# Vibration Reduction in a Pulse Tube-Cooled High Purity Germanium Detector
## 2 Passive Isolation System Design  
In this paper, the specifications for the low-vibration portable EMC system are displayed in Table 1. A schematic illustration of the portable passive isolation PTC system is shown in Figure 1. The compressor assembly was mainly composed of a compressor, spring isolators, housing for the compressor, and an \"S\" shape transfer line. The transfer line connected the cold flange with the compressor. The spring isolators attenuated base plate and cold head flange vibration. To attenuate detector interface (VR stage) vibration, copper heat links were used to connect the cold tip with detector interface. An FPR-supporting plate [13] was mounted on a vacuum vessel flange to support the HPGe detector. To reduce PTC mounting base plate vibration, a CVIK was installed between the compressor and the PTC-mounted interface. In order to ensure cooler multi-orientation operation, the CVIK included eight sets of spring and damper isolators to reduce the transmission of vibration from the compressor. The transmission of the vibration force \(\eta\) is defined as the ratio between the force at the mounted interface and the force exported by the compressor. For a linear single-degree-of-freedom spring and damper system, \(\eta\) is expressed as Equation (1). Figure 2 demonstrates the physical model. \[\eta=\frac{F_{max}}{F_{o}}=\sqrt{\frac{1+\left(2\epsilon\lambda\right)^{2}}{ \left(1-\lambda^{2}\right)^{2}+\left(2\epsilon\lambda\right)^{2}}} \tag{1}\]  
\[|X|=\frac{|F|}{k}\eta \tag{2}\]  
where \(\epsilon\) is a damping ratio, \(\lambda\) is the ratio of vibrational frequency and natural frequency of the spring, \(F_{max}\) is the amplitude of vibration force after the vibration isolators, \(F_{0}\) is the amplitude of vibration force from the vibration source, \(|F|\) is vibration force amplitude, \(|X|\) is the isolation system vibration defection, and k is the axis stiffness of the CVIK. In order to ensure \(\eta\leq 0.1\), the CVIK design parameters are shown in Table 2. The natural frequency of a compressor with the CVIK is less than 12.7 Hz. The axis stiffness of the CVIK is 16,000 N/m. The transfer line deflection is within 3.52 mm under the 2 g sine vibration load. Figure 3 shows the transmissibility of the CVIK at different vibrational frequencies. The figure indicates that the transmissibility is 0.07 at the main frequency 64 Hz and that the CVIK has lower transmissibility at harmonic frequency. The requirement of the CVIK is not only to reduce vibration transmissibility but also to weaken the vibration displacement under the 2 g sine vibration load. According to function 2, the displacement of the compressor is 3.52 mm (which the copper transfer line tube can bear) when the PTC suffers from 2 g acceleration impact. \begin{table}
\begin{tabular}{c c} \hline
**Item** & **Specification** \\ \hline Compressor power consumption & 80 W \\ Cooling performance requirement & 4 W@80 K \\ Power frequency & 64 Hz \\ Cooler power controller (CPC) modulation frequency & 100 kHz \\ Working orientation & Multi-orientation operation \\ Transport standard & 2 g \\ HPGe efficiency & 40\% \\ Typical cooldown time & 6 h \\ \hline \end{tabular}
\end{table} 
Table 1: The specifications for the low-vibration portable EMC system. In this paper, the ultimate requirement was to reduce the vibration of the HPGe detector mounted interface. Especially, HPGe detectors need to extend cold tips because detectors require lead chamber shielding in use. The longer the copper cold tip, the greater the vibration of the detector interface. The CVIK ensured the attenuation of the vibration of the compressor-mounted interface and the cold head flange. In order to further mitigate detector vibration, oxygen-free high-conductivity copper heat links and a glass fiber-reinforced-plastic supporting plate were used. The heat links consisted of several copper wires, each 0.5 mm in diameter, which reduced the heat links' spring constant.