Study on nonstationary oscillation in continuous frequency tunable terahertz gyrotron
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摘要: 太赫兹回旋管可实现高功率输出，并具有一定的频率调谐范围，是核磁共振波谱系统理想的高功率太赫兹辐射源。设计了263 GHz，TE5,2基波连续调谐回旋管，通过磁场调节实现频率调谐范围为1.39 GHz，利用时域多模多频自洽非线性理论对设计的连续调谐回旋管非稳定振荡状态进行了研究。结果表明，在低次纵向谐波模式工作磁场范围内，当工作电流大于起振电流时，连续调谐回旋管先进入稳定状态，高次纵向谐波模式被抑制，工作模式TE5,2的输出功率随时间不变；当电流增大，纵向谐波模式间的竞争引起回旋管由稳定状态进入到非稳定振荡状态，工作模式TE5,2的输出功率随时间呈振荡变化且互作用效率大大降低；随着电流的进一步增大，回旋管又回到与低电流不同的稳定状态，互作用效率进一步降低。同时发现非稳定振荡状态的起始电流随着磁场增加而增大。本研究对需工作于稳定状态的面向DNP-NMR应用的连续调谐太赫兹回旋管的研制具有一定指导意义。Abstract: Terahertz gyrotron can achieve high output power and has a certain frequency tuning range, thus it is an ideal high power terahertz radiation source for NMR spectroscopy system. A 263 GHz, TE5,2 fundamental harmonic frequency continuously tunable gyrotron is designed, the corresponding frequency tuning range can reach 1.4 GHz through adjusting the magnetic field. The unstable oscillation state of the designed gyrotron is studied by using the time domain multi-mode multi frequency self-consistent nonlinear theory. The results show that in the magnetic field range of low order axial mode, when the operating current is greater than the starting current, the continuously tuned gyrotron enters the stable state, where the high order axial mode is suppressed, and the output power of TE5,2 remains unchanged with time. When the current increases, the competition between axial modes causes the gyrotron to enter the unstable oscillation state from the stable state, the output power of TE5,2 oscillates with time and the interaction efficiency decreases greatly. With the further increase of current, the gyrotron returns to another stable state different from that of low current. It is also found that the initial current increases with the increase of magnetic field. The research of this paper has a certain guiding significance for the development of continuously tuned THz gyrotron for DNP-NMR applications.
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Key words:
- terahertz /
- gyrotron /
- nonstationary oscillation /
- continuously frequency tuning
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图 1 互作用高频结构及归一化纵向谐波模式场幅值分布
Figure 1. Interaction circuit and the normalized field profile of high order axial modes
图 2 不同纵向谐波模式起振电流（
$ {\rm{\sigma }}=2.9\times {10}^{7} $ S/m，$ {U}_{0}=20 $ kV，$ {R}_{\rm{g}}=1.4 $ mm，$ {\rm{\alpha }}=1.75 $ ）Figure 2. Starting currents of different order axial modes (wall conductivity
$ {\rm{\sigma }}=2.9\times {10}^{7} $ S/m, beam voltage$ {U}_{0}=20 $ kV, beam guiding center$ {R}_{\rm{g}}=1.4 $ mm, pitch angle$ {\rm{\alpha }}=1.75 $ )
图 3 稳定工作状态（
$ {\rm{\sigma }}={\infty } $ ，$ {U}_{0}=20 $ kV，$ {R}_{\rm{g}}=1.4 $ mm，$ {\rm{\alpha }}=1.75 $ ，$ {B}_{0}=9.65 $ T，$ {I}_{0}=25 $ mA）Figure 3. Stationary oscillation when
$ {\rm{\sigma }}={\infty } $ ,$ {U}_{0}=20 $ kV,$ {R}_{\rm{g}}=1.4 $ mm,$ {\rm{\alpha }}=1.75 $ ,$ {B}_{0}=9.65 $ T,$ {I}_{0}=25 $ mA
图 4 稳定工作状态（
$ {\rm{\sigma }}={\infty } $ ，$ {U}_{0}=20 $ kV，$ {R}_{\rm{g}}=1.4 $ mm，$ {\rm{\alpha }}=1.75 $ ，$ {B}_{0}=9.65 $ T，$ {I}_{0}=25 $ mA）Figure 4. Stationary oscillation when
$ {\rm{\sigma }}={\infty } $ ,$ {U}_{0}=20 $ kV,$ {R}_{\rm{g}}=1.4 $ mm,$ {\rm{\alpha }}=1.75 $ ,$ {B}_{0}=9.65 $ T,$ {I}_{0}=25 $ mA
图 5 模拟得到的连续调谐回旋管非稳定工作状态，其中
${\rm{\sigma }}=2.9\times $ $ {10}^{7}$ ，$ {U}_{0}= 20 $ kV，$ {R}_{\rm{g}}=1.4 $ mm，$ {\rm{\alpha }}=1.75 $ ，$ {B}_{0}=9.74 $ T，$ {I}_{0}=25 $ mAFigure 5. Nonstationary oscillation when
$ {\rm{\sigma }}=2.9\times {10}^{7} $ S/m,$ {U}_{0}= $ $ 20 $ kV,$ {R}_{\rm{g}}=1.4 $ mm,$ {\rm{\alpha }}=1.75 $ ,$ {B}_{0}=9.74 $ T,$ {I}_{0}=25 $ mA
图 6 连续调谐回旋管非稳定工作状态（
$ {\rm{\sigma }}=2.7\times {10}^{7} $ ，$ {U}_{0}=20 $ kV，$ {R}_{\rm{g}}= 1.4 $ mm，$ {\rm{\alpha }}=1.75 $ ，$ {B}_{0}=9.74 $ T，$ {I}_{0}=35 $ mA）Figure 6. Nonstationary oscillation when
${\rm{\sigma }}=2.7\times {10}^{7}$ ,$ {U}_{0}=20 $ kV,$ {R}_{\rm{g}}= 1.4 $ mm,$ {\rm{\alpha }}=1.75 $ ,$ {B}_{0}=9.74 $ T,$ {I}_{0}=35 $ mA;
图 7 连续调谐回旋管稳定工作状态（
$ {\rm{\sigma }}=2.7\times {10}^{7} $ S/m，$ {U}_{0}=20 $ kV，$ {R}_{\rm{g}}=1.4 $ mm，$ {\rm{\alpha }}=1.75 $ ，$ {B}_{0}=9.74 $ T，$ {I}_{0}=85 $ mA）Figure 7. Stationary oscillation when
$ {\rm{\sigma }}=2.7\times {10}^{7} $ S/m,$ {U}_{0}= $ $ 20 $ kV,$ {R}_{\rm{g}}=1.4 $ mm,$ {\rm{\alpha }}=1.75 $ ,$ {B}_{0}=9.74 $ T,$ {I}_{0}=85 $ mA;
图 8 非稳定振荡状态在磁场和电流平面上的分布（
${\rm{\sigma }}=2.7\times $ $ {10}^{7}$ S/m，$ {U}_{0}=20 $ kV，$ {R}_{\rm{g}}=1.4 $ mm，$ {\rm{\alpha }}=1.75 $ ）Figure 8. Categorization of non-stationary oscillation on plane of beam current and magnetic field (
$ {\rm{\sigma }}=2.7\times {10}^{7} $ S/m,$ {U}_{0}=20 $ kV,$ {R}_{\rm{g}}=1.4 $ mm,$ {\rm{\alpha }}=1.75 $ )
图 9 互作用效率和谐振频率随磁场的变化（
$ {\rm{\sigma }}=2.7\times $ $ {10}^{7} $ S/m，$ {U}_{0}=20 $ kV，$ {R}_{\rm{g}}=1.4 $ mm，$ {I}_{0}=20 $ mA）Figure 9. Beam wave interaction efficiency and oscillation frequency variation with magnetic field when
$ {\rm{\sigma }}=2.7\times {10}^{7} $ S/m,$ {U}_{0}=20 $ kV,$ {R}_{\rm{g}}=1.4 $ mm,$ {I}_{0}=20 $ mA表 1 263 GHz，
$ {\bf{TE}}_{{\bf{5,2}}} $ 基波连续调谐回旋管工作参数Table 1. Operating parameters for 263 GHz,
$ {\bf{TE}}_{\bf{{5,2}}} $ fundamental harmonic frequency continuously tunable gyrotronoperating
modebeam
current/mAbeam
voltage/kVguiding center
radius/mmpitch
factoroperating
frequency/GHzwall
conductivity/(S·m−1)frequency tunable
range/GHzpower tunable
range/W${\rm{TE} }_{5,2}$ 20 20 1.40 1.75 263 $ 2.7\times {10}^{7} $ 1.39 80 
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