertation also use particle simulation software MAGIC to optimize and simulate the designed Ka-band two harmonics of the three cavities gyroklystron amplifier.
4. Using the beam wave interaction self-consistent nonlinear theory simplified model, this dissertation study a94GHz second harmonics complex cavity gyrotron. By continuously adjusting the the complex cavity of dimension, it get a set of optimized parameters and give the impact of the changes in different parameters of the complex cavity gyrotron characteristics. Then, this dissertation use MAGIC to optimize and simulate the94GHz two harmonics complex cavity gyrotron.
5. Using the high frequency software HFSS, particle in cell simulation software MAGIC and the generalized telegrapher's equations, this dissertation discusses two kinds of loss structures on the gyrotrons. At the same time, the analysis of the loss of the structure and its application is given. Based on the theory model, this dissertation studied the Gyro-travelling wave tude with loss structure. The loss of the thickness of the dielectric layer, the dielectric constant of the gyrotron traveling wave tube on output power is analyzed, and further the nonlinear characteristics of the Gyro-travelling wave tude is studied in detail. Then, we use simulation software MAGIC to compare and validate the Gyro-travelling wave tude.
引文
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