# Towards the Feasibility of Long Range Wireless Power Transfer over an Ocean Surface
## 4 Discussion  
Consistent with our simulated results and our theoretical prediction, the experimental outcome of this work has clearly demonstrated the fact that the interface between a low-loss non-polar medium and high-loss polar medium can support propagation of a wireless power if and only if the following conditions are satisfied:  
1. The transmitting end and the receiving end are connected to a vertically mounted long monopole antenna. 2. The transmitting end is excited with a high-voltage spark gap transmitter. The original objective of this work was to simulate wireless power transfer over an actual ocean surface. The interface between air and the ocean surface is equivalent to the interface between a low-loss dielectric interface and a high-loss dielectric interface. The main difference between our experimental settings and the actual ocean surface lies in the wavenumber. The relative permittivity for water is 78 at microwave frequencies. If air is chosen to be the low-loss dielectric material, the wavenumber can be calculated using air as the low-loss dielectric is:  
\[k=\frac{\omega}{c}\sqrt{\frac{\varepsilon_{r}}{1+\varepsilon_{r}}}\]  
where \(\varepsilon_{r}\) is the complex permittivity of the high-loss medium. However, a plastic is chosen to be the low-loss dielectric material, then the wavenumber becomes  
\[k=\frac{\omega}{c}\sqrt{\frac{2.2\varepsilon_{r}}{2.2+\varepsilon_{r}}}\]  
As predicted in Section 3.4, the high-loss dielectric medium which potentially fulfills the conditions dictated by (9) can be any conductive and polar substance. These materials cannot be pure water, oil, or any other non-polar substance with virtually no conductivity. Unsalted tap water has a conductivity of \(10^{-60}\) s/m. The plasma frequency of pure water is around 10 Hz. The plasma frequency is definitely lower than the frequency of the 100 kV pulsating source or any other of its harmonic components. Strictly speaking, it cannot be used as medium 2. According to inequality (9), if an unsalted tap water is used as medium 2, then it will be impossible to propagate a surface electromagnetic wave along the interface between air and the unsalted tap water. However, water itself is a polar solvent. Under a high voltage stress, for example, its surface conductivity will increase [32]. The increase in the surface conductivity is equivalent to an increase in the plasma frequency. When the surface conductivity was increased to an extent that the condition of (9) is fulfilled, it will be partially possible to propagate a surface energy along the interface between air and the unsalted tap water. Therefore, with an unsalted water being used as medium 2, the feasibility of wireless power transfer very much depends on the degree of the high voltage stress [31; 32; 33; 34; 35; 42]. Highly salted water such as a seawater is a perfect candidate material for medium 2. The plasma frequency of a seawater is around 250 GHz. The frequencies of the plasma source and its associated harmonic components are definitely lower than this plasma frequency. Below the plasma frequency, the permittivity of a plasma in a highly salted water is negative, thus fulfilling the conditions dictated by inequality (9). \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Antenna Height (m)**} & **Estimated Maximum Propagation Distance (m)** & **Maximum Signaling Distance (m) Based on [PERSON]’s Law of Transmission** \\ \hline
1 & 2.5 & 2.5 \\
1.6 & 7.5 & 6.4 \\
2 & 10 & 10 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison between our estimated maximum propagation distance and the maximum signaling distance based on [PERSON]’s law of transmission. However, fulfilling the conditions dictated by inequality (9) is just a part of the equation. Below the plasma frequency, most of the electromagnetic wave will be reflected by the plasma enclosing the interface, whilst a small portion of the surface electromagnetic energy continues to penetrate through and remains along the interface as an evanescent wave.