# Nb\({}_{3}\)Sn Cavities Coated by Tin Vapor Diffusion Method at Peking University
## 1 Introduction  
Modern particle accelerators have played a crucial role in theoretical physics, material science, radioactive medicine, and environmental science. The superconducting radio-frequency (SRF) cavity is one of the key components in a superconducting accelerator system, which is used to accelerate particles by establishing an electromagnetic field inside. For almost half a century, scientists have been dedicated to improving the performance of niobium cavities that are generally close to the theoretical physical limitation of niobium superconductor. Nb\({}_{3}\)Sn is known to be a feasible alternative for the construction of SRF cavities with a higher quality factor and an accelerating gradient [1]. Nb\({}_{3}\)Sn has almost double the critical temperature (18.1 K) and superheating field (420 mT) compared with niobium. The Nb\({}_{3}\)Sn-coated cavity can contribute to building compact accelerating systems with a much lower cost than that using niobium cavities. The vapor diffusion method is proven to be the most effective method to coat cavities nowadays. In the vapor diffusion method, tin is heated into vapor to be deposited on the inside surface of niobium cavities and forming Nb\({}_{3}\)Sn. The vapor diffusion method was first applied in the preparation of Nb\({}_{3}\)Sn TE and TM mode cavities at Siemens AG during the 1970s [2]. A group from Wuppertal University also performed research, and they suggested the annealing step in the coating profile and proposed the necessity of a slow cooling rate for Nb\({}_{3}\)Sn cavities [3, 4].  
Then, the tin vapor diffusion method was improved and developed from the Wuppertal method by Cornell University after 2009 to eliminate the Q-slope phenomenon [5,6]. Thomas Jefferson National Accelerator Facility and Fermilab also fabricated Nb\({}_{3}\)Sn cavities with high performance via the vapor diffusion method [7,8]. Fermilab's 1.3 GHz single-cell cavity achieves a quality factor of \(1\times 10^{10}\) with a nearly 24 MV/m accelerating gradient at 4.2 K, demonstrating the feasibility and prospect of Nb\({}_{3}\)Sn-coated cavities, and representing the state of the art [8].  
However, some problems regarding this issue remain to be solved. The coating profile, structure of furnaces and preprocessing greatly vary among different experiments at different institutions [9]. Additionally, the superheating field achieved is far lower than its theoretical limit. Most results of Nb\({}_{3}\)Sn coating experiments via vapor diffusion methods exhibit a serious Q-slope phenomenon, which leads to a low accelerating gradient [3,10,11,12,13,14,15]. The grain boundary segregation effect refers to low-tin regions in the grain or the grain boundary, and film defects are confirmed to be harmful to cavity performance [16, 17, 18]. Surface roughness has also been demonstrated to influence the cavity acceleration gradient while traditional polishing methods for niobium are proven not to be so effective for Nb\({}_{3}\)Sn [19, 20, 21].  
In this work, a new coating design is proposed to apply three tin sources inside a cavity at Peking University (PKU) in order to generate uniform high-pressure tin vapor during the coating process. Samples are produced to separately study the two main processes, the nucleation stage, and the coating stage to further elucidate the differences in the deposition mechanism between a single-tin-source design and a three-tin-source design. Nb\({}_{3}\)Sn coating experiments are also carried out on 1.3 GHz single-cell Tesla-type cavities using different recipes, and a detailed analysis is presented in this paper.