# The Design of a High-Intensity Deuteron Radio Frequency Quadrupole Accelerator
## 7 Vacuum Design
### COMSOL Simulation  
Our vacuum design was conducted using a COMSOL simulation. As mentioned, in the presence of ultra-high vacuum conditions, the mean free path of gas molecules largely exceeds the characteristic length of the vacuum cylinder. Consequently, the free-molecular flow solver is chosen.  
Initially, the vacuum of an individual cavity is computed without considering the influence of preceding or subsequent components. In COMSOL, using a tetrahedral grid gives too small of a step size for cavity electrode band modulation, leading to excessive grid division and a slow calculation. To improve computational efficiency, we carried out the electrode simulation without modulation. The thermal desorption rates for the connecting pipe, coupler, tuner and cavity structure of the vacuum pump were all set to 7.98 \(\times\) 10\({}^{-9}\) Pa \(\cdot\) L/(cm\({}^{2}\cdot\) s), in accordance with oxygen-free copper parameters. As shown  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **LEBT Value** & **MEBT Value** \\ \hline D (cm) & 1 & 2.2 \\ S (cm\({}^{2}\)) & 0.79 & 3.80 \\ \(C_{air}\) (L/s) & 9.11 & 44.09 \\ C\({}_{H2}\) (L/s) & 35.26 & 170.65 \\ \(P_{RFQ}\) (Pa) & 10\({}^{-6}\) & 10\({}^{-6}\) \\ \(P_{system}\) (Pa) & 3 \(\times\) 10\({}^{-5}\) & 10\({}^{-5}\) \\ \(\Delta\)P (Pa) & 2.9 \(\times\) 10\({}^{-5}\) & 0.9 \(\times\) 10\({}^{-5}\) \\ Q (Pa \(\cdot\) L/s) & 1.022 \(\times\) 10\({}^{-3}\) & 1.536 \(\times\) 10\({}^{-3}\) \\ \hline \hline \end{tabular}
\end{table}
Table 12: Conductance parameters.  
Figure 33: Schematic of the cylindrical flow guide.  
in Figure 34, pairs of vacuum pumps, set to a speed of 600 L/s each, were placed within the first and last cavities. The simulation included the gas loads over all surfaces and the gas pressure on the beam line.  
Accounting for the effects of the LEBT and the MEBT sections on the vacuum, the gas load was set to 1.022 \(\times\) 10\({}^{-3}\) Pa \(\cdot\) L/s and 1.536 \(\times\) 10\({}^{-3}\) Pa \(\cdot\) L/s separately. The speed of the pumps was set to 1200 L/s, and an ion pump with 440 L/s was added to the second cavity. The 3D vacuum level of the simulated gas is depicted in the left side of Figure 35. Here, the primary concentration of gas molecules at the RFQ entrance indicate that the low-energy transport section yields the largest influence. The right side of Figure 35 shows the pressure along the central axis of the cavity. The pressure at the RFQ end plate is as high as 1 \(\times\) 10\({}^{-4}\) Pa, whereas the pressure along the central axis is approximately 1.2 \(\times\) 10\({}^{-6}\) Pa. To increase the vacuum level, it is necessary to reduce the pressure at the entrance of the low energy section.  
In our first simulations, which focused on a single cavity without any gas load from LEBT or MEBT sections, we observed that a total of four sets of vacuum pumps were necessary, each with a pumping speed of 600 L/s. In this configuration, after reaching a steady state, the vacuum level reaches 10\({}^{-6}\) Pa. When factoring in the influence of both the LEBT and MEBT sections, however, a more robust vacuum system is required. By employing four sets of vacuum pumps with a pumping speed of 1200 L/s and an additional pump with a capacity of 440 L/s, a vacuum level of 1.2 \(\times\) 10\({}^{-6}\) Pa can be obtained. To achieve this standard, the molecular pump is set to FF-200/1200, while the ion pump is set to CF150/SIP500.  
Figure 34: (**Left**): Vacuum pressure distribution. (**Right**): On-axis cavity pressure.  
Figure 35: (**Left**) Vacuum level of the RFQ; (**Right**) on-axis cavity pressure (with inlet gas from LEBT and MEBT).