## 3 Simulation  
As a demonstration, a small-scale copper conductive SR was designed with dimension of 280 mm \(\times\) 280 mm \(\times\) 300 mm, and the wall thickness was 10 mm, as shown in Figure 1a. A pair of CCs was symmetrically configured above and below the \(B_{p}\) coil whose distance to each CC was 46 mm and the distance from \(B_{p}\) coil to the center of floor was 110 mm in the SR. The pair of CCs were connected in series with the \(B_{p}\) coil, so the current in the \(B_{p}\) coil was the same as that in the CC, but with opposite directions. The current was switched off in 2 ms. The parameters of the \(B_{p}\) coil and CC were shown in Table 1. The current through the \(B_{p}\) coil during the simulation is shown in Figure 1b. Figure 2 shows the comparison of residual magnetic field component in z direction without and with CC measured with the magnetic sensor HMC2003. It can be seen from Figure 2 and Table 2, \(B_{r}\) decayed much faster with the 70 turns CC configuration (In this configuration, the number of turns of CC was 70) than with no CC. When \(t>10\) ms, the \(B_{r}\) with 70 turns CC had already entered a very low stage and most of the attenuation occurs before 10 ms. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & \(B_{p}\)**Coil** & **Cancellation Coil (CC)** \\ \hline Material & Copper & Copper \\ Inside diameter & 60 mm & 160 mm \\ Outside diameter & 80 mm & 170 mm \\ Section area & 300 mm2  & 50 mm2  \\ Number of conductors & 750 & 70 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of the \(B_{p}\) coil and the cancellation coil. Figure 1: (**a**) Simulation model of the SR with \(B_{p}\) coil and cancellation coils (CC) inside; (**b**) pulsed current through the \(B_{p}\) coil during the simulation. The number of turns of CC had a significant impact on the effect of the cancellation. Figure 3 shows the residual magnetic field at the measuring point when the number of turns of the CC changed from 64 to 78. Figure 3a shows that the suppression effects of the residual magnetic field were quite obvious and Figure 3b shows the comparison of the suppression effects with different number of turns of CC. From Figure 3, it can be seen that the best result occurs when the CC has 70 turns. However, overshoot of the cancellation of the eddy-current magnetic field can be observed under this condition, partly because the dimensions of the cancellation coil have not been optimized well enough, which will be an important aspect to be studied in the future. Figure 2: Comparison of residual magnetic field component in z direction without and with CC. (**a**) Decay curves of magnetic field in the SR; (**b**) decay curves of eddy current field after \(t_{\rm s}\) = 2 ms. Simulation results in Figure 2 are detailed in Table 2.  
It can be seen from the analysis in Section 2 that the acquired measurements \(B_{r}(t)\) can be treated as a linear combination of exponentially decaying signals with multiple distinct time constants. \[\left\{ \begin{array}{l}B_{r}(t)=B_{r1}(t)+B_{r2}(t)\\ B_{r1}(t)=-(B_{ISR}^{(p)}\star\frac{\mathrm{d}t_{p}}{\mathrm{d}t})(t)=\sum \limits_{i=1}^{N_{1}}A_{i}e^{-t/\tau_{i}}+C_{1}\\ B_{r2}(t)=-(B_{ISR}^{(c)}\star\frac{\mathrm{d}t_{c}}{\mathrm{d}t})(t)=\sum \limits_{j=1}^{N_{2}}A_{j}e^{-t/\tau_{i}}+C_{2}\end{array} \right.. \tag{17}\]  
According to [20], we set \(N_{1}=2\), \(N_{2}=2\), \(C_{1}=C_{2}=0\). \(A_{i}\), \(\tau_{i}\) and \(\tau_{j}\) are positive numbers and \(A_{j}\) is negative. The expression of fitting curve \(B_{z-f\mathrm{z}\mathrm{z}\mathrm{z}\mathrm{z}}\) in Figure 4 is  
\[B_{z-f\mathrm{z}\mathrm{z}\mathrm{z}}=8535\ast e^{(-28.2t)}+8553\ast e^{(-45. 2t)}. \tag{18}\]  
Figure 3: Comparison of residual magnetic field component in z-direction with different number of turns of CC after 2 ms; (**a**) including the decay curve without CC; (**b**) excluding the decay curve without CC.