1 Introduction
High-current continuous-wave (CW) RFQ is greatly needed for basic research [1-3], energy [4], medicine [5], etc., but this goal is filled with challenges. At present, the number of high-current CW RFQs that can operate stably is very limited around the world [6-10]. Therefore, PKU and IMP have been collaborating on a new 973 project that aims to build a 50 mA CW deuteron RFQ and challenge the difficulties in the beam dynamics, RF structure, cooling, and power coupling system. According to the beam dynamics design, this RFQ will operate at 162.5 MHz, accelerating a deuteron beam from 50 keV to 1 MeV with a length of 1.809 m [11]. In recent years, a new kind of four-vane RFQ with magnetic coupling windows, usually called a window-type RFQ, was developed by Argonne National Laboratory of America (ANL) and the Institution of Theoretical and Experimental Physics of Russia (ITEP) [12, 13]. It combines features of a four-vane RFQ and a four-rod RFQ, with the advantages of clear mode separation, compact structure, relatively low power consumption, and simple machining. To date, only a few low-frequency window-type RFQs for accelerating heavy ions worldwide have been built and commissioned. They have relatively small cross sections [14-17]. Thus, it is necessary to build and test cold models to lay a foundation for our power cavity.
2 First cold model experiment
The first cold model was built to study the effect of the magnetic coupling window’s dimensions on the RF properties. As shown in Fig. 1, in the middle of each vane exists a very wide window. The supporting blocks, which are marked in yellow, can installed or detached at different locations with screws. By increasing the number of supporting blocks, the number of windows in each vane can be switched to three or four. Similarly, by changing the widths of the blocks, the window width can be changed to 220, 240, or 260 mm.
Figure 2 shows the resonant frequencies and mode separations (between the operating quadrupole mode and the nearest dipole mode) corresponding to three different values of window width. As can be seen, an increasing window width reduces the frequency and increases the mode separation. The results of the measurements are close to the data from simulations. In addition, the measured results of the three-window and four-window structures listed in Table 1 also agree with the simulated values. Note that to save on processing time and cost, the vanes of this cold model are not modulated, so the radius of the vane tip and the aperture are fixed. Their values are set to the maximum of the tip radius and the minimum of the aperture, respectively, according to the beam dynamics design. Therefore, all of the measured frequencies are much lower than the designed values (162.5 MHz).
| Number of windows | Frequency (MHz) | Mode separation (MHz) | ||
|---|---|---|---|---|
| Simulated | Measured | Simulated | Measured | |
| 3 | 135.971 | 136.606 | 6.255 | 6.843 |
| 4 | 131.379 | 132.195 | 7.130 | 8.236 |
3 Second cold model experiment
The first model was useful in validating the relation of frequency and mode separation to the magnetic coupling windows. However, we noticed that cutting wide windows in the vanes impaired the mechanical strength of the aluminum structure, resulting in large deformations on the vane tips. Moreover, the cavity was assembled from many adjustable components, leading to poor electrical contact and very low quality factor of the cavity. Therefore, we built a second cold model with fixed-size windows. The detailed RF structure design of this cold model was presented in Ref. [18]. Its main parameters are summarized in Table 2. To leave a margin for tuning, the designed quadrupole mode frequency was a bit lower than the target value (162.5 MHz).
| Parameter | Value |
|---|---|
| Designed quadrupole mode (TE210) (MHz) | 161.979 |
| Nearest dipole mode (TE110) (MHz) | 168.229 |
| Nearest quadrupole mode (TE211) (MHz) | 180.206 |
| Mode separation (MHz) | 6.250 |
| Window width (mm) | 240.0 |
| Window depth (mm) | 80.0 |
| Cavity radius (mm) | 156.00 |
| Minimum aperture radius (mm) | 2.63 |
| Vane tip radius (mm) | 2.57 3.32 |
| Length of RFQ vanes (m) | 1.809 |
| Quality factor | 9808 |
3.1 Fabrication
As shown in Fig. 3, the second RFQ cold model has three coupling windows in each vane and four 50-mm-diameter tuners equipped in each quadrant. To further improve electrical contact, the number of cavity walls was reduced from 16 to 8 (see Fig. 4), which is consistent with the power cavity.
Ball-end milling tools were employed when processing vane modulations, as the variable focusing strength in the beam dynamics design requires the transverse radius of the vane tip to change along the RFQ. Figure 5 shows a completed modulated vane. Finally, the eight parts were assembled in four steel frameworks for positioning.
3.2 RF measurement
The test bench to perform RF measurements on the cold model is shown in Fig. 6. It includes a two-port transmission network that consists of the RFQ cavity and two pick-ups, a network analyzer to measure the S-parameters, and a bead-pull system to sample the electric field in the cavity. Figure 7 shows the measurement of the resonant frequency and the loaded quality factor of the cold model, which are in the condition of very weak coupling and are based on an -3 dB method.
The conversion between the loaded and unloaded quality factors is given by
where β1 and β2 are the coupling coefficients of the two pick-ups. In our case, they are far less than 1 and are approximately equal. For this symmetrical coupling, the unloaded quality factor can also be calculated by substituting the measured S21 parameter into the following equation [19]:
Table 3 lists the frequencies and unloaded quality factors we obtained for the first five modes. The measured unloaded quality factors are very close to the simulated values that were calculated with the electrical conductivity of aluminum (σ=1.9×107 S m-1). The actual frequency of the operating mode is lower than that predicted by 0.272 MHz.
| Mode | Simulated | Measured | |||
|---|---|---|---|---|---|
| f (MHz) | Q0 | f (MHz) | Q0 | S21 | |
| TE210 | 161.979 | 5614 | 161.707 | 5064 | -26.6 |
| 0TE110 | 168.229 | 6311 | 167.982 | 5573 | -28.2 |
| TE211 | 180.206 | 2730 | 180.438 | 2561 | -41.4 |
| πTE110 | 181.635 | 3733 | 180.174 | 3210 | -33.5 |
| 0TE111 | 185.675 | 3042 | 185.958 | 3005 | -34.1 |
The classical bead-pull perturbation method was applied in the electric field measurement. When a small dielectric bead is displaced through the cavity, the resonant frequency shift Δω and the electric field E at the bead’s location satisfy the following relationship:
where V0 is the bead volume, and W is the stored energy of the cavity. In addition, the relationship between the frequency change and the phase change of the S21 parameter is
As Δφ is small (Δφ<10o ), we have Δφ≈tanΔφ. Therefore, the electric field measurement acquires the square root of the phase shift Δφ.
We measured the field distribution of the first five modes in quadrant 1 at a distance of 15 mm from the aperture center. The phase shift caused by the network analyzer itself was already calibrated and corrected in raw data processing. As shown in Fig. 8, there is good agreement between the measured and simulated fields. The difference of the frequencies and field distributions between the two dipole modes (0TE110 and πTE110) confirms the asymmetric coupling windows between the horizontal and vertical vanes. The two figures also clearly show the noncoincidence of the zero points of the TE211 and 0TE111 modes owing to their different frequencies.
In addition, we measured the field in aperture by guiding a 4-mm-diameter bead along the axis. Owing to the nonzero volume of the bead, the obtained field was actually the average field inside the bead. Thus, a 1-mm-off-axis field calculated with CST EM [20] was used for comparison. As can be seen in Fig. 9, these two field distribution curves are highly consistent with each other, which confirms the accuracy of the vane modulation of the cold model.
3.3 Tuning
Tuners equipped in the RFQ cavity can change the cavity volume and compensate for the impact of machining and assembly errors and material deformation, thereby tuning both the frequency and field distribution to achieve the design requirements. Owing to the nonuniform magnetic field distribution caused by the coupling windows, there are small differences in tuning capability between the tuners in different longitudinal positions. When all 16 tuners are inserted the same distance into the cavity, the change in the frequency and quality factor for the first mode with distance is shown in Fig. 10. The tuning range of the frequency is approximately 0.9 MHz, and the average tuning sensitivity is 1.11 kHz mm-1 for one tuner.
Before field tuning, we measured the electric field distribution in the four quadrants (see Fig. 11). To analyze the field unflatness, the measured fields were normalized by dividing them by their average value, as shown in Fig. 12a. The black curve is the average field of the four quadrants. Owing to unavoidable material deformation and assembly errors, quadrant 3 has a large deviation compared to the other three quadrants, and the maximal field unflatness for a single quadrant reaches 8.7%. In addition, we notice that the field distribution in the four quadrants is correlated with the distances between adjacent vanes at the entrance and exit (see Table 4). For instance, D4 is much shorter than the other three distances at the entrance, and thus the field in quadrant 4 has the highest field. Similarly, D1 is shorter than D2 at the exit, so the field in quadrant 1 is higher than that in quadrant 2.
| Quadrant | Entrance | Exit | ||
|---|---|---|---|---|
| Measured distance (mm) | Simulated distance (mm) | Measured distance (mm) | Simulated distance (mm) | |
| D1 | 4.01 | 3.98 | 4.29 | 4.31 |
| D2 | 4.02 | 3.98 | 4.38 | 4.31 |
| D3 | 4.01 | 3.98 | 4.33 | 4.31 |
| D4 | 3.91 | 3.98 | 4.33 | 4.31 |
Then, we analyzed the asymmetry of each quadrant field, which can be calculated by the following equation:
where EQk is the measured field at longitudinal position k in quadrant Q, and
After adjusting the inserted distance for each tuner, the fields and asymmetries of the four quadrants are shown in Fig. 12b and Fig. 12d, respectively. Although the average unflatness changed little, the maximal unflatness is down to 5.8% and the average asymmetry is also reduced by half. However, we noticed that to obtain these relatively flat fields, several tuners were inserted at the deepest distance, yet the operating mode frequency was only 162.140 MHz. This indicates that the tuning capability is inadequate for this cold model. Therefore, the number of tuners in each quadrant will be increased from 4 to 7 and the tuner diameter will also be enlarged from 50 to 60 mm for the copper power cavity, thereby increasing the tuning range of the frequency to 2.5 MHz.
3.4 Gap tuning
As the vertical vanes have no coupling windows at either end (see Fig. 3 or 4) and are very close to the endplates, the operating mode frequency and the distribution trend of the electric field are quite sensitive to the gaps between the endplates and the vanes, just as end cuts for a four-vane RFQ. By adding shims between the endplate and the cavity, we increased the gap distance at the entrance from 8 mm to 11 and 14 mm. As shown in Fig. 13, increasing the gap distance at the entrance can correct the slant field and increase the operating mode frequency in a nonlinear fashion. This changing effect can be used as an alternative method for tuning our power cavity.
4 Conclusion
We built and studied two aluminum cold models of a window-type RFQ. By measuring the first model with variable coupling windows, we verified the relationship frequency and mode separation with the dimension and number of the windows. For the second model, we measured the frequencies, quality factors, and electric fields of the first five modes and the field in aperture based on the test bench. The results agree well with the simulated results, thereby confirming the reliability of the simulations. In addition, we carried out an analysis on the unflatness and asymmetry of each quadrant field, and tuned the field using 16 tuners. With limited tuning capability, we obtained relatively flat fields. Finally, we measured the effect of changes in the gap distance on the field distribution and the operating mode frequency. This work provided significant experience for the manufacture and measurement of a power cavity. Now, this cavity is being processed in a factory in Lanzhou. RF measurement and high-power tests will be performed later in 2018.
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