## 3 Simulation Results
### Design of the RF Section  
Figure 12 shows the cut-plane view of the RF section of the proposed four-beams EIK. The simulation geometry has been modeled and simulated using the CST PIC simulation tool. In this structure, six cavities (including the input and output cavities) have been considered. In this model, the center-to-center distance between the cavities has been taken as 5.83 mm and the length of the beam tunnel has been taken as 34.98 mm. The input signal used is a single-frequency sinusoidal signal with a constant amplitude. An axial magnetic field of 0.33 T (calculated according to Equation (15)) has been applied to maintain the focusing of the electron beam throughout the RF section. The frequency of the input signal  
Figure 11: S-parameters obtained from the time-domain simulation. Figure 10: RF cavity considered for simulation: ladder-type multibeam EIK input/output cavities with port. A snapshot of the electron beam trajectory of the PIC simulation is shown in Figure 12. The velocity modulation of the electron beam, which is the main indication of the RF amplification, is clearly visible at the output cavity of the device. Figure 14 shows the combined view of the input and output signals from the RF section. The signals have been recorded after the beam-wave interactions in the RF section. Figure 15 shows the input RF signal. This signal has been applied at the input port of the RF section. Figure 14 shows the output signal from the RF section. The output signal has been recorded at the output waveguide port after the beam-wave interactions in the RF section. From Figure 14, it can be observed that the maximum amplitude of the output signal is 19.39 \(\surd\)(watt), corresponding to an input signal of 2.0 \(\surd\)(watt) (peak). The peak output power calculated from the output signal is more than 375.97 W and the RMS output  
Figure 16: Input port signal of RF section. Figure 15: Port signals (combined view) of RF section. power is 187.98 W. The frequency spectrum of the output signal is shown in Figure 17. Figure 17 clearly shows the peak of the spectrum at 28.5 GHz. The gain of the RF section for different frequencies has been plotted in Figure 18, and the efficiency of the device in different frequencies is plotted in Figure 19. From this plot, the higher (\(f_{h}\)) and lower (\(f_{l}\)) \(-3\) dB frequency points are found to be \(f_{h}\) = 28.66 GHz and \(f_{l}\) = 28.15 GHz. Therefore, the \(-3\) dB bandwidth of the device can be calculated as 510 MHz. Similarly, the \(-1\) dB bandwidth of the device comes out to be 180 MHz. The operating bandwidth of the device can be further increased by employing the stagger tuning of the intermediate cavities, i.e., tuning each individual cavity at slightly different frequencies. Figure 17: Frequency spectrum of the output signal. Figure 18: Graphical representation of gain vs. frequency. The simulation results of the RF section have been provided in Table 6. The slight variation in the gain in the operating band (28.15 GHz to 28.66 GHz) can be managed by gain-equalizing schemes, where the input signal amplitude and beam voltages are adjusted to achieve a flatness of the gain at desired frequency band/sub-bands. This scheme is widely used in travelling wave tube (TWT)-based communication systems, especially in satellite communication. The fabrication of the RF section (with a 34.98 mm total length, gap length of 0.27 mm, ladder wall height of 5.5 mm, and cavity height of 7.96 mm) can be conducted using the wire-cut Electric Discharge Machining (EDM) technique, where the upper and lower walls (top and bottom) of the cavity may be fabricated separately. This fabrication possibility is