## 3 Results and Discussion
### The Propagation of Electromagnetic Waves in Plasma
\tag{7}\]  
From this, it can be derived that:  
\[(\stackrel{{\rightharpoonup}}{{k}}\cdot\stackrel{{ \rightharpoonup}}{{E}})\stackrel{{\rightharpoonup}}{{k}}-( \stackrel{{\rightharpoonup}}{{k}})\stackrel{{ \rightharpoonup}}{{E}}=-\epsilon_{r}\Big{(}\frac{\omega}{c}\Big{)} \stackrel{{\rightharpoonup}}{{E}} \tag{8}\]  
For the attenuation constant \(\alpha\) and the phase constant \(\beta\) of electromagnetic waves in plasma, the following equations apply:  
\[\stackrel{{\rightharpoonup}}{{k}}=(-j\alpha+\beta)\stackrel{{ \rightharpoonup}}{{l}} \tag{9}\]  
where \(\stackrel{{\rightharpoonup}}{{l}}\) is the unit vector in the direction of electromagnetic wave propagation. Thus, the electromagnetic wave can be described as:  
\[\stackrel{{\rightharpoonup}}{{E}}=\stackrel{{ \rightharpoonup}}{{E}}_{0}\epsilon^{(j\omega t-\alpha\stackrel{{ \rightharpoonup}}{{l}}\cdot\stackrel{{\rightharpoonup}}{{r}}-j \beta\stackrel{{\rightharpoonup}}{{l}}\cdot\stackrel{{ \rightharpoonup}}{{r}})} \tag{10}\]  
Furthermore, since  
\[\stackrel{{\rightharpoonup}}{{k}}\cdot\epsilon_{0}\epsilon_{r} \stackrel{{\rightharpoonup}}{{E}}=0 \tag{11}\]  
It can be derived that:  
\[(-j\alpha+\beta)\stackrel{{\rightharpoonup}}{{E}}=\Big{(}\frac{ \omega}{c}\Big{)}^{2}(1-\frac{\omega_{p}^{2}}{\omega^{2}+v^{2}}-j(j\frac{v}{ \omega}\frac{\omega_{p}^{2}}{\omega^{2}+v^{2}}))\stackrel{{ \rightharpoonup}}{{E}} \tag{12}\]  
\[\left\{ \begin{array}{c}\alpha=\big{(}\frac{\omega}{c}\big{)}\sqrt{-\frac{1} {2}\left(1-\frac{\omega_{p}^{2}}{\omega^{2}+v^{2}}\right)+\frac{1}{2}\sqrt{ \left(1-\frac{\omega_{p}^{2}}{\omega^{2}+v^{2}}\right)^{2}+(-j\frac{v}{\omega }\frac{\omega_{p}^{2}}{\omega^{2}+v^{2}})}}\\ \beta=\big{(}\frac{\omega}{c}\big{)}\sqrt{\frac{1}{2}\left(1-\frac{\omega_{p}^ {2}}{\omega^{2}+v^{2}}\right)+\frac{1}{2}\sqrt{\left(1-\frac{\omega_{p}^{2}}{ \omega^{2}+v^{2}}\right)^{2}+(-j\frac{v}{\omega}\frac{\omega_{p}^{2}}{\omega^ {2}+v^{2}})}}\end{array} \right. \tag{13}\]  
In the equation, \(\alpha\) serves as the attenuation constant and can be used to represent the collision absorption effect of plasma on electromagnetic waves. When electromagnetic waves, such as radar signals, propagate into the plasma, the charged particles within the plasma (primarily free electrons and ions) are accelerated under the influence of the electromagnetic field, thereby gaining the energy transmitted by the electromagnetic waves and undergoing changes in motion and position. During this process, the particles will return a portion of the energy to the external environment in the form of electromagnetic waves. Another portion of the electromagnetic wave energy is absorbed and converted into heat during interactions with the plasma, such as scattering. This energy conversion process leads to a reduction in the propagation intensity of the electromagnetic waves within the plasma, resulting in the energy loss of the electromagnetic waves. As a portion of the electromagnetic wave energy is converted into heat within the plasma, the electromagnetic waves attenuate as they traverse the plasma, with their intensity decreasing as the propagation distance increases. This process has significant applications in fields such as radar stealth and electromagnetic interference suppression.