# Study on Electromagnetic Radiation Interference Caused by Rocket Fuel

^{1}

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## Abstract

**:**

## 1. Introduction

^{5}V/m. In 1990, Boronin studied the physical mechanism of an electromagnetic field generated by the deflagration of condensed fuel [8]. Boronin suggested that at the initial moment of metal deformation and failure, potential energy, in both gaseous and solid state, flowed out from cracks, then electrokinesis and potential energy friction resulted in the electrical polarity of the gaseous and solid shells being opposite, and the space charge of the gas and solid potential energy formed effective dipoles because of the asymmetrical scattering of the potential energy. The viewpoint that the mechanism of generating radio-radiation through deflagration is related to the acceleration or deceleration of certain electron genes in the ionized air layer at the front of a shock wave is called the “Boronin Effect” [9]. In 2011, Cao Jingyang used pole antennas and real-time spectrometers to measure the electromagnetic radiation caused by the deflagration of aerospace explosives. Cao found that the electromagnetic radiation generated by the deflagration of shaped fuel had multi-pulses and broadband characteristics, an electronic pulse duration of approximately tens of microseconds, and a frequency distributed below megahertz. It was also found that the energy of the electromagnetic radiation was positively correlated with the quality of fuel, and the electromagnetic pulse was delayed for hundreds of microseconds and continued for a long time after combustion ended [10,11,12]. In 2014, A.L. Kuhl summarized and analysed the experimental results of electromagnetic radiation generated during energetic material deflagration. It was believed that the movement of ionized atoms, ions and electrons was the cause of the electromagnetic waves caused by deflagration. The expansion of detonation products caused a strong vibration in the surrounding air, forming a strong thermal wave (T~11,000 K) with a duration of 20 μs, which caused clear ionization in the air and movement of ion plaques, thereby generating a current [13].

## 2. Methods

#### 2.1. Experimental Setup

^{−9}s and a recording time as long as 1000 ms. As shown in Figure 2, the test point consisted of a shortwave passive omnidirectional antenna, an ultrawideband passive omnidirectional antenna and a signal conditioner. The sampling bandwidth of the shortwave passive omnidirectional antenna was 1.5 MHz~30 MHz, and it adopted a vertical polarization mode with a standing-wave ratio (SWR) of less than 2.5 and a gain greater than −35 dBi. The ultrawideband omnidirectional antenna used a double-cone loading structure with a vertical polarization method, the sampling bandwidth was 30 MHz~3 GHz, the gain was greater than −15 dBi, and the output impedance of both the shortwave antenna and ultrawideband antenna was 50 Ω. The signal conditioner possessed multiple functions, including a combiner, signal amplifier and limiter, which could combine two electromagnetic signals of different frequencies and amplify the signal at the same time with a range of amplification factors of 10~30 dB. The function of the limiter with limiting power greater than 10 W was to prevent the signal power from being excessively high and damaging the acquisition card [15,16,17,18].

#### 2.2. Data Processing Method

## 3. Electromagnetic Radiation Analysis and Modelling

#### 3.1. Analysis and Modelling of the Spatial Characteristics of Electromagnetic Radiation

**E**(

**r**, t), where

**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

**F**(

**r**, t) ×

**F***(

**r**, t). Through a Fourier transform,

**S**(

**r**, t, f), the time-varying power density spectrum of the time-varying correlation function of the analytic signal

**F**(

**r**, t) of

**E**(

**r**, t) can be obtained.

**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

**S**(

**r**, t, f) after propagating through some medium [22].

**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

**E**

_{i}(

**r**

_{i}, t) and the power density spectrum is

**S**

_{i}(

**r**

_{i}, t, f), which is an electromagnetic signal whose intensity and frequency change with time. 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

**A**

_{i}that varies with space and time, which is related to the propagation path. Therefore, the electromagnetic field intensity of radiation from

**r**

_{i}to

**r**

_{j}is

**A**

_{i}

**E**

_{i}(

**r**

_{ji}, t − t

_{ij}). The electromagnetic radiation received by point j can be expressed as the power spectral density

**S**

_{j}(

**r**

_{j}, t, f) of the combined intensity in Equation (4). Without loss of generality,

**S**

_{j}(

**r**

_{j}, t, f) can be written as

**S**(

**r**, t, f), which is the intensity of electromagnetic radiation at any spatial point in the presence of n radiation sources.

_{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.

#### 3.2. Analysis and Modelling of the Time-Domain Characteristics of Electromagnetic Radiation

**r**

_{j}in space can be expressed as S(

**r**

_{j}, t, f). When the location, number, propagation path and antenna gain of an explosive radiation source are determined, the strength of the signal at the measured point, that is, the power density of the signal, is only a function of time. In a certain explosion space V

_{Ω}and frequency range [f

_{1}, f

_{2}], the law of signal intensity with time changing can be expressed by average power density as Equation (7), where the double integration is the integration over frequency and space.

**r**

_{j}, which shows that the intensity and density of electromagnetic radiation are different at different times.

_{S}, the end time is t

_{E}, the operating start time of Device A is t

_{s}, and the operating end time of Device A is t

_{e}, as shown in Figure 4d, according to the operating period of Device A and the interference period of the electromagnetic radiation, the time-domain correlation calculation model at time t is as follows:

#### 3.3. Analysis and Modelling of the Frequency-Domain Characteristics of Electromagnetic Radiation

_{Ω}and time range of [t

_{1},t

_{2}], the average power spectrum of the signal at different frequencies can be expressed using Equation (10), where double integration is used to integrate over time and space.

_{k}(k = 1~n) due to the joint action of n radiation sources, and each radiation source has a different spectrum range of ΔB

_{k}(k = 1~m). If there is no overlapping part of the spectrum, that is, there is no self-interference or mutual interference, as shown in the first coordinate axis of Figure 4c, then the spectrum occupancy is defined as 0, which is $\mathsf{\Delta}\mathrm{B}={\displaystyle \sum}_{k=1~n}\mathsf{\Delta}{B}_{k}$. However, in actual situations, there will be interference from other signals in the range of ΔB, and frequency overlap will occur; then, $\mathrm{S}\left(f\right)$ must exceed the allowable threshold ${S}_{0}$. As shown in the second and third coordinate axes of Figure 4c, the spectrum occupancy will not be 0; if the spectrum width exceeding the threshold is Δ, the spectrum occupancy is $\mathrm{FO}=\frac{\mathsf{\Delta}}{\mathsf{\Delta}\mathrm{B}}$, and the electromagnetic environment becomes more complicated with the spectrum occupancy being greater.

#### 3.4. Analysis and Modelling of the Energy-Domain Characteristics of the Electromagnetic Radiation

_{Ω}, time range of [t

_{1},t

_{2}], and frequency range of [f

_{1},f

_{2}], the signal strength can be expressed as Equation (13), where S expresses the average power density spectrum of the signal [27].

## 4. Experimental Results

_{S},t

_{E}] and the frequency interval [f

_{jmin},f

_{jmax}] of the electromagnetic radiation source. Because the relevant parameters of Device A were known, the parameters of the electromagnetic radiation source and Device A were substituted into Equations (1)–(3) and (6), (9), (12) to obtain the time occupancy of TO, the spectrum occupancy of FO, the average power density spectrum of SO, the spatial threat degree of ST, the time-domain threat degree of TT, and the frequency-domain threat of FT. The above parameters could be used to calculate the electromagnetic radiation complexity index and electromagnetic radiation threat level. The classification standards for the electromagnetic radiation generated by six sets of rocket fuels are shown in Table 4. The data in Table 4 caused the electromagnetic radiation generated by the deflagration of high energetic materials to have a clear evaluation index, and the threat degree of electromagnetic radiation on electronic equipment could be classified in detail, which was helpful in terms of improving the anti-electromagnetic interference of avionics, and finally, to improve the safety of aviation missions.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**Electromagnetic environment modelling. (

**a**) Electromagnetic interference calculation level; (

**b**) Electromagnetic environment description index.

**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.

**Figure 5.**Time-domain signal of electromagnetic radiation measurement experiment under the following conditions: (

**a**) Case 1—Lox-Hydrogen; (

**b**) Case 2—H2O4-Hydrazine; (

**c**) Case 3—AP-HTPB-Al; (

**d**) Case 4—Lox-Methane; (

**e**) Case 5—Lox-Propane; (

**f**) Case 6—Lox-Kerosene.

**Figure 6.**Frequency-domain signal of electromagnetic radiation measurement experiment under the following conditions: (

**a**) Case 1—Lox-Hydrogen; (

**b**) Case 2—H2O4-Hydrazine; (

**c**) Case 3—AP-HTPB-Al; (

**d**) Case 4—Lox-Methane; (

**e**) Case 5—Lox-Propane; (

**f**) Case 6—Lox-Kerosene.

Parameter | Explanation | Unit |
---|---|---|

${\theta}_{1}$ | Start angle of the scanning azimuth of Device A | ° |

${\theta}_{2}$ | End angle of the scanning azimuth of Device A | ° |

${\phi}_{1}$ | Start angle of the pitch scanning azimuth of Device A | ° |

${\phi}_{2}$ | End angle of the pitch scanning azimuth of Device A | ° |

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 |

$\mathrm{S}\left[\begin{array}{c}\theta \left(t\right),\\ \phi \left(t\right),f\end{array}\right]$ | Average power density spectrum of the electromagnetic environment around Device A | W/(m^{2}·Hz) |

$\theta \left(t\right)$ | Azimuth angle of Device X relative to Device A at time t | ° |

$\phi \left(t\right)$ | Pitch angle of Device X relative to Device A at time t | ° |

${S}_{0}$ | Electromagnetic environment threshold for normal operation of Device A | W/(m^{2}·Hz) |

t_{E} | Upper limit of the time of the radiation source | s |

t_{S} | 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 |

Cases | Combination | Mixture Ratio | Mass/kg |
---|---|---|---|

1 | Lox-Hydrogen | 6 | 1000 |

2 | H2O4-Hydrazine | 1.08 | 1000 |

3 | AP-HTPB-Al | 5.17 | 1000 |

4 | Lox-Methane | 2.77 | 1000 |

5 | Lox-Propane | 1.7 | 1000 |

6 | Lox-Kerosene | 2.33 | 1000 |

Classification | Complexity Index | Classification | Threat Level |
---|---|---|---|

Level A | $0\le \sqrt[3]{FO\times TO\times SO}\le 10\%$ | Level I | $0\le \sqrt[3]{FT\times TT\times ST}\le 10\%$ |

Level B | $10\%\le \sqrt[3]{FO\times TO\times SO}\le 30\%$ | Level II | $10\%\le \sqrt[3]{FT\times TT\times ST}\le 30\%$ |

Level C | $30\%\le \sqrt[3]{FO\times TO\times SO}\le 50\%$ | Level III | $30\%\le \sqrt[3]{FT\times TT\times ST}\le 50\%$ |

Level D | $50\%\le \sqrt[3]{FO\times TO\times SO}\le 70\%$ | Level IV | $50\%\le \sqrt[3]{FT\times TT\times ST}\le 70\%$ |

Level E | $70\%\le \sqrt[3]{FO\times TO\times SO}\le 100\%$ | Level V | $70\%\le \sqrt[3]{FT\times TT\times ST}\le 100\%$ |

Case | t_{S}/s | t_{E}/s | f_{jmin}/MHz | f_{jmax}/MHz | ∆t/s | ∆f/MHz | Complexity Index | Threat Level |
---|---|---|---|---|---|---|---|---|

1 | 0.09 | 0.13 | 480 | 515 | 0.04 | 35 | A | I |

2 | 0.18 | 0.34 | 900 | 1150 | 0.16 | 250 | B | IV |

3 | 0.16 | 0.32 | 60 | 160 | 0.16 | 100 | B | II |

4 | 0.42 | 0.60 | 270 | 420 | 0.18 | 150 | B | III |

5 | 1.00 | 1.60 | 1100 | 1550 | 0.60 | 450 | E | V |

6 | 0.95 | 1.30 | 1060 | 1150 | 0.35 | 90 | C | I |

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**MDPI and ACS Style**

Cui, Y.; Jiang, J.; Kong, D.; Gao, S.; Wang, S.
Study on Electromagnetic Radiation Interference Caused by Rocket Fuel. *Sensors* **2021**, *21*, 8123.
https://doi.org/10.3390/s21238123

**AMA Style**

Cui Y, Jiang J, Kong D, Gao S, Wang S.
Study on Electromagnetic Radiation Interference Caused by Rocket Fuel. *Sensors*. 2021; 21(23):8123.
https://doi.org/10.3390/s21238123

**Chicago/Turabian Style**

Cui, Yuanbo, Jian Jiang, Deren Kong, Shang Gao, and Shuai Wang.
2021. "Study on Electromagnetic Radiation Interference Caused by Rocket Fuel" *Sensors* 21, no. 23: 8123.
https://doi.org/10.3390/s21238123