# Experimental Evaluation of the Blackbody Radiation Shift in the Cesium Atomic Fountain Clock
## 2 Theoretical Research on the Blackbody Radiation (BBR) Shift
### Constant Temperature Structure Design of Fountain System  
As shown in Figure 2, the temperature of the laboratory where the fountain clock locates is controlled by a two-stage water-cooled air conditioning system, which has a good temperature stability. During the continuous measurements, the temperature fluctuation range is within \(\pm\)0.5 \({}^{\circ}\)C. When the fountain clock physical system was placed directly in the laboratory environment, the temperature of the overall system fluctuated as the laboratory temperature fluctuated, which does not meet the temperature requirements of the system. Overall temperature control is performed on the physical system of the fountain clock, and an insulation layer is installed on the outer wall of the system for temperature control, thereby reducing the temperature fluctuation of the entire physical system.  
Figure 3 illustrates the physical system temperatures before and after the installation of the insulation layer outside the fountain clock system. Measurements were performed for 20 days for each of the two conditions. Before the insula  
Figure 2: Temperature annunciator.  
temperature fluctuation of the system was 1 \({}^{\circ}\)C. After the insulation layer was added, the temperature fluctuation range was limited to within 0.3 \({}^{\circ}\)C, indicating greatly improved temperature stability performance of the system.  
According to the requirements for the physical system for a temperature and magnetic field environment, a 5 mm-thick aluminum C-field cylinder layer and four layers of 2 mm-thick inter-phase permalloy magnetic shielding cylinder were installed outside the vacuum pipeline of the atomic flight zone. With the insulation protection provided by these five metal layers, the temperature of the vacuum pipeline in the atomic flight zone would become more stable compared with the temperature measured in Figure 3. In addition, the vacuum pipeline of the atomic flight zone of the cesium fountain clock is made of titanium alloy and the resonant cavity is made of oxygen-free copper, both of which are metals that have good thermal conductivity and can make the temperature distribution more uniform. In order to make the temperature distribution of the resonant cavity and the vacuum cavity of the atomic flight zone consistent, the resonant cavity bracket was also made of oxygen-free copper.  
In practical applications, if the temperature sensors and wires are arranged inside the vacuum chamber, the temperature inside the vacuum chamber can be accurately obtained; however, the vacuum degree of the system will be affected. Therefore, in the design of the physical vacuum system, after many measurements and improvements, three Pt100 platinum resistance temperature sensors were installed on the outer wall of the vacuum chamber pipe in the atomic flight zone to obtain the temperature distribution of the outer wall of the vacuum chamber without affecting the vacuum of the system. The specific installation locations are shown in Figure 4.