# Beam Dynamics Design of a Multi-Ion RFQ for Medical Application
## 5 Conclusions  
This study presents the beam dynamics design and error analysis of a 200 MHz multi-ion RFQ for medical applications. A novel design strategy is proposed. By adjusting the dynamic balance between focusing and defocusing forces, the transmission efficiency at 8 mA reaches 84%, effectively enhancing the ability to suppress space charge effects. After improving the RFQ's transverse focusing process, the input transverse emittance of 0.2 \(\pi\) mm\(\cdot\)mrad and the output transverse emittance of 0.1983 \(\pi\) mm\(\cdot\)mrad become nearly equal. After optimizing the modulation and synchronous phase, the beam is well captured, with a beam capture efficiency reaching 98.95%, and the beam quality is improved. The final simulation result achieved a transmission efficiency of over 98% for C\({}^{4+}\) and 97% for He\({}^{2+}\), with a compact structure and RFQ length of 2.5 m.  
Multi-particle simulations using different programs validated the reliability of the proposed design. Furthermore, comprehensive error analyses confirmed the RFQ's sufficient tolerance to input and mechanical errors, ensuring stable operation under practical conditions. The results indicate that this multi-ion RFQ design scheme meets all the predefined requirements for medical accelerators, offering a compact and high compatibility scheme for particle therapy applications. This new proposed design strategy could benefit the next generation of RFQs for medical applications, enhances the feasibility of personalized therapy, and promotes the broader adoption of particle therapy technology in clinical practice.  
Future work will be carried out in several stages. The first stage involves the RF design and multiphysics analysis of the RFQ cavity, including optimization of field flatness, as well as analyses of thermal and structural deformation. The second stage focuses on the construction and experimental validation of an RFQ prototype, encompassing mechanical alignment, low-power testing, and beam commissioning. The ultimate goal is clinical implementation.  
Conceptualization, X.W. and W.Z.; methodology, X.W. and W.Z.; software, X.W. and W.Z.; validation, X.W. and G.C.; formal analysis, X.W. and G.C.; investigation, X.W. and G.C.; resources, X.W. and W.Z.; data curation, X.W. and G.C.; writing--original draft preparation, X.W. and G.C.; Writing--review and editing, X.W.; funding acquisition, W.Z. All authors have read and agreed to the published version of the manuscript.  
The Shanghai Advanced Research Institute, Chinese Academy of Sciences: E06G321C01.  
\begin{table}
\begin{tabular}{c c c} \hline
**Item** & **Value** & **Note** \\ \hline \(\delta R\) [mm] & \(\pm\)0.01 & Longitudinal profile \\ \(d\) [mm] & \(\pm\)0.01 & Transverse curvature for the electrode \\ \(TEp\) [mm] & \(\pm\)0.03 & Perpendicular tilt for electrode \\ \(TEpa\) [mm] & \(\pm\)0.03 & Parallel tilt for electrode \\ \(Depe\) [mm] & \(\pm\)0.02 & Perpendicular displacement for electrode \\ \(Depa\) [mm] & \(\pm\)0.02 & Parallel displacement error for electrode \\ \(DELong\) [mm] & \(\pm\)0.04 & Longitudinal displacement for electrode \\ \(TSVerti\) [mm] & \(\pm\)0.04 & Vertical tilt \\ \(TSHori\) [mm] & \(\pm\)0.04 & Horizontal tilt \\ \(DSVerti\) [mm] & \(\pm\)0.02 & Vertical displacement \\ \(DSHori\) [mm] & \(\pm\)0.02 & Horizontal displacement \\ \(DSLong\) [mm] & \(\pm\)0.04 & Longitudinal displacement \\ \hline \end{tabular}
\end{table}
Table 6: The setting values of the mechanical errors.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Data available on request due to privacy restrictions.  
**Acknowledgments:** The author would like to thank [PERSON] for his useful discussions and for providing the e-book _\"Elements of Ion Linear Accelerators\"_, and [PERSON] and [PERSON] from the Institute of Modern Physics (IMP), Lanzhou, for the code simulation.  
**Conflicts of Interest:** The authors declare no conflicts of interest.