The beam–wave interaction analysis in the RF interaction structure of magnetically insulated line oscillator (MILO) is presented. The analysis is carried out using the linearized Vlasov equation by considering the equivalent circuit approach. Taking into account, the beam present dispersion relation is derived to obtain the temporal growth rate and oscillation frequency. In addition, the RF energy stored and power transfer through the slow wave structure during beam–wave interaction process are calculated. Considering the imaginary part of admittance and coupling coefficient of the cavity, the expression for energy stored and power transfer to the load is also derived. The dispersion relation for electron beam interaction with the phase velocity of the oscillating mode, through the slow wave structure, is explained. Furthermore, the derived analytical results temporal growth rate, RF energy, and output power are validated through reported methods (field analysis and particle-in-cell (PIC) simulation). The results are in agreement with the reported results using the field analysis case.

中文翻译：

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MILO波束相互作用分析的等效电路法

介绍了磁绝缘线振荡器 (MILO) 的 RF 相互作用结构中的波束相互作用分析。使用线性化进行分析考虑等效电路方法的 Vlasov 方程。考虑到光束存在色散关系，推导出时间增长率和振荡频率。此外，还计算了束波相互作用过程中通过慢波结构存储的射频能量和功率传输。考虑空腔导纳和耦合系数的虚部，推导出储能和向负载传输功率的表达式。通过慢波结构解释了电子束相互作用与振荡模式相速度的色散关系。此外，派生的分析结果时间增长率、RF 能量和输出功率通过报告的方法（场分析和粒子在细胞 (PIC) 模拟）得到验证。