## 3 Experimental Application
### Pre-Tuning Process and Observations  
The pre-tuning process involved iterative measurements and adjustments to achieve the target frequency of 648 MHz and a field flatness of over 95%. The process was divided into several key steps shown below, which provided valuable insights into the cavity's behavior during tuning.  
1. Initial field distribution: Before pre-tuning, the copper cavity exhibited poor field flatness, with a calculated flatness of approximately 2%, its S21 phase curve shown in Figure 10 by a network analyzer [22]. The start and stop frequencies of the network analyzer were set to the cavity's \(\pi\) mode resonant frequency. With the setting of appropriate sweep time and number of sweep points and the synchronization of these parameters with the bead movement, the phase distribution can be measured. By observing the phase minima in each cell (the trough positions in the curve), the electric field flatness can be calculated, and the subsequent tuning strategy can be determined. The target frequency was set at 648 MHz, and the goal was to improve the field flatness to above 95%.  
Figure 9: The bead-pull system with a fishing line.  
2. Tuning mechanism: The pre-tuning process relied on compressing or stretching individual cell units to adjust their equivalent capacitance, as depicted in Figure 11. Compression increases a cell's capacitance, thereby reducing resonant frequency and field amplitude, while stretching has the opposite effect. This principle was used to fine-tune the cavity's performance.  
The relationship between the pre-tuning machine's travel distance and frequency change was nonlinear. Initially, a 1 mm travel distance resulted in a frequency shift of approximately 10 kHz, but this shift increased to several hundred kHz in later stages.  
During tuning, the copper cavity underwent elastic deformation (causing temporary frequency shifts) and plastic deformation (resulting in permanent adjustments). For example, compressing Cell-4 temporarily reduced the frequency to 647.559 MHz, but upon release, the frequency stabilized to 647.673 MHz after the cavity rebounded.  
3. Iterative tuning and measurement: The tuning process was performed iteratively, with each cell adjusted individually. After each adjustment, the high-frequency characteristics were re-measured to evaluate the impact of the tuning. This cycle was repeated  
Figure 11: Compress or stretch the individual cell units.  
Figure 10: Field distribution of the elliptical superconducting cavity before pre-tuning.  
multiple times until the desired electric field flatness was achieved [23]. The changes in field distribution during the tuning process are illustrated in Figure 12.  
Adjusting a single cell often impacts adjacent cells, especially end cells, which interact with two neighboring cells. For example, stretching Cell-1 by 18 mm increased its frequency but also caused a slight frequency shift in Cell-2.  
4. Final results: After multiple iterations of tuning and measurement, the field flatness of the superconducting cavity was successfully improved from an initial 2% to 96.5%, as shown in Figure 13. The final results met the target requirements, demonstrating the effectiveness of the pre-tuning machine algorithm and tuning device. The resonant frequency was stabilized to 648 MHz, with a field distribution that satisfied the design specifications.  
Figure 12: Changes of the electric field during the pre-tuning process.  
Figure 13: Field distribution of the elliptical superconducting cavity after pre-tuning.