## 3 Simulation Results
### Design of the Input/Output Cavities  
The input and output cavities are the essential parts of the RF section of a klystron. In this section, the design and simulation of the input and output cavities have been discussed. This step introduces a coupler in the output RF cavity to extract the power from the bunched electron beams. In addition, a coupler is introduced in the input RF cavity to introduce the RF signal for the modulation with the electron beams. The designed input and output cavities with the slot coupling and attaching the WR28 waveguide for the standard Ka-band are shown in Figure 6. The optimized geometrical design parameters of the input/output cavities for the Ka-band are given in Table 4, and the simulated results are presented in Table 5. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value (mm)** \\ \hline X & 5.8 \\ Y & 7.96 \\ Z & 4.83 \\ H & 5.5 \\ D & 0.36 \\ GAP & 0.27 \\ P & 1.14 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Optimized design parameters (intermediate cavity). Figure 6: RF cavity considered for simulation: ladder-type multibeam EIK input/output cavities. Figure 7 shows the cutting plane view of the electric field distribution of the proposed input and output cavities while Figure 8 shows a cutting plane view of the magnetic field pattern of the proposed input and output cavities. The mode frequency is found to be 28.53 GHz from the CST simulations, considering the gap and drift tube radius to be the same as those of the intermediate cavities. The quality factor of the cavities has been obtained as 720, and the calculated shunt impedance of the operating mode across the gaps is 31.85 M\(\Omega\). According to the CST calculations, the R over Q is estimated to be 44.2. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Values from CST** & **Values from HFSS** \\ \hline Resonant Frequency (GHz) & 28.53 & 28.52 \\ Q & 720 & 702 \\ R (M\(\Omega\)) & 31.85 & 34.04 \\ R/Q & 44.2 & 48.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of the simulated cavity parameters (input/ output cavities). Figure 7: Electric field distribution of the 2\(\pi\) mode (cut-plane view) for the input and output cavities with CST. For the validation of the results, the same simulation has been performed using ANSOFT HFSS, considering the exact geometrical cavity dimensions considered for the CST simulation. Figure 9a,b show the electric and magnetic field distribution of the cavity. The operating-mode frequency and quality factor are 28.52 GHz and 702, respectively. The input and output cavities have an external Q factor (\(Q_{e}\)) of about 38, dictated by the coupling of the cavity with the waveguide. During the computation of the Q factor (using the eigenmode computation) of the operating mode, the standard material properties of copper (with an electrical conductivity of 5.96 \(\times\) 107 S/m) were considered. Because there are several metallic walls inserted within the cavity (the walls of the ladder structure), the wall losses are higher in the case of these cavities compared to the Ka-band cavities with a conventional structure. Therefore, the Q factor is lower compared to the conventional Ka-band cavities. Figure 8: Magnetic field distribution of the 2\(\pi\) mode (cut-plane view) for the input and output cavities with CST. Figure 9: Electric field distribution and magnetic field distribution of the input and output cavities with HFSS; **(a)** E-field distribution; **(b)** M-field distribution. Figure 10 shows the geometry used for the time-domain simulation of the input and output cavities.