# The Pin Structure Design of LaVai-1.5-1400 Microwave Vertical Tubular Furnace Based on COMSOL
## 4 Pin Structure Design
### Design of Pin Insertion Depths  
#### 4.3.1 Analysis When Pins Are Inserted at the Same Depth  
The insertion depth of the pins involves both the volume of the perturbation and the electric field (or magnetic field strength) at the location of the perturbation. This section presents simulations and discussions focusing on the case where the insertion depths of post1 and post2 are the same. With both pins having a radius of 0.01 m and a center-to-center spacing of 0.04 m, simulations were conducted for four different insertion depths: 1 cm, 2 cm, 3 cm, and 4 cm. The microwave source power was set to 500 W. The cross-sectional views of the electric field distribution in the resonant cavity for the last four cases are shown in Figure 9 below:  
Figure 8: Cross-section of the electric field distribution in the resonant cavity when different radius pins are used at 0 min (**A**) 1 cm and (**B**) 0.75 cm. Figure 9: Cross-sectional views of the electric field distribution in the resonant cavity with different pin insertion depths at 0 min (**A**) 1 cm, (**B**) 2 cm, (**C**) 3 cm, and (**D**) 4 cm. Based on the cross-sectional views of the electric field distribution in the resonant cavity with different pin insertion depths, we can observe that when the pin insertion depth is 2 cm, the electromagnetic field distribution within the resonant cavity is most affected, and the average field strength in the central region is also the highest. However, when the pin insertion depth is 4 cm, the field strength in the central region is the lowest, indicating poor microwave coupling with the Al\({}_{2}\)O\({}_{3}\)/SiC composite material. This results in poor load matching within the resonant cavity and excessively high reflected power, which can cause irreversible damage to the microwave source. To more intuitively demonstrate the degree of microwave coupling by the sample under the four different pin insertion depths, we have calculated and plotted the curves of average electromagnetic loss power density over time corresponding to each of the five insertion depths:  
According to Figure 10, it can be observed that when using excessively large pin insertion depths (3 cm and 4 cm), the coupling of the Al\({}_{2}\)O\({}_{3}\)/SiC composite material with microwaves is extremely poor. When the pin insertion depth is 0 cm or 1 cm, the coupling of the Al\({}_{2}\)O\({}_{3}\)/SiC composite material with microwaves is generally average. However, when the pin insertion depth is 2 cm, the coupling of the Al\({}_{2}\)O\({}_{3}\)/SiC composite material with microwaves is extremely strong and exhibits an upward trend over time. This trend occurs because the electromagnetic parameters of the Al\({}_{2}\)O\({}_{3}\)/SiC composite material in this model are dynamic, with the imaginary part of the relative permittivity gradually increasing as the temperature rises. Since the average electromagnetic power loss density is positively correlated with the imaginary part of the relative permittivity, the average electromagnetic power loss density also increases over time. Next, we analyze the heating uniformity of the samples when using five different pin insertion depths. We use the ratio of the maximum temperature difference to the average temperature (both in degrees Celsius) within the sample region as a reference metric. A higher ratio indicates poorer heating uniformity, while a ratio closer to 0 represents better heating uniformity. We calculate these ratios and plot a curve accordingly. From Figure 11, it can be observed that when a pin insertion depth of 2 cm is used, the ratio of the maximum temperature difference to the average temperature in the sample region is relatively high, and this value continues to increase over time. This indicates that the heating uniformity of the sample is poor when using this approach. However, when using other pin insertion depths, the ratio stabilizes below 0.2 over time, resulting in better heating uniformity compared to the former.