## 4 Wireless Access for Vactrain
### Simulation
#### 4.3.2 Field Distribution in the Tube  
In this subsection, the field distribution of the leaky waveguide inside the vacuum tube will be studied and analyzed. Similar to the above subsection, the leaky waveguide with carrier frequency of 3.3 GHz is adopted. In the simulation configuration, the metal vacuum tube is made of lossy copper material, with length of 18 m and the radius of 2 m.  
The simulation results of field distribution inside the vacuum tube with different values of \(\alpha\) are shown in Figure 3a [42]. Only the \(E_{z}\) component is shown since it is the co-polarized component. It can be seen that the field distribution near the ends of the vacuum pipe has a obvious truncation effect, but that of the area along the longitudinal direction of the vacuum pipe is uniform, indicating leaky waveguide solution is applicable to the vacuum tube transportation. The results show that the field distribution of the leaky waveguide is greatly affected by the values of \(\alpha\) in terms of field strength and coverage area. When \(\alpha\) increases, which means that the amplitude of the leaky wave propagated in the waveguide will be further attenuates, thus the results show that the fields in the vacuum tube show an attenuation trend along the longitudinal direction. In addition, with the increase of \(\alpha\), the longitudinal range that leaky wave radiated from waveguide can cover is also decreasing. According to the results  
Figure 2: Phase distribution of the leaky waveguide method: (**a**) Configuration of leaky waveguide and receiving antenna. (**b**) The phase distribution of different measuring point.  
of the field distributions in the cross section of \(z=0\) plane, the reflected waves also become weak as the radiated wave reduces rapidly in z direction if \(\alpha\) is larger.  
The variations of electric fields along the vacuum tube at different heights \(x\) when \(\alpha=0\) is presented in Figure 3b [42]. Note that the leaky waveguide is arranged at \(x=2\) m. In addition, for the exhibition clarity, the results only present the field distribution of range from \(z=-1\) m to 1 m. It can be seen that the fluctuations of the field distribution are more obvious as \(x\) gradually increases. Thus, it can be inferred that the higher harmonics mainly exist in the near region of the waveguide, making the fluctuation more obvious. On the contrary, as the observation height \(x\) decreases, the results show that the field magnitude decreases rapidly and the field fluctuation tends to be smoother. This primarily occurs because only the radiating mode (\(-1\) harmonic) can reach the far field region, thus the much smoother distribution can be observed far away from the waveguide. In practical situation, the distance between the leaky waveguide and the user equipments is relatively large, for example, 2 m, thus the signal coverage can be flat for the receiving ends. According to this, it can be inferred that if the structure of the leaky waveguide is reformed to make the \(-1\) harmonic carrying more power, the near field region might also have smooth field distribution, making the which wireless communication for vactrains more flexible and stable.