# Design Studies of Re-Entrant Square Cavities
###### Abstract  
V-band Klystrons find applications in satellite communications and 5G technology. Here, we present a V-band Klystrons using radial re-entrant square cavities (RRSCs). The RRSCs are easy to fabricate, assemble, align, and tune to the operating frequency, which are significant concerns in V-band. We have optimized the number of cavities and the gap for best possible gain and bandwidth. The eigenmode and particle-in-cell (PIC) simulation results of the CST microwave studio are presented. The optimum design uses eleven equidistantly placed RRSCs, producing the maximum gain of 27.17 dB at 60.1 GHz with a bandwidth of \(\sim\)150 MHz.  
re-entrant cavity; vacuum electronic amplifiers; V-band Klystron; V-band RF section Article Design Studies of Re-Entrant Square Cavities for V-Band Klystrons for V-Band Klystrons  
[PERSON], M.S., [PERSON], S.  
radiation pressure (Lorentz detuning, especially for high power applications) [15], affecting the dimensions of the cavities. The re-entrant types of RF cavities are a very popular choice for Klystrons to achieve all the required cavity parameters such as frequency, Q factor, shunt impedance and R/Q value. Besides the Klystrons, these types of cavities are also used in electromagnetic cavity based transducers, particle accelerators, synchrotron radiation facilities etc. [15; 16].  
The input RF signal in the first cavity initiates the velocity modulation process. It becomes more pronounced as the beam traverses through the series of intermediate cavities. As a result, the electron beam forms denser bunches, intensifying the induced RF field in the successive intermediate cavities. The electron bunches cross the output cavity's gap while the cavity fields oppose their motion. Under these conditions, maximum energy is transferred from the electron beam to the output cavity. The field grows as the beam's kinetic energy is transferred to the cavity's field.  
A novel topology of high frequency Klystrons (operating in higher order mode) has been proposed by [PERSON] [17], where simple cavity geometry is employed to overcome high frequency fabrication limitations of conventional re-entrant and extended interaction Klystron cavities. In the current design, the approach of periodically allocated cavities operating in fundamental mode has been followed with the redesign of the RF section for V-band operation. A re-entrant square cavity is designed first as an intermediate cavity of the Klystron [18]. The design is then optimized for the maximum R/Q ratio. A coupler [19] is attached to the cavity to facilitate the input/output, and several intermediate cavities are assembled and aligned to form the Klystron's RF section. PIC simulation is carried out to probe the performance of the proposed Klystron. The optimum number of cavities is also determined to maximize the gain. The designed structure can easily be fabricated with conventional fabrication tools, unlike structurally complicated internal coupling multi-gap cavities [20; 21; 22].  
Reported Klystrons at this frequency band (around 60 GHz) are rare and, in most of the reported cases of high frequency Klystrons, extended interaction types of topology (with complex geometries) have been utilized. Here, the proposed device is of simple structure, is microfabrication compatible and compact in form factor, offering 256 W of output power.  
This paper is organized as follows. Section 2 presents the design equations of the various RRSCs and the RF section, followed by the cold simulation results. Section 3 concentrates on the PIC simulation results and the RF performance of the RRSC Klystron. Finally, Section 4 summarizes the principal findings of the present work and suggested domains for further improvements along with the potential application areas.