A. Review on pre-tuning theory

The first thing of pre-tuning is to calculate the field flatness and the frequencies needed to tune each cell. When a metal bead passing through the axis of a cavity, the TM₀₁₀-π mode electric field shall be [6]

where Δφ is the phase shift of S₂₁ and Δf is TM₀₁₀-π mode frequency excursion of the cavity. By measuring QL and (Δφ_max)_i (i=1,2,…,N, is the cell number), one obtains the maximum phase shift of Cell i, (Δf_max)_i and the relative (E_max)_i. Substituting (E_max)_i into Eq. (2) to calculate the field flatness

The frequencies needed to tune each cell [7] can be calculated by Eq. (3)

where $\Delta f_{\text{tune}}=(f_{\text{desired}}^{\pi }-f_{\text{measured}}^{\pi })/N$, $f_{\text{desired}}^{\pi }$ and $f_{\text{measured}}^{\pi }$ are the desired and measured frequency of the TM₀₁₀-π mode, respectively, and (Δf_c)_i is related to $f_{\text{measured}}^{i\pi /N}$ and (Δf_max)_i.

Pre-tuning a cell is a physical procedure: axially squeezing or stretching the cells to be tuned. Squeezing a cell lowers its resonant frequency, while stretching a cell increases its resonant frequency. So by pushing or pulling cells, the resonant frequency can be tuned to the desired frequency and a good field distribution can be obtained.

B. Establishing pre-tuning frame

A pre-tuning frame based on the bead-pull method was applied to pre-tune the 500 MHz 5-cell cavity. Fig. 2 is the schematics, which includes the data acquisition of field distribution and cavity frequency tuning. The hardware (Fig. 3) contains a perturbation bead, a computer, a vector network analyzer (VNA), a step motor and its controller, etc. The software is a LabVIEW and MATLAB hybrid codes. The LabVIEW code is performed for data acquisition between the VNA and the computer, and for the step motor control. The MATLAB code is used for calculation. In this pre-tuning frame, the VNA is set to work in the continuous wave mode [8] at the unperturbed TM₀₁₀-π mode frequency, and the step motor is set to move at a constant speed so that the perturbation bead pass through each cell in a uniform manner in fixed frequency. The phase shift when the bead pass through each cell is obtained from S₂₁ curve.

Fig. 2.Full-screen View

Schematics of bead-pull pre-tuning apparatus at SINAP.

Fig. 3.Full-screen View

(Color online) Bead-pull pre-tuning frame at SINAP.

C. Pre-tuning of the copper prototype cavity

Before making the niobium cavity, a copper prototype cavity was built to explore the fabrication procedures and develop the measurement techniques. The pre-tuning process executed on the Cu cavity showed that the $f_{\text{measured}}^{\pi }$ was 497.618 MHz, and the reasonant frequencies of Cells 1;2;3;4;5 were lower than the target frequency by 0.181 MHz, 0.271 MHz, 0.256 MHz, 0.297 MHz and 0.163 MHz, respectively. With frequency control, the field flatness of the copper cavity reached (91.7±0.6)% and frequency deviation from target was 1.2 MHz. The strong cell-to-cell coupling (k_cc = 3.18%) due to the cavity’s large aperture, and the deep-drawing technology employed also played an important role.

Regulating cell by cell is an easy approach for pre-tuning [8, 9]. For the 500 MHz 5-cell copper cavity, Cells 2, 3 and 4 were close to each other in Δf_tune, with a differences of just 0.041 MHz, while Cells 1 and 5 were over 0.1 MHz less in Δf_tune than other cells. We attempted to tune the cavity in two methods. One was to squeeze Cells 1 and 5 to enlarge their Δf_tune to 0.27 MHz, so as to get a field flatness better than 98%, followed by stretching the whole cavity to increase the TM₀₁₀-π mode frequency to 498.8 MHz. However, after 600 ℃ annealing, the copper cavity was very soft. When stretching the whole cavity, deformation occurred on Cells 1 and 5, and the field flatness decreased to about 92%.

The second way was to pull the whole cavity from 2221 mm to 2229 mm to reach 499.1 MHz, which is a little higher than the desired frequency (Fig. 4), followed by pushing Cells 1 and 5 to tune frequency to 498.8 MHz and to acquire a field flatness better than 98%. The field flatness of 98.9% was achieved and the TM₀₁₀-π mode frequency was tuned to 498.798 MHz, being just 2 kHz lower than the desired frequency. The electric field distribution profile in Fig. 5 was uniform, a nice field in good accordance with the simulation results [5]. After pre-tuning, the total length of the copper cavity returned back to 2224 μm. The 5 modes frequencies of TM₀₁₀ measured by VNA after pre-tuning were given in Table 1.

Fig. 4.Full-screen View

TM₀₁₀-π mode frequency vs total length of the cavity.

Fig. 5.Full-screen View

Field distribution of the copper cavity before pre-tuning and after pre-tuning.

D. Pre-tuning of the niobium cavity

Pre-tuning consequences of the copper cavity laid a solid foundation for pre-tuning the niobium cavity. For the 500 MHz 5-cell niobium cavity before pre-tuning, the $f_{\text{measured}}^{\pi }$ was 497.754 MHz, the reasonant frequencies of Cells 1;2;3;4;5 were 0.131 MHz, 0.241 MHz, 0.223 MHz, 0.221 MHz and 0.225 MHz lower than the target frequency, respectively, and the field flatness was just 78.6%. It was pre-tuned in the similar way as the copper cavity. However, after 680 ℃ annealing, the niobium cavity was still of high hardness. It was difficult to obtain plastic deformation by manual squeezing or expanding. So we decided to squeeze just Cell 1 to get good field flatness and abandon the frequency adjustment. The tuning process is shown in Fig. 6. Eventually, the field flatness was tuned to 98.5%, and the TM₀₁₀-π mode frequency was 497.728 MHz, i.e. 1.1 MHz lower than the desired frequency.

Fig. 6.Full-screen View

Pre-tuning process of the 500 MHz 5-cell niobium cavity, by squeezing just Cell 1.

After pre-tuning, vertical testing was done on the niobium cavity on December 17, 2012. A good result, V_acc=7.5 MVQ₀=1 × 10⁹, was achieved. The TM₀₁₀-π mode frequency was approximate 498.3 MHz at 4.2 K.