高功率双频相对论返波振荡器研究
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摘要
随着高功率微波(HPM)技术在高功率、高效率、长脉冲、重复频率运行方面取得长足的进步，高功率微波源也出现了一些其他的研究发展趋势，比如说双频以及多频高功率微波源技术。双频以及多频高功率微波可以用于电子系统攻击以及各种通信系统，具有重要的学术价值和应用前景。相对论返波振荡器(RBWO)在HPM领域中占有重要的地位，具有高功率、高效率、适合重复频率工作等特点，是HPM领域目前最具有发展和应用潜力的器件之一。
以此为背景，本论文对双频同轴相对论返波振荡器(CRBWO)开展了全面、深入的研究，包括理论研究、数值模拟计算和粒子模拟(PIC)研究，并在实验上利用单电子束在CRBWO上实现了X波段双频输出，成功探索出采用单电子束产生双频微波的技术路径，也对CRBWO在双频以及多频领域的开拓研究奠定了理论以及实验基础。论文的主要研究工作体现在以下几个方面：
1．运用场匹配原理和Fourier级数理论，推导了自洽的同轴周期慢波结构(SWS)的线性色散理论方程。理论模型适用于任意同轴周期慢波结构，考虑了同轴内外双波纹结构以及内外波纹相位差，并考虑了电子束的径向厚度，相比其他模型更加接近HPM实验。分析了同轴SWS相对于空心SWS在空间电荷限制流、微波产生效率以及电子频率调谐带宽方面的优势。数值分析了实验器件模型的冷、热腔色散曲线以及微波时间增长率和耦合阻抗。研究中发现:波纹幅值相等时，外波纹同轴慢波结构的色散曲线上限截止频率比双波纹及内波纹结构的更高，色散曲线比较陡峭，更加有利于频率调谐;耦合阻抗随着波纹深度的增大而增大，随着周期长度的增大而减小;对于内外双波纹慢波结构，在腔体的横截面内，准TEM模式与TM01模的-1次谐波的耦合阻抗都得到了提高，可以保证电子束横截面内的电子都进行有效的波束相互作用，提高微波产生效率;微波时间增长率随着波纹周期的增大而降低，随着波纹幅值的增大而增大;随着电子束位置靠近同轴SWS外波纹表面，表面波幅值增大，耦合阻抗增大，微波时间增长率随之增大；随着电子束流增大，微波增长率增大，有利于CRBWO的微波起振。
2．提出了一种单电子束双频CRBWO模型，对其运行机制和工作特性进行了深入系统的粒子模拟研究，模拟结果显示:在引导磁场0.82T，束电压500kV，束电流8.7kA，漂移段长度L20.5mm下，模拟获得了X波段的TM01模式双频微波输出，双频频率为10.06GHz和10.49GHz,并观察到了明显的拍频电场信号和功率信号;微波峰值功率2.3GW，平均功率700MW，两个频率分量的功率分别为383MW和317MW，微波产生平均效率为16.1%。对微波输出进行时频分析，发现双频信号起振以及饱和时间不同，双频共同输出的功率饱和时间约为8ns。对模型两段SWS(SWS1与SWS2)工作频率的独立性进行了模拟验证。
3．首次设计了带有同轴谐振腔的双频CRBWO并开展了模拟研究。在电子束加速电压c520kV，电子束流I b8.5kA时，器件辐射双频为9.43GHz、10.30GHz；微波平均功率为1.07GW，微波产生效率为24.2%；随着两段SWS之间漂移段长度Ld的改变，双频频谱近似周期性出现，周期近似为f2波长的12；SWS1的主频f1实现了频率捷变输出，频率捷变带宽400MHz。
4．对X波段双频器件的频谱进行了拓展研究，开展了带有非对称反射腔的C波段和X波段CRBWO的模拟研究。器件采用耦合阻抗跃变型的分段慢波结构，优化和改善了器件中轴向电场分布和电子束的能散。在电压510kV，电流9.03kA，轴向引导磁场0.73T下，器件实现了C波段和X波段双频输出,频率分别为8.09GHz和9.91GHz，微波辐射平均功率为1.0GW，微波产生效率达到21.9%，效率高于其他双波段高功率微波器件。此外，双频频率随着漂移段长度的变化而准周期性变化，这也是首次在双频以及双波段器件中观察到双频频率捷变现象。
5．在脉冲加速器上，开展了单电子束X波段双频CRBWO实验研究。首先简单介绍了电子束参数的测量方法，然后详细描述了微波参数（包括微波模式、频率以及功率）的测量方法，之后给出了实验测量系统的定标方法以及引导磁场、同轴双排支撑及辐射系统的设计结果。当磁场为0.82T，电压为512kV，电流为11.5kA时，器件产生微波功率为509MW，微波效率为8.6%，微波脉宽约为50ns；实验测量得到纯净的双频频谱，双频频率分别为9.97GHz与10.52GHz，双频频差f550MHz，与粒子模拟结果比较接近。同时，实验观察到明显的双频拍波信号，与单频微波信号输出形成明显对比；微波辐射模式测量采用远场法与荧光阵列靶板测量法，结果表明器件辐射模式为TM01模；实验结果与理论分析、数值分析以及粒子模拟研究结果相吻合，验证了本文提出的单电子束双频CRBWO的物理设计思想。
最后，对本论文的主要工作和创新点进行了总结，并对下一步的研究工作进行了展望。
Great progress has been made with the high-power microwave (HPM) technologyat high power, high efficiency, long pulse and high repetition operation, and the researchtrends on some other kind of HPM source emerge, such as dual-frequency andmulti-frequency HPM generators. HPM sources with dual-frequency andmulti-frequency are worthy of great academic value and potential project application,which could be applied to electronic warfare, as well as various communication systems.The relativistic backward-wave oscillator (RBWO) plays an important role in HPMfield and is one of the most promising HPM sources due to its essential characteristics,such as high power, high efficiency and high repetitive rate.
In this context, a thorough and comprehensive research on the dual-frequencycoaxial relativistic backward-wave oscillator (CRBWO) has been conducted in thisdissertation, including theoretical research, numerical simulation and calculation,particle-in-cell (PIC) simulation, as well as experimental research, and experimentallyan X-band dual-frequency output is got with a single electron beam in a CRBWOdevice, which not only successful explored a new technological path for generatingdual-frequency microwave with a single electron beam, but also lays a theoreticalfoundation and provides an experimental basis for the pioneering research on theCRBWO applications in dual-frequency and multi-frequency HPM fields. Thefollowing contents have been studied in this dissertation:
1． The linear and self-consistent dispersion equation for coaxial periodicslow-wave structure (SWS) is derived on the electronic field matching theorem andFourier series theory, in which the factors of inner and outer corrugations, the phaseshift between inner and outer conductors and the radial thickness of the electron beamare included, and can be applied to arbitrary coaxial periodic SWS, and compared toother models, this theory gets closer to the real HPM experiments. In comparison withhallow SWS, coaxial SWS permits higher space-charge limiting current, is competent toachieve more efficient microwave production and wider electronic frequency tuningbandwidth. The characteristics of dispersion curves of the experimental model with the electron beam (“cold” cavities) and without the electron beam (“hot” cavities) andmicrowave time growth rate and the coupling impedance are numerically analyzedbased on the derived dispersion equation, which indicate that: when the ripples remainthe same, the upper cut-off frequencies of the dispersion curves of outer-ripple-onlycoaxial SWS are higher than the curves of inner-ripple-only and double-ripple (bothinner and outer) coaxial SWSs, which is beneficial for frequency tuning; the couplingimpedance increases with the increase of the ripple, whereas decreases with the increaseof the SWS periodic length; the coupling impedance of the1st harmonic of TEMmode andTM01of double-ripple coaxial SWS within the cross section of the electronbeam are enhanced, which permits more efficient synchronous beam-wave interactionand a higher RF power conversion efficiency; the microwave time growth rate increaseswith the increase of the ripple and decreases with the increase of the SWS periodiclength; the strength of the surface wave and the coupling impedance, as well as themicrowave time growth rate, increase as the electron beam gets close to the surface ofthe outer SWS; the microwave time growth rate increases as the electron currentbecomes larger, which is conducive to the microwave oscillation of CRBWO.
2．A dual-frequency CRBWO with a single electron beam is proposed, and athorough and comprehensive research on the dual-frequency operational mechanismand performance is conducted by use of a2.5-dimentional PIC code. The simulationresults show that with an electron beam of500kV and8.7kA guided by a magnetic fieldof0.82T andL2=0.5, an X-band dual-frequency microwave output is acquired, the dualfrequencies are10.06GHz and10.49GHz, respectively, both corresponding to aradiation pattern ofTM01mode. Clear and obvious beat frequency electric field signalsis observed with peak microwave power of2.3GW and average power of700MW, inwhich the power of the two frequency components are383MW and317MW,respectively, and the average microwave efficiency of the generator is16.1%.Time-frequency analysis of the microwave output demonstrates that the times of startingoscillation and saturation of the two frequency components are different and thesaturation time of the dual-frequency output is about8ns. The independence of theoperating frequency of the two SWS sections (SWS1and SWS2) are studied andverified by use of PIC simulation.
3．A dual-frequency CRBWO with coaxial resonator is firstly proposed and investigated in detail by use of a2.5-D PIC code. When the cathode potential is520kV,an electron beam of-8.5kA is emitted and microwave with average power of1.07GW isproduced, the power conversion efficiency is24.2%and the dual frequencies are9.43GHz and10.30GHz. Furthermore, quasi-periodic occurrence of the dual-frequencyspectrum is obtained by changingLd with the cycle length about a half of thewavelength off2, simultaneously, a frequency agility bandwidth of about400MHz off1is acquired.
4．Extended research on the dual-frequency output is performed and a CRBWOwith an asymmetric reflector cavity generating the C-band and X-band microwaves isproposed and designed. Improved sectioned coaxial SWS by introducing stepwisevariation of coupling impedance and phase velocity is designed and introduced tooptimize the axial electric field in the SWS sections and decrease the energy scatter ofthe electron beam. The model is investigated by use of a PIC code which reveals thatwith an electron beam of510kV and9.03kA and an axial guiding magnetic field of0.73T, dual-band microwaves are generated with dominant frequencies of8.09GHz and9.91GHz, corresponding to C-band and X-band, respectively. The power of thedual-band microwave is1.0GW with efficiency of21.9%, which is higher than otherdual-band HPM devices. Meanwhile, the dual-band frequencies demonstrateperiodic-like dependence on the length of the tapered waveguide between SWS1andSWS2, and this is the first time to obtain dual-band frequency agility in thedual-frequency HPM field.
5．The experiments of the X-band dual-frequency CRBWO are performed with apulsed accelerator. Firstly, the measurement methods of the electron beam parametersare described briefly, then a detailed description of the microwave diagnostics(including radiation pattern, microwave frequencies and power) is provided, after whichthe calibration methods of the experimental measurement systems and the design of theguiding magnetic field coils and the double-row coaxial support post, as well as theradiation system, are given. When the magnetic field is0.82T, the diode voltage is512kV and the beam current is11.5kA, microwave radiation with power of509MW isobtained, the power efficiency is8.6%and the pulse width is about50ns.Dual-frequency output with frequencies of9.97GHz and10.52GHz and frequencydifference of550MHz are achieved, which are close to the PIC simulation results. Clear and stable beating phenomenon of the electric field in frequency of about500MHz isobserved, which is in stark contrast to the single frequency radiations. The microwaveradiation pattern is measured both with the far-field method and the fluorescencemethod, which jointly prove that the radiation pattern isTM01mode. In a word, thetheoretical and numerical analysis and the PIC simulation results and experimentalresults coincide with each other, which confirm the idea of the design of adual-frequency CRBWO with a single electron beam proposed in this dissertation.
Finally, the primary work and innovation of this thesis are summarized andprospected the next research work.
以此为背景，本论文对双频同轴相对论返波振荡器(CRBWO)开展了全面、深入的研究，包括理论研究、数值模拟计算和粒子模拟(PIC)研究，并在实验上利用单电子束在CRBWO上实现了X波段双频输出，成功探索出采用单电子束产生双频微波的技术路径，也对CRBWO在双频以及多频领域的开拓研究奠定了理论以及实验基础。论文的主要研究工作体现在以下几个方面：
1．运用场匹配原理和Fourier级数理论，推导了自洽的同轴周期慢波结构(SWS)的线性色散理论方程。理论模型适用于任意同轴周期慢波结构，考虑了同轴内外双波纹结构以及内外波纹相位差，并考虑了电子束的径向厚度，相比其他模型更加接近HPM实验。分析了同轴SWS相对于空心SWS在空间电荷限制流、微波产生效率以及电子频率调谐带宽方面的优势。数值分析了实验器件模型的冷、热腔色散曲线以及微波时间增长率和耦合阻抗。研究中发现:波纹幅值相等时，外波纹同轴慢波结构的色散曲线上限截止频率比双波纹及内波纹结构的更高，色散曲线比较陡峭，更加有利于频率调谐;耦合阻抗随着波纹深度的增大而增大，随着周期长度的增大而减小;对于内外双波纹慢波结构，在腔体的横截面内，准TEM模式与TM01模的-1次谐波的耦合阻抗都得到了提高，可以保证电子束横截面内的电子都进行有效的波束相互作用，提高微波产生效率;微波时间增长率随着波纹周期的增大而降低，随着波纹幅值的增大而增大;随着电子束位置靠近同轴SWS外波纹表面，表面波幅值增大，耦合阻抗增大，微波时间增长率随之增大；随着电子束流增大，微波增长率增大，有利于CRBWO的微波起振。
2．提出了一种单电子束双频CRBWO模型，对其运行机制和工作特性进行了深入系统的粒子模拟研究，模拟结果显示:在引导磁场0.82T，束电压500kV，束电流8.7kA，漂移段长度L20.5mm下，模拟获得了X波段的TM01模式双频微波输出，双频频率为10.06GHz和10.49GHz,并观察到了明显的拍频电场信号和功率信号;微波峰值功率2.3GW，平均功率700MW，两个频率分量的功率分别为383MW和317MW，微波产生平均效率为16.1%。对微波输出进行时频分析，发现双频信号起振以及饱和时间不同，双频共同输出的功率饱和时间约为8ns。对模型两段SWS(SWS1与SWS2)工作频率的独立性进行了模拟验证。
3．首次设计了带有同轴谐振腔的双频CRBWO并开展了模拟研究。在电子束加速电压c520kV，电子束流I b8.5kA时，器件辐射双频为9.43GHz、10.30GHz；微波平均功率为1.07GW，微波产生效率为24.2%；随着两段SWS之间漂移段长度Ld的改变，双频频谱近似周期性出现，周期近似为f2波长的12；SWS1的主频f1实现了频率捷变输出，频率捷变带宽400MHz。
4．对X波段双频器件的频谱进行了拓展研究，开展了带有非对称反射腔的C波段和X波段CRBWO的模拟研究。器件采用耦合阻抗跃变型的分段慢波结构，优化和改善了器件中轴向电场分布和电子束的能散。在电压510kV，电流9.03kA，轴向引导磁场0.73T下，器件实现了C波段和X波段双频输出,频率分别为8.09GHz和9.91GHz，微波辐射平均功率为1.0GW，微波产生效率达到21.9%，效率高于其他双波段高功率微波器件。此外，双频频率随着漂移段长度的变化而准周期性变化，这也是首次在双频以及双波段器件中观察到双频频率捷变现象。
5．在脉冲加速器上，开展了单电子束X波段双频CRBWO实验研究。首先简单介绍了电子束参数的测量方法，然后详细描述了微波参数（包括微波模式、频率以及功率）的测量方法，之后给出了实验测量系统的定标方法以及引导磁场、同轴双排支撑及辐射系统的设计结果。当磁场为0.82T，电压为512kV，电流为11.5kA时，器件产生微波功率为509MW，微波效率为8.6%，微波脉宽约为50ns；实验测量得到纯净的双频频谱，双频频率分别为9.97GHz与10.52GHz，双频频差f550MHz，与粒子模拟结果比较接近。同时，实验观察到明显的双频拍波信号，与单频微波信号输出形成明显对比；微波辐射模式测量采用远场法与荧光阵列靶板测量法，结果表明器件辐射模式为TM01模；实验结果与理论分析、数值分析以及粒子模拟研究结果相吻合，验证了本文提出的单电子束双频CRBWO的物理设计思想。
最后，对本论文的主要工作和创新点进行了总结，并对下一步的研究工作进行了展望。
Great progress has been made with the high-power microwave (HPM) technologyat high power, high efficiency, long pulse and high repetition operation, and the researchtrends on some other kind of HPM source emerge, such as dual-frequency andmulti-frequency HPM generators. HPM sources with dual-frequency andmulti-frequency are worthy of great academic value and potential project application,which could be applied to electronic warfare, as well as various communication systems.The relativistic backward-wave oscillator (RBWO) plays an important role in HPMfield and is one of the most promising HPM sources due to its essential characteristics,such as high power, high efficiency and high repetitive rate.
In this context, a thorough and comprehensive research on the dual-frequencycoaxial relativistic backward-wave oscillator (CRBWO) has been conducted in thisdissertation, including theoretical research, numerical simulation and calculation,particle-in-cell (PIC) simulation, as well as experimental research, and experimentallyan X-band dual-frequency output is got with a single electron beam in a CRBWOdevice, which not only successful explored a new technological path for generatingdual-frequency microwave with a single electron beam, but also lays a theoreticalfoundation and provides an experimental basis for the pioneering research on theCRBWO applications in dual-frequency and multi-frequency HPM fields. Thefollowing contents have been studied in this dissertation:
1． The linear and self-consistent dispersion equation for coaxial periodicslow-wave structure (SWS) is derived on the electronic field matching theorem andFourier series theory, in which the factors of inner and outer corrugations, the phaseshift between inner and outer conductors and the radial thickness of the electron beamare included, and can be applied to arbitrary coaxial periodic SWS, and compared toother models, this theory gets closer to the real HPM experiments. In comparison withhallow SWS, coaxial SWS permits higher space-charge limiting current, is competent toachieve more efficient microwave production and wider electronic frequency tuningbandwidth. The characteristics of dispersion curves of the experimental model with the electron beam (“cold” cavities) and without the electron beam (“hot” cavities) andmicrowave time growth rate and the coupling impedance are numerically analyzedbased on the derived dispersion equation, which indicate that: when the ripples remainthe same, the upper cut-off frequencies of the dispersion curves of outer-ripple-onlycoaxial SWS are higher than the curves of inner-ripple-only and double-ripple (bothinner and outer) coaxial SWSs, which is beneficial for frequency tuning; the couplingimpedance increases with the increase of the ripple, whereas decreases with the increaseof the SWS periodic length; the coupling impedance of the1st harmonic of TEMmode andTM01of double-ripple coaxial SWS within the cross section of the electronbeam are enhanced, which permits more efficient synchronous beam-wave interactionand a higher RF power conversion efficiency; the microwave time growth rate increaseswith the increase of the ripple and decreases with the increase of the SWS periodiclength; the strength of the surface wave and the coupling impedance, as well as themicrowave time growth rate, increase as the electron beam gets close to the surface ofthe outer SWS; the microwave time growth rate increases as the electron currentbecomes larger, which is conducive to the microwave oscillation of CRBWO.
2．A dual-frequency CRBWO with a single electron beam is proposed, and athorough and comprehensive research on the dual-frequency operational mechanismand performance is conducted by use of a2.5-dimentional PIC code. The simulationresults show that with an electron beam of500kV and8.7kA guided by a magnetic fieldof0.82T andL2=0.5, an X-band dual-frequency microwave output is acquired, the dualfrequencies are10.06GHz and10.49GHz, respectively, both corresponding to aradiation pattern ofTM01mode. Clear and obvious beat frequency electric field signalsis observed with peak microwave power of2.3GW and average power of700MW, inwhich the power of the two frequency components are383MW and317MW,respectively, and the average microwave efficiency of the generator is16.1%.Time-frequency analysis of the microwave output demonstrates that the times of startingoscillation and saturation of the two frequency components are different and thesaturation time of the dual-frequency output is about8ns. The independence of theoperating frequency of the two SWS sections (SWS1and SWS2) are studied andverified by use of PIC simulation.
3．A dual-frequency CRBWO with coaxial resonator is firstly proposed and investigated in detail by use of a2.5-D PIC code. When the cathode potential is520kV,an electron beam of-8.5kA is emitted and microwave with average power of1.07GW isproduced, the power conversion efficiency is24.2%and the dual frequencies are9.43GHz and10.30GHz. Furthermore, quasi-periodic occurrence of the dual-frequencyspectrum is obtained by changingLd with the cycle length about a half of thewavelength off2, simultaneously, a frequency agility bandwidth of about400MHz off1is acquired.
4．Extended research on the dual-frequency output is performed and a CRBWOwith an asymmetric reflector cavity generating the C-band and X-band microwaves isproposed and designed. Improved sectioned coaxial SWS by introducing stepwisevariation of coupling impedance and phase velocity is designed and introduced tooptimize the axial electric field in the SWS sections and decrease the energy scatter ofthe electron beam. The model is investigated by use of a PIC code which reveals thatwith an electron beam of510kV and9.03kA and an axial guiding magnetic field of0.73T, dual-band microwaves are generated with dominant frequencies of8.09GHz and9.91GHz, corresponding to C-band and X-band, respectively. The power of thedual-band microwave is1.0GW with efficiency of21.9%, which is higher than otherdual-band HPM devices. Meanwhile, the dual-band frequencies demonstrateperiodic-like dependence on the length of the tapered waveguide between SWS1andSWS2, and this is the first time to obtain dual-band frequency agility in thedual-frequency HPM field.
5．The experiments of the X-band dual-frequency CRBWO are performed with apulsed accelerator. Firstly, the measurement methods of the electron beam parametersare described briefly, then a detailed description of the microwave diagnostics(including radiation pattern, microwave frequencies and power) is provided, after whichthe calibration methods of the experimental measurement systems and the design of theguiding magnetic field coils and the double-row coaxial support post, as well as theradiation system, are given. When the magnetic field is0.82T, the diode voltage is512kV and the beam current is11.5kA, microwave radiation with power of509MW isobtained, the power efficiency is8.6%and the pulse width is about50ns.Dual-frequency output with frequencies of9.97GHz and10.52GHz and frequencydifference of550MHz are achieved, which are close to the PIC simulation results. Clear and stable beating phenomenon of the electric field in frequency of about500MHz isobserved, which is in stark contrast to the single frequency radiations. The microwaveradiation pattern is measured both with the far-field method and the fluorescencemethod, which jointly prove that the radiation pattern isTM01mode. In a word, thetheoretical and numerical analysis and the PIC simulation results and experimentalresults coincide with each other, which confirm the idea of the design of adual-frequency CRBWO with a single electron beam proposed in this dissertation.
Finally, the primary work and innovation of this thesis are summarized andprospected the next research work.
引文
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