Department of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, Michigan 48109, USA.
Leidos Corporation, Reston, Virginia 20190, USA.
Phys Rev Lett. 2015 Sep 18;115(12):124801. doi: 10.1103/PhysRevLett.115.124801. Epub 2015 Sep 16.
Applying the Briggs-Bers "pole-pinch" criterion to the exact transcendental dispersion relation of a dielectric traveling wave tube (TWT), we find that there is no absolute instability regardless of the beam current. We extend this analysis to the circuit band edges of a linear beam TWT by approximating the circuit mode as a hyperbola in the frequency-wave-number (ω-k) plane and consider the weak coupling limit. For an operating mode whose group velocity is in the same direction as the beam mode, we find that the lower band edge is not subjected to absolute instability. At the upper band edge, we find a threshold beam current beyond which absolute instability is excited. The nonexistence of absolute instability in a linear beam TWT and the existence in a gyrotron TWT, both at the lower band edge, is contrasted. The general study given here is applicable to some contemporary TWTs such as metamaterial-based and advanced Smith-Purcell TWTs.
将 Briggs-Bers“极 pinch”准则应用于介电行波管（TWT）的确切超越色散关系，我们发现无论束流如何，都不存在绝对不稳定性。我们通过将电路模式近似为频波数（ω-k）平面上的双曲线来将这种分析扩展到线性束 TWT 的电路频带边缘，并考虑弱耦合极限。对于群速度与束流模式方向相同的工作模式，我们发现下频带边缘不受绝对不稳定性的影响。在上频带边缘，我们发现存在一个超过该电流的阈值，超过该阈值将激发绝对不稳定性。对比了线性束 TWT 中不存在绝对不稳定性而回旋管 TWT 中存在的情况，均在下频带边缘。这里给出的一般性研究适用于一些现代 TWT，如基于超材料的和先进的 Smith-Purcell TWT。
