1 INTRODUCTION

The SC200 proton therapy superconducting cyclotron will be able to accelerate protons to an energy of 200 MeV with a maximum beam intensity of 1 μA. The average magnetic field of the cyclotron is up to 3.6 T [1-2]. As a key component of the cyclotron, the superconducting magnet provides the isochronous magnetic field with a strong focusing force to restrict beam movement. However, the asymmetry of sectors and the superconducting coils (SCs) generates a radial component, B_r, of the magnetic field in the median plane, directly affecting the vertical deviation of the beam orbit from the median plane [3-6].

A number of measurement methods have been proposed to measure the average radial component of the magnetic field (B_rav), including nuclear magnetic resonance (NMR) [7], hall probes [8-10], and flux measurements with search coils [3][11-14]. To design such a measurement system, the field strength, homogeneity, variation in time, and required accuracy should be considered⁸. Search coils are highly sensitive and less strongly influenced by the vertical component of the magnetic field (B_z), which is more accurate than the hall probes for magnetic field measurement. The use of a variety of search coils is the most-often used tool for characterizing field qualities in cyclotrons [15-18].

For SC200, the B_rav measurement system was designed to measure the B_rav of the magnetic field by using search coils with a high testing accuracy. The B_rav measurement system mainly includes a drive system, control system, and data acquisition system. In particular, based on the electromagnetic induction principle, there are 15 search coils moving in the magnetic field to measure the B_rav. The minimum and maximum measurement radii were 30 mm and 620 mm, respectively. The search coils are made of copper and covered with an insulating varnish. Owing to the quality differences in the winding process, it is necessary to perform the commissioning of the search coil outside of the SC200 cyclotron.

In this study, we present develop a detailed design and investigate the required commissioning work to improve B_rav measurement accuracy. This paper describes the B_rav tolerance analysis, the commissioning platform design, and research. The analysis and results are of great significance for the B_r measurement of the SC200 proton therapy superconducting cyclotron.

2 B_rav TOLERANCES FOR SC200 SUPERCONDUCTING CYCLOTRON

Owing to the asymmetry of sectors and SCs, the B_rav existing in the Azimuth-Varied Field cyclotron, which causes the effective median plane (EMP) of the magnetic system, does not coincide with the median plane of the cyclotron. The EMP was formulated by J. I. M. Botman and H. L. Hagedorn for the cyclotron work region [3]. Thus, the tolerances for the B_rav of the magnetic field should be estimated.

When the magnetic system symmetry is broken, stable vertical oscillations exist near the EMP. The horizontal field component exists in the median plane. To separately identify the tolerances for the horizontal field components from the permitted vertical beam offset, the B_rav can be written as

where Z_eff is the vertical position of the EMP, B_zav is the average vertical component of the magnetic field at radius R, Q_z represents the vertical betatron frequency, and R is the magnetic field radius.

The SC200 superconducting cyclotron has been proposed and designed [17,19-21]. The isochronous field B_zav distribution is shown in Fig.1(a), and the maximum magnetic field was approximately 3.54 T [20,22]. From the computed vertical betatron frequency Q_z in Fig.1(b), Eq. (1) shows the tolerance distribution of B_rav for the acceptable vertical offset of the beam of 1 mm shown in FIG.2.

Fig.1.Full-screen View

(a) B_zav distribution along the radius for SC200 cyclotron, (b) Vertical betatron frequency Q_z for SC200 cyclotron.

Fig. 2.Full-screen View

B_rav for the acceptable vertical offset of the beam of 1 mm.

With the frequency Q_z close to 0.32 in the extraction region, the isochronous field B_zav was approximately 3.54 T. The B_rav tolerance in the median plane was approximately 3–7 G, shown in Fig.2. Consequently, the testing resolution of the B_rav measurement system should be smaller than 1 G.

3 COMMISSIONING PLATFORM DESIGN

3.1 TESTING PRINCIPLE

The magnetic flux distribution produced by the test coil had an excitation current of 2 A, as shown in Fig.3. It generates a magnetic field of 3–7 G, the same as the magnetic field B_rav tolerance of SC200 superconducting cyclotron.

FIG.3.Full-screen View

Magnetic flux distribution.

A commissioning diagram comprising a test coil and 15 concentric search coils is shown in Fig.4. According to the electromagnetic induction principle, when the search coils move in the magnetic field, the induced voltage U is generated, which can be integrated by the fluxmeter. The testing flux change △Φ_t can be written as

FIG.4.Full-screen View

Testing diagram of the search coil.

$\text{Δ}{\Phi }_{\text{t}}={\displaystyle \int U}\text{d}t.$ (2)

The radial component change △B_r can be calculated using

$\Delta B_{\text{r}}=\Delta {\text{Φ}}_{\text{t}}/A.$ (3)

The effective sensitive area of the search coil A is

$A=N\cdot 2\pi R\cdot 2\Delta Z.$ (4)

where N is the number of search coil turns, R is the coil radius, and ΔZ is the distance shift from the median plane.

The search coil was first connected to the fluxmeter, which was shifted from its initial position of –Δz to a terminal position of +Δz. The fluxmeter acquired the magnetic flux generated by the coil. Subsequently, the other coils were changed to connect to the fluxmeter, and the previous steps were repeated.

3.2 PLATFORM DESIGN

Based on the testing principle, the search coils must be a priority during design. The search coils comprised copper wire, with a diameter of 0.3 mm, covered with insulating varnish. The search coils were numbered from C1 to C15. Each coil could be connected to the LINKJOIN LZ840 fluxmeter by a coil selector. Then, the coil parameters, including the radius, the number of turns, and the coil resistance, were sent to the fluxmeter. The distribution of the search coils on the disk is shown in FIG.5.

FIG.5.Full-screen View

Distribution of search coils.

The input coil parameters are shown in Table I.

Table IFull-screen View

search coil parameters

Coil No.	C1	C2	C3	C4	C5	C6	C7	C8	C9	C10	C11	C12	C13	C14	C15
Radius R (mm)	30	55	80	105	130	155	180	205	230	255	280	305	330	355	380
Number of turns N	34	26	20	16	10	10	8	8	8	6	6	6	6	6	6
Coil resistance（Ω）	7.705	7.822	8.038	7.847	7.914	8.15	8.051	8.236	8.547	7.91	8.108	8.237	8.53	8.622	8.855

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The commissioning platform of the B_rav measurement system was designed with a drive system, control system, and data acquisition system, as shown in Fig.6. The self-aligning system includes two groups of cross screws and linear guide structures. These institutions can adjust the disk center coinciding with the geometric center of the superconducting cyclotron. The drive system can drive the search coils to move along the vertical axis of the cyclotron. The control system comprises the parameter settings area, the data and status display area, and the logic control area. The data acquisition system is responsible for collecting the measurement signals. The LINKJOIN LZ840 fluxmeter collects the flux signal with high sensitivity, which should be warmed for five minutes and done zero setting and drift setting before using.

FIG.6.Full-screen View

Commissioning platform.

To avoid the magnetic field influence from B_z, it is necessary to adjust and confirm the relative position between the test coil and search coil. An angular error of 1 mrad will produce an approximately tenfold error in the B_r value. Therefore, the parallelism of the search coil and test coil must be less than 0.4 mm, and that of the concentricity must be less than 0.5 mm. In this way, the B_r value will not be influenced by the B_z value.

4 COMMISSIONING AND DISCUSSION

To confirm that the B_rav measurement system operates well, based on the testing principle above, system commissioning should be conducted outside the cyclotron. The drive system made the search coils move from their initial position of -10 mm to the terminal position of +10 mm. The fluxmeter acquired the first flux Φ1 generated by the first search coil C1. Subsequently, the second flux Φ'1 was generated when the disk moved in reverse. Following this, C2 was switched to connect to the fluxmeter, and the previous steps were repeated. This was performed sequentially until coil C15, and all the measurement data were collected for further analysis.

We found that the coil speed affects the B_rav results. Thus, the testing was conducted with five different speeds in the range of ±10 mm. The collected flux was fitted by the least square method. The B_rav was calculated using Eq.3 in FIG.7, and the trend of the B_rav curves are consistent. The theoretical value (B_rth)was provided by the TOSCA software. The B_rav was closer to the B_rth as the coil speed increased from 1 mm/s to 2.5 mm/s. There were no obvious relative error changes between the 2.5 mm/s and 3 mm/s speeds.

FIG.7.Full-screen View

B_rav measurement results under different search coil speeds.

Compared with B_rth, the relative error of B_rav was calculated and is shown in FIG.8. The relative error of B_rav with a speed of 2.5 mm/s was the smallest. The relative error of the curves is greater in two edge radius ranges. When increasing the coil speed, the flux variation within a unit time will increase correspondingly. Thus, the signal-to-noise ratio will be promoted. For the fluxmeter, the disturbance caused by noise will comprise a smaller proportion and the measurement results will be more accurate at the points where the value of the signal-to-noise ratio is larger. Otherwise, owing to the structure parameters of the fluxmeter, the original right signal completely becomes the interfering signal. In the case of a severe signal drift, the effective signal is often submerged. Therefore, 2.5 mm/s is considered to be the optimal speed for the search coil.

FIG.8.Full-screen View

Relative error results under different search coil speeds.

Following this, the search coils were shifted four times with a speed of 2.5 mm/s. The B_rav distributions were deduced and are shown in Fig.9. The B_rth and B_rav curves are consistent, as shown in Fig.10. The B_rav denotes the average measured value from four B_rav values.

FIG.9.Full-screen View

B_r measurement results with a vertical movement of ± 10 mm.

FIG.10.Full-screen View

Theoretical curve and measured curve.

As shown in Fig.11, the relative error curve first increases then decreases with the radius increase. The minimum error occurred at R = 205 mm, corresponding to C8. The minimum relative error was 0.09513% with a B_rav of 7 G, which continued increasing to approximately 12.37% for B_rav of 1 G at the edge point. In addition, the smallest absolute error and biggest absolute error of △B_rav were 0.006857 G and 0.05402 G, respectively, both less than 1 G.

FIG.11.Full-screen View

Relative error of the search coil.

The measurement accuracy of the B_rav changed with the radial location. For the radial range of 0-205 mm, the magnetic field intensity increased together with the measuring accuracy. For the radial range of 205-380 mm, the measuring accuracy decreased. There is a low intensity at both ends of the B_r distribution curve as the measurement accuracy is susceptible to interference. The measurement accuracy was high under the high intensity field in the middle radial position.

5 CONCLUSION

In summary, this paper presents the detailed design and commissioning for a B_rav measurement system. The commissioning platform was designed to verify the measurement precision based on the electromagnetic induction principle. Under the testing magnetic field, the coil speed of 2.5 mm/s is considered to be the optimal speed for the search coil. The relative error was approximately 0.1% under the maximum B_r of 7 G. The measurement precision reached 1.0×10^-3, which satisfies the measurement requirements.

The analysis and results are of great significance for the B_r measurement of the SC200 proton therapy superconducting cyclotron. However, the measurement error of the system exceeds 10% in edge radius ranges; thus, in future, we must improve the measurement precision by optimizing the system structure or researching a reasonable optimization method.