1.School of Physics, University of Electronic Science and Technology of China, Chengdu 610054, China 2.Terahertz Research Center, School of Electronic Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054, China
Abstract:Quasi-optical confocal cylindrical waveguide possesses a lot of good characteristics, such as big power capacity and low mode density, which can suppress the mode competition in beam-wave interaction. So quasi-optical waveguide has a great advantage in designing high harmonic terahertz gyrotrons. For the reason that part of electron beams located in a region of weak field intensity play a limited role in beam-wave interactions, the beam-wave interaction is not efficient in confocal cavity. Motivated by enhancing the beam-wave interaction efficiency of quasi-optical gyrotron, we propose a novel terahertz harmonic gyrotron cavity with double confocal waveguide in this paper. The transverse field distribution and the mode spectrum in double confocal waveguide are analyzed and presented. A 330 GHz second harmonic gyrotron with double confocal cavity is designed, theoretically analyzed and simulated by using a particle-in-cell (PIC) code. The results obtained for double confocal cavity are compared with the results for single confocal cavity, and the physical mechanism of beam-wave interaction enhancement in double confocal cavity is discussed. Theoretical results show that the double confocal cavity is able to increase the coupling strength of beam-wave interaction, thus, to improve the output power and the interaction efficiency of quasi-optical gyrotron. The PIC simulation results suggest that a high-order waveguide mode in double confocal cavity can steadily interact with the high harmonic cyclotron mode of electron beam without mode competition. Driven by a 40 kV, 2 A electron beam with a guiding center radius of 1.65 mm and velocity ratio equal to 1.5, output power of 9.9 kW at 328.93 GHz can be generated in the designed double confocal cavity. The beam-wave interaction efficiency increases from 5.3% in single confocal cavity to 12.4% in dual confocal cavity under the same operation parameters. The double confocal cavity has great potential applications in terahertz band. Moreover, this study indicates that the eigen mode in double confocal waveguide is a kind of hybrid mode superimposed by two independent single confocal waveguide modes. This mode characteristic will be beneficial to designing a multifrequency gyrotron oscillator operated in two modes and two cyclotron harmonics, simultaneously, with a single electron beam used, which provides a new possibility to develop the novel terahertz radiation source. Keywords:terahertz gyrotron/ high harmonic/ quasi-optical cavity/ double confocal waveguide
如图2所示, 给出了TE0,11模在两种共焦波导结构中的场分布图. 对于普通共焦波导结构, 由于其电磁场集中在有限的区域内, 只有场分布较强区域内的回旋电子能够与电磁波充分互作用, 因此环形电子束整体的互作用效率不高. 而在双共焦波导结构中, 场分布区域增大, 能够与电磁波相互作用的回旋电子明显增多, 电子注整体的注波互作用效率将得到提高. 当环形电子注的引导中心半径大于模式场分布的束腰半径时, 相同电子注参数下, 双共焦波导结构对应的输出功率和工作效率应是普通共焦波导的2倍左右. 图 2 两种波导中TE0, 11模的横向电场及环形电子注分布图 (a)普通共焦波导; (b)双共焦波导 Figure2. Transverse geometry with the annular electron beam and electric field distributions of TE0, 11 mode in two types of quasi-optical waveguides: (a) Normal confocal waveguide; (b) double confocal waveguide.
式中, e为电子电荷量, λ为自由空间的波长, L为腔体长度, γ0为初始时刻的相对论因子, Q为谐振腔的品质因数, S⊥为互作用结构的横截面. 图7(a)为计算得到的双共焦结构谐振腔中不同模式的起振电流Ist随工作磁场B0的变化. 结果表明, 工作模式${\rm{TE}}_{0, 11}^2$的最小起振电流为0.29 A, 且其磁场工作区间与其他竞争模式保持很大的间隔. 可见, 双共焦结构回旋管中模式竞争要弱于传统圆波导回旋管, 通过控制工作磁场的大小, 可以有效地抑制二次谐波准光回旋管中的模式竞争. 图 7 起振电流Ist的计算结果(V0 = 40 kV, α = 1.5, Rb = 1.65 mm) (a) 双共焦腔中各模式对应的Ist; (b) ${\rm{TE}}_{0, 11}^2$模式在双共焦腔和普通共焦腔中的Ist Figure7. Calculated results of starting current Ist (V0 = 40 kV, α = 1.5, Rb = 1.65 mm): (a) For different modes in double confocal cavity; (b) for ${\rm{TE}}_{0, 11}^2$ mode in double and single confocal cavity.
此外, 如图7(b)所示, 对比${\rm{TE}}_{0, 11}^2$模式在双共焦腔和普通共焦中的起振电流, 两者随磁场变化的趋势相同. 但由于双共焦腔的Q值更大, 双共焦腔对应的起振电流较小, 因此双共焦腔中的模式更容易起振. 在相同工作电流条件下, 双共焦腔对应的工作磁场范围也略大于普通共焦腔. 4.粒子模拟粒子模拟方法可对真空电子学器件进行仿真, 是一种验证理论分析并优化设计参数的重要技术手段[29]. 根据表1所列出的结构参数, 在三维粒子模拟软件CHIPIC[30]中对所设计的谐振腔进行三维建模. 选定电子注的工作参数: 工作电压V0 = 40 kV、电子注电流Ib = 2 A, 电子注引导中心半径Rb = 1.65 mm, 横纵速度比α = 1.5. 仿真结果表明, 谐振腔的输出功率最大可达到9.9 kW, 电子效率为12.4%. 图8为此时双共焦腔输出端口电场分量Ex和Ey的时域和频域结果图, 可以看出输出电磁波的频率为328.93 GHz, 频谱单一, 谐振腔中保持单模稳定的注波互作用. 图9和图10分别给出了电场分量Ex和Ey的场分布图, 其横向场分布为TE0,11模, 纵向场幅值分布与图4(b)所示的冷腔计算结果相似, 可以确定此时谐振腔中的工作模式为TE0,11,1模式. 粒子模拟的结果证明, 双共焦谐振腔中的高阶模式能够与高次电子回旋谐波发生稳定的相互作用, 并且没有模式竞争现象, 具备工作在太赫兹波段的潜力. 图 8 双共焦腔输出端口电场分量Ex和Ey的仿真结果 (a) 时间变化图; (b) 频谱图 Figure8. Simulation results of output field Ex and Ey for double confocal cavity: (a) Time variation; (b) spectrum.
图 9 双共焦腔Ex分量的场分布仿真结果 (a) 输出端口; (b) xz (y = 0)平面; (c) yz (x = 0)平面 Figure9. Simulation results of the distribution of electronic field Ex in double confocal cavity: (a) At output port; (b) at the xz plane (y = 0); (c) at the yz plane (x = 0).
图 10 双共焦腔Ey分量的场分布仿真结果 (a) 输出端口; (b) xz (y = 0)平面; (c) yz (x = 0)平面 Figure10. Simulation results of the distribution of electronic field Ey in double confocal cavity: (a) At output port; (b) at the xz plane (y = 0); (c) at the yz plane (x = 0).
为了与普通共焦腔的注波互作用进行比较, 不改变电子注的参数, 对同样尺寸的单组共焦结构谐振腔进行了粒子模拟. 图11给出了输出端口电场的时间变化及频谱图, 可以看出普通共焦腔也能单模稳定工作于TE0,11,1的二次谐波, 输出频率为328.93 GHz, 与双共焦腔的输出频率相同. 图 11 普通共焦腔仿真结果 (a) 输出端口电场Ex和Ey的时间变化图; (b) Ex的输出频谱图 Figure11. Simulation results for single confocal cavity: (a) Time variation of the output field Ex and Ey; (b) spectrum of the output field Ex.
改变工作磁场B0的大小, 双共焦腔和普通共焦腔输出功率的变化如图12所示. 计算结果表明, 工作磁场的改变对二次谐波模式的输出功率影响很大, 且两种谐振腔中工作模式输出功率的变化规律相似. 根据理论分析中起振电流的计算结果, 由于双共焦腔中的起振电流更低, 工作模式更容易起振, 因此双共焦腔对应的工作磁场范围略大于普通共焦腔. 在所计算磁场区间内, 粒子模拟时均未观测到其他竞争模式. 图12中单组共焦结构的最大输出功率为4.2 kW, 对应的互作用效率为5.3%, 而双共焦谐振腔的最大输出功率为9.9 kW, 互作用效率提高了一倍以上达到12.4%. 由此可见, 双共焦结构谐振腔能够在控制模式竞争的前提下有效增大回旋管的输出功率, 提高器件的工作效率, 有利于大功率高次谐波太赫兹回旋管的研制. 图 12 双共焦腔和普通共焦腔输出功率随磁场的变化 Figure12. Simulation results of output power for double confocal cavity and single confocal cavity.
此外, 从图11(a)可以看出, 普通单组共焦波导中的电磁波是一种线极化波, 对竖直方向上的单组共焦结构谐振腔而言(参考图9), 横向电场主要集在在Ex方向, Ey分量很弱. 而在图8(a)给出的双共焦谐振腔输出端口电场分量Ex和Ey随时间的变化结果中, Ex和Ey的起振时间并不完全相同, Ey要晚于Ex起振. 在注波互作用稳定以后, 如图13所示, 在100 ns附近Ex与Ey两者之间的时间差约为0.756 ps, 对应于1/4个周期(328.93 GHz电磁波对应的周期为3.04 ps), 即Ex与Ey之间存在π/2的相位差. 上述仿真结果证明, 双共焦波导结构中的电磁波模式是一种混合模式, 是水平和竖直方向上两个独立的共焦波导模式的矢量叠加. 图 13 输出稳定时(100 ns)双共焦腔输出端口电场Ex和Ey随时间的变化展开图 Figure13. Expanded results of the output field Ex and Ey for double confocal cavity around 100 ns.