# The Pin Structure Design of LaVai-1.5-1400 Microwave Vertical Tubular Furnace Based on COMSOL
## 4 Pin Structure Design
### Design of Pin Position and Pin Spacing  
From the perspective of industrial design applications, the pins of the LaVAi-1.5-1400 microwave vertical tubular furnace should be vertically inserted into the cavity wall at the horn (where the area is larger, facilitating the introduction and adjustment of the pins). Taking the cavity wall at the horn as the working plane, calculations and analysis were conducted based on the principle of pin-adjusting the resonant cavity state and the electromagnetic field distribution within the resonant cavity without pins. It was found that  
Figure 4: (**A**) 3D model meshing diagram. (**B**) Crucible and sample meshing diagram. Figure 3: Histogram of cell mass for different division accuracies. when the pins are located at a y-axis coordinate of 0.05 m on the working plane, they have a significant impact on the resonant cavity state (due to the high magnetic field strength at this location, the degree of cavity wall perturbation is more intense). Therefore, two pins are introduced at the y-axis coordinate of 0.05 m on the resonant cavity wall. To ensure uniform microwave heating of the sample, the two pins should be symmetrically distributed with the straight line X = 0 within the working plane as the symmetric axis (to ensure the symmetry of the electric field distribution in the sample area). The location of the pins is shown in the Figure 5 below:  
Naming the two pins as post1 and post2, respectively, if the x-coordinate of post1 on the working plane is n, then the x-coordinate of post2 on the working plane will be \(-\)n. Assuming a radius of 0.01 m for both pins and an insertion depth of 0.02 m for each, we simulate and analyze three scenarios with a microwave source power of 500 W and different values of n: 0.01 m, 0.02 m, and 0.03 m. These correspond to center-to-center distances between the two pins of 0.02 m, 0.04 m, and 0.06 m. The field intensity distributions in the sample area for these three cases are shown in Figure 6 below:  
Based on the field intensity distribution maps in the sample area under the three different conditions, it can be observed that, with equal pin insertion depths and pin radii, the smaller the spacing between post1 and post2, the greater the field intensity within the  
Figure 5: (**A**) Schematic diagram of working plane and (**B**) the 3D model. Figure 6: Electric field distribution in the sample area with three different pin spacings at 0 min (**A**) 0.02 m, (**B**) 0.04 m, and (**C**) 0.06 m.  
sample area. When a larger spacing is used for the pins, the average field intensity within the sample area is the smallest and significantly lower than that when using a center-to-center pin spacing of 0.02 m or 0.04 m. From the perspective of field intensity distribution uniformity, the field intensity distribution within the sample area is most uniform when using a center-to-center pin spacing of 0.04 m, while the uniformity is poorer when using a pin spacing of 0.02 m.  
Next, we calculate the average electromagnetic loss power density in the sample area corresponding to the three different pin spacings to analyze the impact of different pin spacings on the ability of the sample to couple with microwaves. Using the post-processing function of COMSOL Multiphysics, the curves of average electromagnetic loss power density varying with time for the three different pin spacings are plotted as shown in Figure 7 below:  
Based on the above curves, we can observe that regardless of the time point, the average electromagnetic loss power density in the sample area with a pin center spacing of 0.06 m is the lowest, indicating poor microwave coupling ability. Initially, when using a pin center spacing of 0.04 m, the average electromagnetic loss power density is higher than when using a spacing of 0.02 m. However, as time passes, the average electromagnetic loss power density with a pin center spacing of 0.02 m becomes the highest, indicating the best microwave coupling effect.