## 1 Introduction
### Sc RFQ  
The RFQ accelerator is well suited for the acceleration and focusing of low-energy beams, with NC RFQs demonstrating robust operating stability under pulse mode [11].  
Figure 1: Four-vane RFQ structure [9]: (**a**) the four electrodes are excited with \(\pm V/2\) quadrupole-mode RF voltages; (**b**) the modulated electrode structure with a modulation factor of m; (**c**) the electromagnetic field distribution in the cross-section of the RFQ; (**d**) the equivalent circuit of the quadrupole mode of a four-vane cavity.  
However, as large-scale scientific devices increasingly shift towards CW operation and higher current requirements, some RFQs' power consumption even reaches the level of megawatts [12; 13; 14], which restricts the stability and economy of RFQs' long-term operation. Fortunately, superconductivity offers a solution by significantly reducing power losses and enabling CW operation; the combination of these two technologies presents a pathway for the more efficient acceleration of high-current beams [15].  
Compared with NC RFQs, an SC RFQ has the following advantages:  
1. Reduced Power Loss: The high quality factor (\(Q\)) of the SC cavity results in significantly lower power loss, thereby diminishing the operating costs of linear accelerators [16]. The \(Q\) value of the SC cavity is typically five orders of magnitude higher than that of the NC cavity. Even taking the power consumption to maintain the low-temperature environment required for the superconducting state into account, the total power requirement of an SC cavity is about two orders of magnitude lower than that of an NC cavity.
2. Higher Accelerating Gradient: The accelerating field of the RFQ increases as the inter-vane voltage applied between the electrodes increases. As discussed in Section 2, the SC RFQ can withstand higher voltages between electrodes without being constrained by RF power loss. This capability results in a significantly higher accelerating gradient compared to the NC RFQ, which shortens the cavity's length and makes the device more compact [17].
3. Enhanced Beam Aperture: The beam-focusing force is proportional to the inter-vane voltage and inversely proportional to the aperture [18]. The SC RFQ, without being constrained by RF power loss, is capable of accommodating higher voltages between electrodes. This flexibility allows for a significantly larger aperture compared to NC RFQs, which has two benefits: firstly, it increases the transverse acceptance of the accelerator, promoting the efficient transmission of high-intensity beams; secondly, it mitigates beam instability arising from the beam-cavity interaction.  
As discussed above, SC RFQs are going to be an indispensable part of the low-energy end of high-intensity accelerators. However, due to numerous challenges in the design and construction of SC RFQs, only the National Institute for Nuclear Physics (INFN) in Italy successfully built two 80 MHz SC RFQs around 2000, which have been in steady operation for a long time [19; 20; 21; 22; 23]. It is urgent to conduct further research on SC RFQs.  
This paper describes the design of a 162.5 MHz 10 mA CW proton SC RFQ and is organized as follows: Firstly, a comprehensive introduction of the beam dynamics design is given, focusing on optimizing acceleration and transmission efficiency; secondly, the RF design of the cavity is presented, emphasizing structural enhancements to minimize peak surface electric and magnetic fields; thirdly, the paper encompasses a multi-physics analysis and a tuning study of a 30 cm model cavity, providing conclusive evidence regarding the accelerator's reliability.