## 3 Results and Analysis  
The dipole magnetic field involved in the present study is supposed to be generated by a coil. According to (4), the magnetic field intensity along the wave propagation path is:  
\[\mathbf{B_{0}}=\frac{\mu_{0}I}{2a}\frac{a^{3}}{(a^{2}+z^{2})^{3/2}}\mathbf{e_{z}}=B_{c }\frac{a^{3}}{(a^{2}+z^{2})^{3/2}}\mathbf{e_{z}}, \tag{28}\]  
where \(I\) is the current in the coil, and \(B_{c}\) is the magnetic field strength at the center of the coil. In the present study, the plasma sheath parameters are obtained with a statistical model based on the RAM C-II experiment [16]. In particular, in the present study, the concerned plasma parameters are along the wave propagation path. Those parameters are shown in Figure 2a. The magnetic field intensity along the wave propagation path is shown in Figure 2b. The total length for the wave propagation path is \(L_{max}=0.23\) m.  
Figure 2c,d shows an example of wave propagation in the given plasma layer. In that example, the incident wave frequency \(f=94\) GHz, \(a=0.01\) m, and \(B_{c}=1\) T.  
In Figure 2c, \(E\) denotes the amplitude of the electric field of the propagating wave by considering the dissipation yielded by \(v\). \(E^{{}^{\prime}}\) is the electric field by considering the dissipation yielded by \(v^{{}^{\prime}}\). The red line indicates the difference between the two. It can be seen that the magnitudes of \(E^{{}^{\prime}}-E\) are only \(10^{-4}\epsilon_{0}^{0.5}\). In addition, according to the blue line, the magnitudes of the damping \(v^{{}^{\prime}}-v\) are \(10^{0}\), while, according to Figure 2a, the magnitudes of \(v\) are \(10^{10}\). In such a case, the collisions are still the dominant cause of signal attenuation in the magnetized plasma sheath. The drift caused by \(\mathbf{\mathcal{F}}\) makes little contribution to the signal attenuation. The dipole magnetic field mainly affects the attenuation via its spatial inhomogeneity, which is illustrated in detail in Figure 2d. In Figure 2d, the attenuation coefficients in plasma sheaths magnetized by a uniform magnetic field and a dipole magnetic field are represented by green and blue lines, respectively. The attenuation coefficient in an unmagnetized plasma sheath is denoted by the red line, which almost coincides with the blue line. In other words, the dipole magnetic field makes an ignorable contribution to the weakening of the signal attenuation. On the other hand, the uniform magnetic field is obviously weakened by the signal attenuation in the plasma sheath. The reasons for such differences could be found from Figure 2.  
According to Figure 2a,d, it can be seen that the spatial distributions of the attenuation coefficient and the electron densities are similar. Both the maxima of the attenuation coefficient and the electron density along the wave propagation path is at \(L=0.03\) m, regardless of the external magnetic field. In other words, the energy loss of the propagating wave mainly occurs in a very small region around \(L=0.03\) m. On the other hand, according to Figure 2b, the dipole magnetic field strength decreases with \(L\) increasing. The maximum field strength is at \(L=0\), which is the wall of the vehicle. The strong magnetic field region is beyond the region of wave energy loss. In addition, the field strength around \(L=0.03\) m is too weak to effectively mitigate the wave energy loss. On the other hand, under the assumption of a uniform external magnetic field, the wave energy loss is always suppressed by the magnetic field over the whole propagation path. Therefore, the dipole magnetic field makes a poor contribution to the weakening of the wave attenuation, compared to a uniform magnetic field. Nevertheless, it should be noted that a uniform magnetic field is only an idealized assumption, although it was employed in some previous works and showed good performance for mitigating the wave attenuation. In a realistic scenario, a dipole magnetic field generated by the coil is more feasible.