## 4 Multi-Physics Simulation Analyses of GMM-FBG Current Sensor
### Temperature Drift Characteristics and Mechanism of Ferrite-GMM  
By means of setting the magnitude of the DC current at the magnetizer center as a scanning variable, the quasi-static variation of the strain-magnetic coupled fields in the ferrite-GMM assemblage with an excitation current at different temperatures is simulated to analyze the characteristics and mechanism of temperature-drift magnetostrictions. For the purpose of analyzing the temperature drift of the GMM magnetostrictive response deriving from the thermal strain in the ferrite magnetizer, in addition to modeling the GMM rod with a full coupling of solid mechanics, magnetic field and temperature, the magnetic field in the ferrite magnetizer is simulated comparatively with and without the coupling correlation of thermal expansion, as the results show in Figure 3. Under the thermal-magnetic coupled  
Figure 3: Magnetostrictive coefficient varying with the magnetic field magnitude at the center of the GMM rod at 0–200 \({}^{\circ}\)C temperatures for the simulations with and without consideration of thermal strain in ferrite loop, being shown in the left panel and right panel, respectively. fields of the GMM rod, the temperature elevation affecting the ferrite magnetization can be seen as the decrements in the saturation magnetization and saturation magnetostrictive coefficient, which conforms to the basic law of restraining a magnetic domain turning to magnetization in a ferromagnet by exacerbating atomic vibrations when the temperature increases, as shown in the right panel of Figure 3, illustrating that the current detection performances of the ferrite-GMM assemblage working in a linearly magnetostrictive region will not shift with temperature variation. Since the GMM magnetization under thermal-magnetic coupled fields is characterized by the nonlinearity and saturation of changing permeability with the increasing magnetization, the introduction of magnetic flux into a GMM rod will also affect its magnetostrictive performance. As a result of thermal expansion in the ferrite magnetizer, the air gap at the tip of the GMM rod decreases in width, and thus, the magnetic flux density of the GMM rod increases, which means a higher magnetic conductivity of ferrite magnetizer, accounting for the shrinkage and low-field drift of the linear working region and the increase in magnetostrictive efficiency (curve slope of magnetostriction characteristics). Therefore, temperature elevation will cause the shift of static working point and the sensitivity increment of the current-strain response, leading to a nonlinear drift of detection signal from the highly sensitive FBG wavelength modulator. In addition, the measuring range of the GMM-FBG current sensor decreases with the increase in temperature, and the scale gauge of the current measurement needs to be readjusted. It is thereby suggested that the temperature drift of the ferrite-GMM-FBG current sensor in the process of current detection mainly comes from the thermal strain of the ferrite magnetizer. Moreover, the change in the FBG center refractive index as a function of temperature (photoelasticity) can also cause temperature drift in the modulation signal of the Bragg wavelength, which will be further discussed and analyzed in the next section. The magnetostrictive stress-strain curves of the GMM rod at the center position during the change in quasi-static DC current at different temperatures are shown in Figure 4, which indicates the thermal-mechanical coupling attributes of the GMM rod in the ferrite-GMM assemblage. The shift of the GMM stress-stain curve with temperature elevation, which has been modeled by the temperature variation coefficient \(\beta\) of a GMM material property as listed in Table 1, represents the fact that the steering magnetization of magnetic domains inside the GMM rod will be substantially inhibited by increasing the temperature, resulting in a degradation of magnetostrictive performance.