# Study on Electromagnetic Radiation Interference Caused by Rocket Fuel
## 3 Electromagnetic Radiation Analysis and Modelling  
### Analysis and Modelling of the Spatial Characteristics of Electromagnetic Radiation  
The spatial characteristics represent the distribution of electromagnetic radiation in different spaces and the changes of the electromagnetic signals in space, which are strictly represented by an electromagnetic signal power density spectrum corresponding to a specific location. According to the theory of electromagnetics, the electromagnetic environ \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Explanation** & **Unit** \\ \hline \(\theta_{1}\) & Start angle of the scanning azimuth of Device A & \(\circ\) \\ \(\theta_{2}\) & End angle of the scanning azimuth of Device A & \(\circ\) \\ \(\varphi_{1}\) & Start angle of the pitch scanning azimuth of Device A & \(\circ\) \\ \(\varphi_{2}\) & End angle of the pitch scanning azimuth of Device A & \(\circ\) \\ U & Unit step function & - \\ \(f_{1}\) & Start frequency of Device A & MHz \\ \(f_{2}\) & Stop frequency of Device A & MHz \\ \(t_{1}\) & Start time of Device A & s \\ \(t_{2}\) & End time of Device A & s \\ S\(\left[\begin{array}{c}\theta(t),\\ \varphi(t),f\end{array}\right]\) & Average power density spectrum of the electromagnetic environment & W/(m\({}^{2}\cdot\)Hz) \\ \(\theta(t)\) & around Device A & \(\circ\) \\ \(\theta(t)\) & Azimuth angle of Device X relative to Device A at time t & \(\circ\) \\ \(\varphi(t)\) & Pitch angle of Device X relative to Device A at time t & \(\circ\) \\ S\({}_{0}\) & Electromagnetic environment threshold for normal operation of Device A & W/(m\({}^{2}\cdot\)Hz) \\ t\({}_{\text{E}}\) & Upper limit of the time of the radiation source & s \\ fs & Lower limit of the time of the radiation source & s \\ \(f_{jmax}\) & Upper limit of the signal bandwidth of the radiation source & MHz \\ \(f_{jmin}\) & Lower limit of the signal bandwidth of the radiation source & MHz \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Meaning of parameters. Figure 3: Electromagnetic environment modelling. (**a**) Electromagnetic interference calculation level; (**b**) Electromagnetic environment description index. ment at any point in space can be represented by an electric field intensity \(\mathbf{E(r,t)}\), where \(\mathbf{r}\) represents the three-dimensional coordinates of some point in space and \(t\) represents time. For plane electromagnetic waves, the power density of an electromagnetic signal at a certain position in space is proportional to \(\mathbf{F(r,t)}\times\mathbf{F^{*}(r,t)}\). Through a Fourier transform, \(\mathbf{S(r,t,f)}\), the time-varying power density spectrum of the time-varying correlation function of the analytic signal \(\mathbf{F(r,t)}\) of \(\mathbf{E(r,t)}\) can be obtained. \(\mathbf{S(r,t,f)}\) expresses the electromagnetic energy that flows through a unit area and a unit bandwidth at a certain spatial location at any time with any frequency. The signal intensity of the electromagnetic wave generated during deflagration at any position can be expressed by the power density spectrum \(\mathbf{S(r,t,f)}\) after propagating through some medium [22]. During the launch or return of a spacecraft, the electromagnetic radiation generated by the combustion of rocket fuel does not present a point-like distribution, but rather, a three-dimensional state. For the electronic equipment on spacecraft, there are multiple radiation sources, as shown in Figure 4a, which assumes that there are many points in the radiation area with one radiation source, and their three-dimensional coordinates are expressed as \(\mathbf{r}_{i}(i=1\)-\(n\)). At a certain time, each radiation source radiates a signal with a certain pattern and frequency, the electric field intensity of which is \(\mathbf{E}_{i}(\mathbf{r}_{i},t)\) and the power density spectrum is \(\mathbf{S}_{i}(\mathbf{r}_{i},t,f)\), which is an electromagnetic signal whose intensity and frequency change with time.