Stability of Brillouin Flow in Slow-Wave Structures

For the first time, we include a slow-wave structure (SWS) to study the stability of Brillouin flow in the conventional, planar, and inverted magnetron geometry. The resonant interaction of the SWS circuit mode and the corresponding smooth-bore diocotron-like mode is found to be the dominant cause for instability, overwhelming the intrinsic negative (positive) mass property of electrons in the inverted (conventional) magnetron geometry [1]. It severely restricts the wavenumber for instability to the narrow range in which the cold tube frequency of the SWS is within a few percent of the corresponding smooth bore diocotron-like mode in the Brillouin flow. This resonant interaction is absent in a smooth bore magnetron. [1] D. H. Simon, et al., \textit{Physics of Plasmas} \textbf{22}, 82104 (2015).