## 4 Experiments  
For further validation, we performed simulations and experiments using the proposed STC, where the conditions in simulations and experiments were the same. Figure 5 shows the longitudinal magnetic field distribution of the STC using the optimal design in Section 4 at different inner casing radii and times. As shown in Figure 5a, the longitudinal magnetic field distribution of the STC had a narrow main lobe and a short side lobe at \(\{r=55.98\) mm, \(t=0\) ms}. The magnetic field distribution differed with the time and radii. Figure 5b-d compare the performances of the no-MF case, MTF-based MF, and STC-based MF at \(\{r=55.98\) mm (inner radius of the casing pipe), \(t=10\) ms}, \(\{r=59.74\) mm (center of wall of the casing pipe), \(t=0\) ms}, and \(\{r=63.5\) mm (outer radius of the casing pipe), \(t=0\) ms}, respectively. The designed FoM can be used to select appropriate winding parameters for the STC and optimize the MF performance to approach that of the ideal MTC-based MF. Comparing with the no-MF case, the longitudinal magnetic field distribution at other radii and observation times can also be focused. Without loss of a generality, we further simulated the FoM in a five-section case. Figure 6 shows the MF performance of the five-section STC. The total number of turns was set to 300, and the other parameters were the same as those shown in Figure 4. As shown in Equations (8) and (9), \(S_{1}\), \(S_{3}\), and \(S_{5}\) were P-sections, \(S_{2}\) and \(S_{4}\) were N-sections, and \(n_{1}=n_{5}\) and \(n_{2}=n_{4}\). Compared with the three-section STC in Figure 4, the five-section STC had a more complex design, and its parameters were related to the coil turns of multiple sections; thus, two uncorrelated factors, \(n_{3}/300\) and \(n_{1}/(n_{1}+n_{2})\), were used to represent the winding parameters of the five-section STC in Figure 6.  
Figure 5: Longitudinal magnetic field distributions with no-MF, MTC-based MF, and STC-based MF: (**a**) \(r=55.98\) mm, \(t=0\) ms; (**b**) \(r=55.98\) mm, \(t=10\) ms; (**c**) \(r=59.74\) mm, \(t=0\) ms; and (**d**) \(r=63.5\) mm, \(t=0\) ms.  
From Figure 6, we can conclude that the MF performance was closely related to the probe design. The maximum FoM value of the five-section STC (FoM = 0.7254) was obtained at \(n_{3}/300=0.3867\) and \(n_{1}/(n_{1}+n_{2})=0.2391\) (\(n_{3}=116\), \(n_{2}=n_{4}=70\), \(n_{1}=n_{5}=22\)). The above winding scheme with the optimal FoM was used to design the structures of the three- and five-section STCs, as shown in Figure 7, in which the PEC inspection system used for the experimental prototype was also included. In Figure 7, the no-MF probe is also shown for comparison. All probes had 300 turns in total. For the three-section STC, \(S_{1-3}\) had 58, 184, and 58 turns, respectively; while for the five-section STC, \(S_{1-5}\) had 22, 70, 116, 70, and 22 turns, respectively. In our experiment, an  
Figure 6: Variation in MF performance of the five-section STC with different winding parameters. Figure 7: Probe structures and PEC inspection system for the experiments: (**a**) non-focusing probe structure; (**b**) five-section STC probe; (**c**) three-section STC probe; and (**d**) the PEC inspection system. observation array with 25 giant magnetoresistance (GMR) sensors (AAH002-02 from NVE Corporation, Minneapolis, MN, USA) was used to measure the longitudinal magnetic field on the inner wall of the casing. Figure 8 shows the normalized magnetic field of the no-MF, MTC-based MF, and STC-based MF cases with three and five sections in the experiment and simulation. The experimental and simulation conditions were identical. As shown in Figure 8, the experimental results for the no-MF, MTC-based MF, and STC-based MF cases showed good agreement with the simulation results. The error can be attributed to the inductance error of the additional inductor [15] and differences in the coil geometry.