磁旋管(gyrotron)是在毫米波與太赫茲頻段的高功率波源系統，而過去的磁旋管研究主要都集中於TE模態(軸向電場為零)，因為從特徵模態可以看出，當操作在接近截止頻率區域時，橫向磁場趨會近於零，因此對於軸向電子速度的調製幾乎是零，也就是只需要考慮橫向聚束機制即可，也因為沒有聚束機制的競爭，其可以產生比較單純的高功率波源。
對於TM 模態(軸向磁場為零)磁旋管，即使操作在接近截止頻率區域，因為軸向電場的存在，導致其軸向聚束機制與橫向聚束機制都會存在，而過去大家都認為這兩種聚束機制永遠都會是互相競爭的，進而導致能量轉換效率會很差；另外TM 模態因為軸向電場與橫向磁場都會對軸向速度造成影響，因此很容易會出現嚴重的速度逸散，這也會導致效率的下降，這兩個主要的原因，導致過去認為TM模態並不適合做為磁旋管的操作條件[8-14]。
然而經過我們實驗室最近的聚束研究分析發現，當操作在後退波時，TM模態的兩種聚束機制作用會互相合作[8,10]，與過去的結論並不相同，且經過小訊號模型計算的起振電流也顯示了TM模態的可行性[9,11]，甚至經過非線性定場的模擬發現操作在後退波的情況下，TM11與TE01展現出一樣好的結果[11]，以上的種種結果都證明了，TM模態是個與TE模態相同有競爭力的磁旋管系統，另外在日本福井大學的實驗中[15]發現有非TE模態的訊號出現，這些不確定的模態，很有可能就是過去不夠了解的TM模態，為此TM模態的模擬與分析對於整個磁旋管系統的完整性與重要性不言而喻。
在此篇論文我們將會介紹TM模態非線性且自洽系統的波動方程式與電子運動方程式的推導過程，接著利用得到的這些耦合的微分方程式來進行非線性且自洽的模擬，透過對均勻結構的模擬結果分析，我們可以研究其中的能量交換機制，與其背後的物理概念，接著利用我們分析出的物理機制來設計優化我們的模擬結構，最後我們成功實現三種優化的極限: 在W-band具有6GHz的高頻寬操作、最高效率超過50%的高效率操作以及操作電壓只需要2kV的超低電壓操作，配合我們對TM01的模擬結果，我們可以宣稱此磁旋管系統模擬是一個具泛用性且嚴謹的模擬系統。

Gyrotrons have been regarded as high-power sources of millimeter and terahertz waves. The previous researches about gyrotrons are mainly forced on TE-mode gyrotrons, whose axial magnetic field is equal to zero ( ). When operating at near-cutoff of TE-mode, the axial electric field is approximately zero and the azimuthal bunching dominate the system. As a result of no bunching competition, TE-mode gyrotrons can generate high power radiation.

For TM-mode gyrotrons, the existence of axial electric field can induce both of the bunching mechanisms process through the relativistic effect. Traditional understanding usually expect these two bunching mechanisms would always compete with each other, which would lead to reduction of interaction efficiency. Besides, for TM-mode both axial electric field and azimuthal magnetic field would modulate axial velocity of electrons and induce serious velocity spread, which will also reduce the efficiency of gyrotrons. These two primary reasons lead to the inappropriate operation of TM-mode gyrotrons in previous understanding [8-14].

However, by the recent study of bunching mechanisms the axial bunching and azimuthal bunching can cooperate with each other under the backward operation [8,10], which is contradictory with the previous believing. Besides, the research of starting current behavior confirm the feasibility of TM-mode gyrotrons [9,11]. In the results of nonlinear and fixed field simulation [11], the linear gain and bandwidth of the TM11-mode gyrotron are as good as those of TE01-mode gyrotron [9,11]. Also, in the experiments [15], many non-TE mode oscillations have been observed in the overmoded interaction structures. Those unidentified peaks might be the evidence of TM-mode. All the result above shows that the TM-mode is competitive with respect to TE-mode gyrotrons. As a result, for the completion of gyrotrons system, the simulation and analysis of TM-mode is obviously very important and necessary.

This work develops a nonlinear and self-consistent framework for the single-mode simulation of TM-mode gyrotrons. Together with the electrons’ equations of motion, particle tracing simulation is conducted to model TM-mode oscillation. For a uniform
Structure, its beam-current, beam-voltage, and pitch-factor tuning properties are investigated under different magnetic fields. By optimizing the interaction structure of the proposed gyrotron backward-wave oscillator (gyro-BWO), three outstanding optimization limits are conducted. In first operation, the maximum frequency tuning range is more than 6 GHz at the pitch factor of 1.5 in the W-band. Second, The peak efficiency can be reached higher than 50%. in third operation, we need only 2-kilovolte to get more than 10% efficiency. These special features may facilitate the development of low-cost and compact gyrotron systems and show great potential in the applications for TM-mode gyro-BWOs.

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