Equivalent Circuit Approach for Beam–Wave Interaction Analysis of MILO

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.