# Research and Design of the RF Cavity for an 11 MeV Superconducting Cyclotron
## 1 Introduction  
Cyclotrons are pivotal tools for the production of medical radioisotopes due to their lower construction and operational costs compared to reactors [1, 2, 3]. With the growing prominence of positron emission tomography (PET) in biomedical imaging, the demand for positron-emitting isotopes has surged. Notably, \({}^{11}\)C and \({}^{18}\)F stand out as the most effective PET isotopes, characterized by their short half-lives of 20 and 108 min, respectively. Currently, the predominant method of producing \({}^{11}\)C and \({}^{18}\)F involves the use of low-energy cyclotrons (with energies below 15 MeV). A prevailing trend in the development of these cyclotrons is the emphasis on creating more compact, lightweight, and cost-efficientmodels [4; 5; 6]. Furthermore, there is a growing preference for cyclotrons that can operate in smaller settings and produce isotopes in proximity to patients. This approach aims to mitigate transportation challenges, minimize isotope activity loss, substantially reduce production costs, decrease the demand for associated infrastructure, and curtail expenses related to subsequent auxiliary equipment [7]. In the overall design of the cyclotron, a modularized assembly approach is adopted, allowing for the independent design of its key systems, including the particle source system, magnet system, and RF system [8; 9]. During the preliminary design phase, it is essential to determine the specific parameters for each system and finalize the design of each independent module. Assembly is then carried out upon the completion of the research and design for each system. This modular design strategy not only curtails the research costs but also offers flexibility during maintenance, enabling the replacement of only the malfunctioning system. Such an approach enhances the development efficiency of the cyclotron, simplifies its debugging process, and reduces both operational and maintenance expenses. For low-energy superconducting cyclotrons, the heightened magnetic field necessitates a reduced magnet radius for particle acceleration, leading to a diminished radial dimension for the RF cavity situated between the upper and lower magnets. Employing a conventional quarter-wavelength coaxial cavity would result in a length that significantly surpasses the radius of both the magnet and the vacuum chamber. This underscores the need for research into a more compact RF cavity design. To address the impedance matching challenge, an SIR (Stepped Impedance Resonator) structure is introduced. This resonator comprises a combination of two or more transmission lines, each with distinct characteristic impedances. The design permits an adjustment of the impedance ratio based on the radial size requirement, facilitating the resonator's miniaturization. Furthermore, the quarter-wavelength coaxial SIR structure employed in this design is straightforward and amenable to fabrication [10]. The RF cavity is a pivotal component of the cyclotron primarily responsible for harnessing the accelerating electric field produced by high-frequency power coupling to propel charged particles. The RF cavity's performance is intricately tied to its structural dimensions. Precise modeling and simulations are imperative to ascertain the design dimensions that align with the desired frequency. Cyclotron RF cavities, given their intricate structures, are typically analyzed and designed through both numerical and equivalent circuit calculations. For numerical evaluations, the common numerical method of high-frequency electromagnetic field calculation is the Finite Element Method (FEM), so the Finite Element Method is predominantly employed in the article [11]. For complex cavities, a unified computer modeling and calculation method can be used, which greatly simplifies the process and difficulty of resonant cavity analysis. At the same time, it can also be compared and verified with the equivalent circuit method.