# 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
Since the intensity of electromagnetic radiation generated by different radiation sources is different and its direction changes with time, the electromagnetic radiation on electronic equipment generated by each source needs to be multiplied by a vector factor \(\mathbf{A}_{i}\) that varies with space and time, which is related to the propagation path. Therefore, the electromagnetic field intensity of radiation from \(\mathbf{r}_{i}\) to \(\mathbf{r}_{j}\) is \(\mathbf{A}_{i}\mathbf{E}_{i}(\mathbf{r}_{j},t-t_{ij})\). The electromagnetic radiation received by point j can be expressed as the power spectral density \(\mathbf{S}_{j}(\mathbf{r}_{j},t,f)\) of the combined intensity in Equation (4). Without loss of generality, \(\mathbf{S}_{j}(\mathbf{r}_{j},t,f)\) can be written as \(\mathbf{S(r,t,f)}\), which is the intensity of electromagnetic radiation at any spatial point in the presence of n radiation sources. \[E_{j}(\mathbf{r}_{j},t)=\sum_{i=1\sim m}A_{i}E_{i}\big{(}\mathbf{r}_{ij},t-t_{ij} \big{)} \tag{4}\]  
Figure 4: Analysis and modelling of electromagnetic radiation. (**a**) Distribution of electromagnetic radiation sources; (**b**) Schematic diagram of time-domain characteristics; (**c**) Schematic diagram of frequency-domain characteristics; (**d**) Schematic diagram of electronic equipment affected by electromagnetic interference. According to Equation (4), within a certain time range [\(t_{1}\),\(t_{2}\)] and frequency range [\(f_{1}\),\(f_{2}\)], the signal intensity of any point r can be expressed, using Equation (5), by the average power density spectrum, where the double integral is the integration over time and frequency. \[\text{S(r)}=\frac{1}{(t_{2}-t_{1})(f_{2}-f_{1})}\int_{t_{1}}^{t_{2}}\int_{f_{1}} ^{f_{2}}S(\textbf{r},t,f)dft \tag{5}\]  
Spatial threat assessment modelling uses a spatial threat level as an indicator to quantitatively analyse the threat of an electromagnetic environment with electronic equipment as a threatened object. The spatial threat degree of the electromagnetic environment to the electronic equipment is expressed by the ratio of the azimuth and elevation range where the average power density spectrum of the electromagnetic environment exceeds the electromagnetic environment threshold of the working azimuth and the elevation range of Device A. According to Equation (1), the spatial threat degree of Device A is:  
\[\text{ST}=\frac{1}{\theta_{2}-\theta_{  
Time-domain threat assessment modelling uses a threat degree as an indicator to quantitatively analyse the time-domain threat of the electromagnetic environment with equipment as the threatened object. The time-domain threat degree of an electromagnetic environment to Device A is expressed by the ratio between the period of the average power density spectrum of the electromagnetic environment threshold and the working period of Device A. According to Equation (2), the time-domain threat degree of Device A is:  
\[\text{TT}=\frac{1}{t_{2}-t_{1}}\int_{t_{1}}^{t_{2}}U\bigg{\{}\frac{1}{\varrho_{ 2}-\varrho_{1}}\cdot\frac{1}{\varphi_{2}-\varrho_{1}}\cdot\frac{1}{f_{2}-f_{1} }\int_{\theta_{1}}^{\theta_{2}}\int_{\varphi_{1}}^{\varphi_{2}}\int_{f_{1}}^{ f_{2}}S[\theta(t),\varphi(t),f]dfd\varphi d\theta-S_{0}\bigg{\}}\text{dt} \tag{9}\]