## 4 Experimental Results
Compared with  
Figure 9 indicates that the \(B_{r}\) (residual magnetic field in z direction) attenuates exponentially as a result of the eddy currents in the SR, therefore the time constants and amplitude of the magnetic field modes can be obtained by the measured data through curve fitting. It was necessary to pay more attention to the range of data selected for curve fitting. The end time of the data to be fitted should be the time when \(B_{r}\) enters into an almost unchanged steady state, which corresponds to the end of the attenuation process. The reason was that the accuracy of the used magnetoresistance sensor was not high enough and when the magnetic field \(B_{r}\) enters the steady state and gradually tends to zero, the measured data of the magnetoresistance sensor was disturbed by noises, which will oscillate around zero. If the end time was too long, it affected the fitting accuracy. As shown in Figure 9, the blue and black curves represent the original value of \(B_{r}\) without and with CC, respectively. We fit the two curves after \(t_{s}\) = 2 ms in Figure 10 respectively when currents were completely switched off. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Attenuation** & **From 0 ms to** & **From 2 ms to** & **From 2 ms to** & **From 2 ms to** \\
**Percentage of** & **2 ms** & **10 ms** & **50 ms** & **100 ms** \\
**Modulus Value of \(B_{r}\)** & & & & \\ \hline Without CC & 98.42\% & 28.40\% & 83.59\% & 97.00\% \\ With CC & 99.89\% & 63.82\% & 97.09\% & 97.75\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Attenuation percentage of modulus value of \(B_{r}\) without and with CC at different times. Figure 9: Comparison of the residual magnetic fields in z-direction without and with CC. In Equation (17), we still set \(N_{1}=2\), \(N_{2}=2\), \(C_{1}=C_{2}=0\). The expression of fitting curve \(B_{z-f\mathrm{z}\mathrm{z}\mathrm{z}\mathrm{z}}\) in Figure 10a is  
\[B_{z-f\mathrm{z}\mathrm{z}\mathrm{z}}=15123*e^{(-29.78t)}+15174*e^{(-50.79t)}. \tag{24}\]  
Because there is no CC in this configuration and only the residual magnetic field in z direction is considered, eddy-current magnetic field is generated only by \(B_{p}\) coil. Hence,  
\[ \begin{array}{ll}B_{r}&=B_{r1}=B_{z-f\mathrm{z}\mathrm{z}\mathrm{z}\mathrm{z }}\\ &=15123*e^{(-29.78t)}+15174*e^{(-50.79t)}\end{array}  \tag{25}\]  
\(B_{r1}\) represents eddy-current magnetic field generated by \(B_{p}\) coil. Figure 10: (**a**) Curve fittings of the residual magnetic in z direction field without CC. Circled blue curve is experimental data after \(t_{s}=2\) ms; red curve \(B_{z-f\mathrm{z}\mathrm{z}\mathrm{z}}\) is the fitting curve; (**b**) curve fittings of the residual magnetic field in z direction with CC. ‘+’ type of the black curve is experimental data after \(t_{s}=2\) ms; red curve \(B_{z-f\mathrm{z}\mathrm{z}\mathrm{z}}\) is the fitting curve. The expression of fitting curve \(B_{z-f\kappa 2}\) in Figure 10b is  
\[B_{z-f\kappa 2}=15123*e^{(-29.78l)}+15174*e^{(-50.79l)}-14251*e^{(-47.3l)}-14452*e^{(- 29.39l)} \tag{26}\]  
Because there is CC in this configuration and only the residual magnetic field in z direction is considered, eddy-current magnetic field is generated by \(B_{p}\) coil and CC. Hence,  
\[ \begin{array}{ll}B_{r}&=B_{r1}+B_{r2}=B_{z-f\kappa 2}\\ &=15123*e^{(-29.78l)}+15174*e^{(-50.79l)}-14251*e^{(-47.3l)}-14452*e^{(-29.39l) }\end{array}  \tag{27}\]  
Combining Equations (25) and (27), we can get the expression of the eddy-current magnetic field generated only by CC,  
\[B_{r2}=-14251*e^{(-47.3l)}-14452*e^{(-29.39l)}. \tag{28}\]  
Therefore, we decouple the eddy-current magnetic field produced by \(B_{p}\) coil and CC in the SR after the current is completely switched off at \(t_{s}\) = 2 ms into two parts:  
\[\left\{ \begin{array}{ll}B_{r1}=15123*e^{(-29.78l)}+15174*e^{(-50.79l)}\\ B_{r2}=-14251*e^{(-47.3l)}-14452*e^{(-29.39l)}\end{array} \right. \tag{29}\]  
It can be seen from 10 that the curve fittings are satisfactory.