高功率微波大气传播非线性问题的数值研究
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摘要
本文主要研究了高功率微波(HPM)脉冲的大气传播与击穿等问题。通过对高功率脉冲的大气传播模型的特点分析,以及考虑到以前类似研究的效率问题,我们采用了时域有限差分(FDTD)法对其进行数值模拟,力图通过该过程来揭示高功率微波脉冲大气传播的规律,为高功率微波脉冲的传播和工程应用提供有参考意义的结论。
本论文首先综述了高功率微波的应用背景,对国内外相关领域的研究现状进行了分析,并且简要介绍了FDTD的基本原理及应用、高功率微波的大气传播模型、该传播模型的FDTD差分格式及其在大气中的传播和击穿特点。
结合高功率微波大气传播的物理意义及严格的数学证明,推导了由时域有限差分法对高功率微波大气传播模型中心差分所得的按时间步进的显示差分格式的稳定性条件和数值色散要求。数值结果显示了FDTD在处理高功率微波大气传播问题上具有很好的可行性和精确性,并相比其他处理方法具有很高的计算效率。通过对高功率微波的击穿条件的分析,对其在背景大气中的击穿阈值作了估算。估算结果与FDTD计算结果和实验数据对比,都比较符合。击穿场强的估算对高功率微波的工程应用和相关实验能提供重要的参考依据。
为了进一步提高高功率微波大气传播问题的数值模拟效率,提出了一种新的处理方法,即分段FDTD计算方法。该方法是直接基于传统FDTD算法,通过将计算空间进行分段,每段之间再进行数据传递的思想来实现。分段FDTD的提出使得高功率微波脉冲长距离传播问题的数值模拟效率得以极大的提升,同时由于该方法在计算效率上具有的优势,为本文在超宽带高功率电磁脉冲的大气传播问题的研究方面提供了坚实的技术保障。
通过对超宽带高功率微波脉冲场强有效值的求解,获取超宽带高功率微波与大气相互作用的参数。并结合改进的分段FDTD方法对超宽带高功率微波脉冲的大气传播具体过程进行数值计算。研究了高斯脉冲、调制高斯脉冲、微分高斯脉冲、阻尼正弦波等超宽带高功率微波脉冲的大气传播过程、尾蚀效应和其它非线性物理问题,同时分析了大气击穿对其频谱的影响。
对处于高功率微波作用下的大气中自由电子密度的变化及该变化对高功率微波的反作用的过程分析,将由高功率微波电离电子所得的自生等离子体混合而成的非均匀混合大气进行分层处理,利用电磁波在非均匀介质中传播问题的FDTD求解方法,对高功率微波脉冲在该混合大气中传播过程和反射特性进行数值分析。
在重复频率高功率微波脉冲大气传播问题的研究中,我们构建了一种半解析模型。并且提出了一个临界重复频率,同时推导出来重复频率高功率脉冲场强的击穿阈值。并且分析了重复频率高功率脉冲不同参数对该临界重复频率和击穿场强的影响。
最后概括了本文在高功率微波脉冲大气传播方面取得的研究成果,并展望了该研究的发展方向。
The propagation and breakdown mechanism of High Power Microwave (HPM) pulse is researched in this dissertation. Taking into account the characteristics of HPM atmosphere propagation model and the efficiency of previous similar studies, the finite-difference time-domain (FDTD) method is employed to simulate the HPM atmospheric propagation model. By this approach, the law of atmospheric propagation of high power microwave pulse is revealed and an important reference for high power microwave pulse propagation and engineering applications is given.
At first, the application background of the HPM pulse is reviewed, and the basic principles of FDTD are briefly introduced. Meanwhile, the FDTD difference schemes for high-power microwave atmospheric propagation model and the characteristics of HPM propagation and breakdown are introduced.
Combined with the physical meaning of high power microwave atmospheric propagation and the strict mathematical proof, the stability condition of the FDTD difference schemes for high-power microwave atmospheric propagation model is derived, as well as the corresponding numerical dispersion is analyzed. The numerical results show the FDTD method has a good feasibility and validity in dealing with the issue of high-power microwave atmospheric propagation, and has a higher computational efficiency compared with other methods. By analyzing the breakdown conditions of high-power microwave, the breakdown threshold is estimated. The estimation results and FDTD results and experimental data are consistent. The estimation results of breakdown threshold can provide important reference for high-power microwave engineering applications and related experiments.
To further enhance the simulation efficiency of high-power microwave atmospheric propagation, a new approach, that is, subsection FDTD method is proposed. The method is realized by separating computation space and transferring the data between each subsection, which directly based on the traditional FDTD algorithm. The proposed method improves the simulation efficiency of high-power microwave pulse long-distance propagation. At the same time, its high efficiency provides a solid technical support for the issue of the ultra-wideband high power microwave pulse atmospheric propagation.
By solving the effective E field strength of the ultra-wideband HPM atmospheric propagation, the parameters of ultra-wideband high power microwave interacts with the atmosphere can be obtained. And combined with the improved subsection FDTD method, the specific process of ultra-wideband HPM atmosphere propagation is calculated. The propagation process of the atmosphere, tail erosion effect and other non-linear physical problems of Gaussian pulse, modulated Gaussian pulse, differential Gaussian pulse, damped sine wave such as ultra-wideband high power microwave pulse are studied, and the inference of air breakdown to its spectrum is analyzed.
At first, the electron density evolution due to the HPM pulses and the reaction to HPM pulses caused by electron density evolution is studied. And then the mixture-atmosphere which is composited by plasma and non-plasma can be layered as inhomogeneous medium. Finally, the reflection characteristics of the HPM propagation in the mixture-atmosphere are investigated by FDTD in inhomogeneous medium.
A semi-analytical model for the propagation of the repetition frequency HPM pulses is established. And a critical repetition frequency for the HPM pulse is presented. As well as the breakdown threshold of the repetition frequency HPM pulses is derived. Fianlly, the effects of different parameters of the repetition frequency HPM pulses on air breakdown are analyzed.
At last part of the dissertation the study of propagation mechanism of HPM pulse is summarized, and the development directions of these researches are predicted.
本论文首先综述了高功率微波的应用背景,对国内外相关领域的研究现状进行了分析,并且简要介绍了FDTD的基本原理及应用、高功率微波的大气传播模型、该传播模型的FDTD差分格式及其在大气中的传播和击穿特点。
结合高功率微波大气传播的物理意义及严格的数学证明,推导了由时域有限差分法对高功率微波大气传播模型中心差分所得的按时间步进的显示差分格式的稳定性条件和数值色散要求。数值结果显示了FDTD在处理高功率微波大气传播问题上具有很好的可行性和精确性,并相比其他处理方法具有很高的计算效率。通过对高功率微波的击穿条件的分析,对其在背景大气中的击穿阈值作了估算。估算结果与FDTD计算结果和实验数据对比,都比较符合。击穿场强的估算对高功率微波的工程应用和相关实验能提供重要的参考依据。
为了进一步提高高功率微波大气传播问题的数值模拟效率,提出了一种新的处理方法,即分段FDTD计算方法。该方法是直接基于传统FDTD算法,通过将计算空间进行分段,每段之间再进行数据传递的思想来实现。分段FDTD的提出使得高功率微波脉冲长距离传播问题的数值模拟效率得以极大的提升,同时由于该方法在计算效率上具有的优势,为本文在超宽带高功率电磁脉冲的大气传播问题的研究方面提供了坚实的技术保障。
通过对超宽带高功率微波脉冲场强有效值的求解,获取超宽带高功率微波与大气相互作用的参数。并结合改进的分段FDTD方法对超宽带高功率微波脉冲的大气传播具体过程进行数值计算。研究了高斯脉冲、调制高斯脉冲、微分高斯脉冲、阻尼正弦波等超宽带高功率微波脉冲的大气传播过程、尾蚀效应和其它非线性物理问题,同时分析了大气击穿对其频谱的影响。
对处于高功率微波作用下的大气中自由电子密度的变化及该变化对高功率微波的反作用的过程分析,将由高功率微波电离电子所得的自生等离子体混合而成的非均匀混合大气进行分层处理,利用电磁波在非均匀介质中传播问题的FDTD求解方法,对高功率微波脉冲在该混合大气中传播过程和反射特性进行数值分析。
在重复频率高功率微波脉冲大气传播问题的研究中,我们构建了一种半解析模型。并且提出了一个临界重复频率,同时推导出来重复频率高功率脉冲场强的击穿阈值。并且分析了重复频率高功率脉冲不同参数对该临界重复频率和击穿场强的影响。
最后概括了本文在高功率微波脉冲大气传播方面取得的研究成果,并展望了该研究的发展方向。
The propagation and breakdown mechanism of High Power Microwave (HPM) pulse is researched in this dissertation. Taking into account the characteristics of HPM atmosphere propagation model and the efficiency of previous similar studies, the finite-difference time-domain (FDTD) method is employed to simulate the HPM atmospheric propagation model. By this approach, the law of atmospheric propagation of high power microwave pulse is revealed and an important reference for high power microwave pulse propagation and engineering applications is given.
At first, the application background of the HPM pulse is reviewed, and the basic principles of FDTD are briefly introduced. Meanwhile, the FDTD difference schemes for high-power microwave atmospheric propagation model and the characteristics of HPM propagation and breakdown are introduced.
Combined with the physical meaning of high power microwave atmospheric propagation and the strict mathematical proof, the stability condition of the FDTD difference schemes for high-power microwave atmospheric propagation model is derived, as well as the corresponding numerical dispersion is analyzed. The numerical results show the FDTD method has a good feasibility and validity in dealing with the issue of high-power microwave atmospheric propagation, and has a higher computational efficiency compared with other methods. By analyzing the breakdown conditions of high-power microwave, the breakdown threshold is estimated. The estimation results and FDTD results and experimental data are consistent. The estimation results of breakdown threshold can provide important reference for high-power microwave engineering applications and related experiments.
To further enhance the simulation efficiency of high-power microwave atmospheric propagation, a new approach, that is, subsection FDTD method is proposed. The method is realized by separating computation space and transferring the data between each subsection, which directly based on the traditional FDTD algorithm. The proposed method improves the simulation efficiency of high-power microwave pulse long-distance propagation. At the same time, its high efficiency provides a solid technical support for the issue of the ultra-wideband high power microwave pulse atmospheric propagation.
By solving the effective E field strength of the ultra-wideband HPM atmospheric propagation, the parameters of ultra-wideband high power microwave interacts with the atmosphere can be obtained. And combined with the improved subsection FDTD method, the specific process of ultra-wideband HPM atmosphere propagation is calculated. The propagation process of the atmosphere, tail erosion effect and other non-linear physical problems of Gaussian pulse, modulated Gaussian pulse, differential Gaussian pulse, damped sine wave such as ultra-wideband high power microwave pulse are studied, and the inference of air breakdown to its spectrum is analyzed.
At first, the electron density evolution due to the HPM pulses and the reaction to HPM pulses caused by electron density evolution is studied. And then the mixture-atmosphere which is composited by plasma and non-plasma can be layered as inhomogeneous medium. Finally, the reflection characteristics of the HPM propagation in the mixture-atmosphere are investigated by FDTD in inhomogeneous medium.
A semi-analytical model for the propagation of the repetition frequency HPM pulses is established. And a critical repetition frequency for the HPM pulse is presented. As well as the breakdown threshold of the repetition frequency HPM pulses is derived. Fianlly, the effects of different parameters of the repetition frequency HPM pulses on air breakdown are analyzed.
At last part of the dissertation the study of propagation mechanism of HPM pulse is summarized, and the development directions of these researches are predicted.
引文
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