Observation of quenching-induced magnetic flux trapping using a magnetic field and temperature mapping system

Highly efficient superconducting radio-frequency cavities exhibit low heat loss and are used as components in accelerators and superconducting devices due to their high $Q$-values. The precise location of magnetic flux trapping in cavities is necessary to identify its effects on the performance of superconducting cavities. In this study, we report a new combined mapping system to measure the temperature and magnetic field on the equator. The proposed system comprehensively maps local magnetic field changes as magnetic flux trapping due to quenching. Our experimental results show that magnetic flux trapping due to quenching increases the local surface resistance of superconducting cavities at 2 K. Thus, the proposed system elucidates the relationship between local flux trapping due to quenching and surface resistance in superconducting cavities and highlights the effect of quenching on the surface resistance. This system can aid in the development of superconducting cavities with higher $Q$ values.

Figure 1

Schematic model of the mapping board setting for the single cell 1.3-GHz cavity. The cavity was suspended on an aluminum plate jig. The top and bottom slotted disks constrained the mapping boards to fix the vertical axis. The solenoid coil covered the cavity and mapping board to control the vertical axis magnetic field (see Fig. 3). Four fluxgate sensors were mounted every 90° on the outer surface of the boards as a reference value of the magnetic field.

Figure 2

Magnetic field and temperature mapping board. Fifteen carbon resistors ($100\mathrm{\Omega }$, Allen Bradley) were mounted on the side of the board in contact with the outer wall of the cavity. Numbers show the locations of the surface of the cavity. Three magnetic field sensors were mounted on the center of the board. Each sensitive axis of sensors is $z$, $r$, and $\theta$ directions, respectively.

Figure 3

Photo of the setup of the mapping boards. (a) 36 boards were mounted around the cavity along the circumferential direction. (b) A solenoid coil that controls the ambient $z$-axis magnetic field covered the mapping boards and cavity.

Figure 4

Results of $Q_0\text{−}{E}_{\mathrm{acc}}$ measurements at 2 K. “Full expulsion” which refers to the result of the cavity was not trapped the magnetic flux because the cavity was in the superconducting state. “Trapped at **$\mu \mathrm{T}$” refers to results with the trapped magnetic flux due to quenching when each magnetic field was applied.

Figure 5

The sequence of the flux trapping experiment: 1. State demonstrates that the cavity did not trap magnetic flux, and the environment magnetic field was canceled. 2. State demonstrates that the cavity did not trap magnetic flux, and the environment magnetic field was applied. 3. State demonstrates that the cavity trapped magnetic flux, and the environment magnetic field was applied. 4. State demonstrates that the cavity trapped magnetic flux, and the environment magnetic field was canceled. The cavity state can therefore be changed by quenches, and the environment magnetic field was controlled by the solenoid coil current. The arrows show the manipulated coil or quench event between each state.

Figure 6

Temperature rises during repeated quenching at 2 K, as indicated by “canceled $<0.5\mu \mathrm{T}$” in Fig. 4. (a) shows temperature mapping results of the spatial spreading of heating by quenches. (b) shows the time-series measurement of the heating observed at the sensors at the 20° board. (a) and (b) temperature mapping data were measured during regularly repeated quench events so-called self-pulsing quenching. Notably, these temperature mapping results were not simultaneous.

Figure 7

The temperature rises during heating cycles with a pulsed rf operation. (a) shows temperature mapping results of the spatial spreading of heating by magnetic flux trapping at a local area of the cavity. (b) shows the time-series measurement of the heating observed at the sensors at the 20° board in plot (a). It is noted that these temperature mapping results were not simultaneous because it takes time to switch channels.

Figure 8

When the cavity was in the superconducting state, the cavity expelled the applied external magnetic field after phase transition (flux exclusion).

Figure 9

The magnetic field change during flux exclusion with the applied magnetic field excited by a coil current of 10 mA ($\mathrm{\Delta }B\sim -1.8\mu \mathrm{T}$). (a) shows the $z\text{−}\theta$ projection and (b) shows the $r\text{−}\theta$ projection. In the plot (a), the numbers next to the arrows show the absolute value ($\mu \mathrm{T}$) of magnetic field change.

Figure 10

Magnetic field distribution difference before and after several quenches. When the cavity was quenching, a magnetic field of $-18\mu \mathrm{T}$ was applied along the $z$-direction.

Figure 11

Example of a 2D image of the change in the magnetic field between, before, and after quenching with a $-18\mu \mathrm{T}$ magnetic field. (a) shows the $z\text{−}\theta$ projection and (b) shows the $z\text{−}\theta$ projection. In the plot (a), the numbers next to the arrows show the absolute value ($\mu \mathrm{T}$) of magnetic field change.

Figure 12

Comparison of the difference in the magnetic fields before and after quenching with different applied magnetic fields. The top plot shows the $z$ and $\theta$ relationship of the change in magnetic fields. The bottom plot shows the $r$ and $\theta$ relationship of the change in magnetic field.

Figure 13

Linearity of the change in the magnetic field trapping to the applied magnetic field (closed markers) and releasing case (open markers) at 15°. The solid lines denote linear regression.

Figure 14

Relationship between the applied magnetic field and surface resistance of the cavity with locally trapped magnetic flux. The horizontal axis is the absolute strength of the magnetic field and the vertical axis is the surface resistance of the cavity obtained via rf measurement. The surface resistance is proportional to the applied magnetic field at each accelerator gradient.

Figure 15

Slope of surface resistance with applied magnetic field and accelerating gradient.