# Bandwidth Enhancement of a V-Band Klystron with Stagger-Tuned Multiple Radial Re-Entrant Cavities
## 2 Design Approach  
The radio frequency section is a crucial component of a Klystron. The design of the RF section of a multi-cavity Klystron involves the design of intermediate, input, and output resonant cavities (shown in Figure 1) and beam-wave interaction structure. The first cavity with the coupler of the radio frequency section is called the input cavity, or \"buncher\" cavity, while the last cavity with the coupler of the radio frequency section is called the output cavity, or \"catcher\" cavity and other cavities are called the intermediate cavities. The structure of the RF section for the proposed Klystron is shown in Figure 2.  
Radial re-entrant square cavities (RRSC) have been considered for the multi-cavity Klystron because they are designed to concentrate strong electric fields and are commonly used in high-gain and high-power applications. Two different types of RRSC have been considered for the V-Band RF structure. The model of the input and output cavity with a coupler is shown in Figure 1a, and the model of the intermediate cavity is shown in Figure 1b. A schematic diagram of the designed radial re-entrant square structure intermediate cavity is shown in Figure 1c. In the schematic diagram, the dimensions a, b, c, w, and g represent the height of the cavity, re-entrant height, radius of the beam tunnel, width of the cavity, and beam interaction gap, respectively. Dimensions of the designed input, output, and intermediate cavities, along with Eigenmode simulation results, are shown in Table 1. From Table 1, it has been observed that different frequencies have been used for tuning the intermediate cavity and simulation results like R over Q and quality factor (unloaded). The detailed design approach of the Klystron cavities and the drift length between the cavities can be found in reference [28]. Figure 1: Perspective view of RRSC: (**a**) input/output cavity, (**b**) intermediate cavity, and (**c**) schematic diagram indicating a geometrical parameter of an intermediate cavity. Figure 2: Structure of the RF section for proposed MCK. Slot coupling is a popular choice for the input and output cavities, which provides several advantages. It offers enhanced coupling efficiency, allowing for an efficient exchange of electromagnetic energy between the cavity gap and external structures. The placement and optimization of coupling slots are important considerations to achieve desired coupling effects in cavity design. To design the input and output cavities, slot coupling has been used. A parametric optimization approach using CST-Microwave Studio [29] has been employed to achieve the desired coupling with an optimum Q-factor. The cross-section views (perspective, top, and front, respectively) of the input and output cavities with the coupler are shown in Figure 3a-c. Details of the coupler dimensions are (Figure 3): coupler heights CH = 0.2 mm and waveguide height WH = 0.3 mm; iris lengths CL = 1 mm, WL1 = 1 mm, and WL2 = 1 mm; and width W = 0.6 mm. Staggered tuning has been used for increasing the bandwidth of Klystron through beam-wave interaction simulation. The staggered tuning technique involves tuning each stage of a multi-stage amplifier to slightly different frequencies. It provides benefits such as wider bandwidth and sharper pass-band-stop-band transitions. After the finalization of the cavity geometrical parameter, the RF section was designed using the CST-PIC (particle-in-cell) solver. The primary objectives of PIC simulation are to achieve a sufficiently amplified stable output RF, considering a single frequency input signal for a particular frequency point. If the output signal is not stable, the fifth point of the Klystron design process (Figure 4) is repeated until we obtain a stable RF signal. After obtaining the stable output, the stagger tuning process has been started for enhancement of the bandwidth. The PIC simulation process of designing the multi-cavity Klystron employing the stagger tuning technique is represented in the flow chart shown in Figure 4.