Analysis of the Electromagnetic Effect Mechanism of EED under Continuous Wave Radiation

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Introduction
EED refers to the electric detonator or the component that adopts electric energy to initiate and ignite the explosives, propellants, or pyrotechnic materials inside.It has vital characteristics such as a large energy-mass ratio, controllable input/output energy, small size and compact structure, and good long-term storage performance [1,2].In the weapon system, the EED is mainly employed to ignite and detonate explosives or to complete the work, start, and other key operational tasks.It is not only the control device in the process of the device but also the work component [3].Te functional primacy and sensitivity of EED determine their position and role in the weapon system; their safety and reliability directly afect the safety and reliability of the weapon system, as well as the play of the combat efectiveness of the weapon system and the safety of combatants [4][5][6].Te EED in the weapon equipment is primarily used to assure the safe and reliable operation of the launching system and delivery system of the weapon for the ignition, fre transmission, delay, and control system of the weapon equipment to achieve accurate strikes on enemy targets for the initiation, transmission, and control system of weapons and equipment, as well as the role of the control warhead.It is employed for pulling, pushing, cutting, separating, throwing, attitude control, and other work sequences and control systems in weapons and equipment to guarantee that weapons and equipment can adjust themselves, change states, and control safety [7,8].
With the rapid development of electronic technology, the combat system and electromagnetic weapons and equipment based on electromagnetic technology are accelerating the change of the combat system and attack and defense style of modern war, making the electromagnetic environment on the battlefeld increasingly harsh and thus leading to more severe electromagnetic environment threats faced by weapons and equipment in military operations [9][10][11][12][13][14][15].EED, as a miniaturized electromagnetic sensitive element, is not only the "source" for weapon systems to complete the predetermined functions but also the "root" for these systems to have possible accidental ignition, explosion, and other accidents [16][17][18].Accurate analysis of battlefeld electromagnetic environment, scientifc protection and reinforcement measures, and enhancement of battlefeld survivability of weapon systems are critical to improving combat efectiveness [19][20][21][22].Terefore, the electromagnetic efect mechanism of the EED should be analyzed to ensure that the weapon system has good combat efectiveness.
Given the mechanism of the electromagnetic efect of EED, Pantoja et al. proposed an input impedance model of bride-wire EED based on diferential mode measurement [3].Tey studied the infuence of diferent coupling conditions on the hot bride-wire EED by measuring the input impedance and gain of the transmitting circuit of the EED.Te correctness of the equivalent antenna theoretical model and Monte Carlo simulation theoretical model to analyze the electromagnetic response of the transmitting circuit of bridge wire EED is verifed.With EED as the research object, Galuga J and Bray J R evaluated the feasibility of induced current detonation in EED by analyzing the magnetic susceptibility of EED under the irradiation of continuous wave and linearly polarized plane wave so as to investigate the electromagnetic efect mechanism of EED [23].Wang et al. from the Beijing Institute of Technology designed an analytical method following the feld line coupling theory to explore the damage mechanism of EED under electromagnetic irradiation, obtained the mathematical model of the transmission line of EED through theoretical analysis, and determined the relationship between the absorbed power and radiation frequency of EED [24].
Although some researchers have studied the electromagnetic damage mechanism of EED, there is little research on the electromagnetic damage mechanism of EED from the aspects of bridge wire temperature rise and radiation feld strength, only involving the induced current, impedance model, and radiation frequency of EED.In this paper, the bridge wire type EED is taken as the research object.Te structural characteristics of the EED and the RF environment are combined to determine the efective aperture of the equivalent antenna of the EED.Besides, the power coupling model of the electromagnetic irradiation of the EED is established, and the relationship between the temperature rise of the bridge wire and the electric feld strength of the EED is demonstrated.Furthermore, the authenticity of the analysis of the electromagnetic efect mechanism of the EED is verifed under the action of high-frequency continuous waves.Tis study provides a new idea for the electromagnetic safety assessment of the EED.

Mechanism Analysis
In a complex battlefeld electromagnetic environment, electromagnetic radiation forms a certain antenna structure on the two-foot leads of the EED and then the electromagnetic energy is coupled [25].Te efective aperture of the antenna is a parameter representing the ability of the antenna to receive electromagnetic waves.Te equivalent antenna constituted by the foot line of the EED also has an efective aperture.According to the reciprocity theorem of the antenna, the efective aperture of the antenna is the same in the transmitting state and the receiving state [26][27][28][29][30]. Terefore, the total power received by the receiving antenna can be calculated by the sum of the power density radiated to the efective aperture of the receiving antenna.Since a typical bridge wire EED is sensitive to electromagnetic radiation in equilibrium mode, the equivalent antenna of EED in the equilibrium mode is analyzed.Te equivalent antenna and equivalent circuit of EED in the equilibrium mode are exhibited in Figure 1.R EED denotes the bridge wire resistance of the EED, R r expresses the radiation resistance of the equivalent antenna, R L represents the loss resistance of the equivalent antenna, X EED indicates the bridge wire reactance of the EED, and X r signifes the reactance of the equivalent antenna.
Under the condition of far feld, the electromagnetic radiation feld is made up of right angles to each other and spread their direction of the electric feld and magnetic feld of two components, and the power density of the incident wave (Poynting vector) is the product of the two [31].
where P denotes the power density of the incident wave, E expresses the electric feld strength of the incident wave, and H represents the magnetic feld strength of the incident wave.Te available power is calculated using the maximum efective aperture (the receiving area of the antenna).Te incident wave power received by the receiving antenna is directly proportional to the maximum efective aperture of the antenna.
where P A indicates the received power of the incident wave, and A e signifes the maximum efective aperture of the antenna.
Te induced voltage of the equivalent ring antenna of EED is where U represents the induced voltage of the antenna, S denotes the loop area of the equivalent antenna of the EED, and μ 0 expresses the permeability with the size of 4π × 10 −7 .
Te efective aperture of the equivalent antenna of the EED is From equations ( 2) to (4), the efective aperture of the equivalent antenna of the EED can be obtained as 2 International Journal of Antennas and Propagation Generally, R r ≪ R EED .Equation ( 5) can be simplifed as Te ratio of the electric feld to the magnetic feld represents the characteristic impedance of free space, namely, where Z 0 expresses the characteristic impedance of free space.Te electromagnetic radiation feld's average power density P with E or H can be represented as Following ( 2) and ( 8), the electromagnetic radiation power received by the equivalent antenna of the EED can be expressed as When the pin structure state of the EED is determined to be a half-wave dipole antenna mode [25], the electromagnetic wave radiation power received by the foot line of the EED can be obtained by (9) as follows: Te abovementioned analysis suggests that the accepted power on the EED is proportional to the square of the electric feld intensity when the electromagnetic wave frequency is constant.
Te combustion of EED is a law of conservation of energy, comprising the heat required by the heating of the bridge wire of EED, the heat released by the chemical reaction of the pyrochemical, the heat lost by the bridge wire, and the coupled radiation power.Terefore, the heat balance equation of the EED can be obtained [32] as where ρ 1 denotes the material density of bridge wire; c 1 expresses the heat capacity of the bridge wire; T represents the temperature of the bridge wire; P stands for the coupling radiated power of the bridge wire; ρ 2 indicates the material density of the pyrotechnic reagent; q signifes the heat of reaction of the chemical reagent; Z refers to the frequency factor; e expresses the base of natural logarithm; E a refects the activation energy of the pyrotechnic reagent; R is the gas constant; λ means the heat conductivity coefcient; and ∇ 2 terms the Laplace operator.
According to (11), the ignition condition of the EED is Te frst item on the right of ( 11) is the heat energy released by the chemical reaction of the pyrochemical agent.It indicates the product of the drug dose consumed by the reaction and the heat release of the explosive per unit mass.Te consumption of chemical agents in the EED before ignition is very small and thus neglected in the analysis of the electromagnetic efect mechanism of the EED.Te second item on the right of ( 11) is the heat lost by the bridge wire.Since the EED is placed in an electromagnetic feld environment, the temperature of the bridge wire rises rapidly.It can be assumed that all the coupled energy is adopted for the temperature rise of the bridge wire.Hence, In other words, the temperature rise on the bridge wire of the EED is directly proportional to the square of the electric feld when the frequency of the electric radiation is constant.

Experimental Verification
Te electromagnetic efect test of the EED was performed under the action of the continuous wave to verify the authenticity of the analysis of the electromagnetic efect mechanism of the EED.Te RF signal emitted by the RF signal generator was amplifed by the broadband power amplifer, and the amplifed RF signal was converted into RF continuous wave by the antenna to irradiate the EED under     International Journal of Antennas and Propagation Considering spatial electromagnetic feld distribution and efective aperture of the equivalent antenna of EED in conducting electromagnetic efect test of EED under RF continuous wave, the transmitting frequency of RF continuous wave was selected as 5 GHz; the corresponding half wavelength was 3 cm and the length of foot line of EED was transformed into 3 cm.During the test, the electromagnetic feld used vertical polarization to irradiate the EED, and the foot line of the EED was perpendicular to the ground.Te electromagnetic efect testing system of the EED under the action of the continuous wave is displayed in Figure 3.
Te researcher turned on the RF signal generator, broadband power amplifer, optical fber temperature measurement system, and electromagnetic feld strength tester.Ten, the output of the signal source was adjusted, and the electric feld intensity near the EED was tested with the feld intensity tester.Te radiant electric feld intensity was adjusted successively to 108 V/m, 123 V/m, 138 V/m, 157 V/m, 212 V/m, and 232 V/m and the temperature rise of the bridge wire under the corresponding feld intensity was examined using the optical fber temperature measurement system.Te test results are listed in Table 1.
With respect to the relationship between the temperature rise of the bridge wire of the EED and the intensity of the continuous wave irradiation feld, curve ftting and residual error calculation were conducted on the test results.Te results are presented in Figure 4.
Under the irradiation of 5 GHz RF continuous wave, the mathematical relationship between the temperature rise and the electric feld intensity of the bridge wire of the EED was obtained through the test as

Conclusions
Trough the analysis of the electromagnetic damage mechanism of the EED, the efective aperture of the equivalent antenna of the EED was determined, the radiation power model accepted by the EED under the action of an electromagnetic feld was established, and the relationship between the temperature rise of the bridge wire of the EED and the electric feld strength was demonstrated by combining the thermal equilibrium equation of the EED.In addition, the correctness of the proportional relationship between the temperature rise of the bridge wire and the square of the electric feld strength of the EED was verifed by the electromagnetic efect tests on the bridge wire of the EED under a 5 GHz RF continuous wave.Te ftted curve of the temperature rise of the bridge wire and the electric feld strength was obtained, with the maximum residual error and root mean square error of the curve of 0.74 °C and 0.54 °C, respectively.By analyzing the electromagnetic efect mechanism of EED, the relationship between the irradiation power of EED and the electric feld intensity was studied, and a mathematical model for bridge line temperature rise and electric feld intensity was established.Te establishment of this model lays a theoretical foundation for the electromagnetic safety margin analysis of EED and guides the antielectromagnetic interference transformation of EED in weapon equipment and the development of new EEDs.It has vital military benefts and practical value for improving the survival ability of EED in weapon equipment and enhancing the combat efectiveness of weapon equipment.

Figure 1 :Figure 2 :Figure 3 :
Figure 1: Equivalent circuit equivalent antenna and equivalent circuit of EED in the equilibrium mode.(a) Equivalent receiving antenna of EED in the equilibrium mode.(b) Equivalent circuit.

Figure 4 :
Figure 4: Bridge wire temperature rise ftting curve and ftting residual under RF continuous wave.(a) Fitting curve of bridge wire temperature rise.(b) Residual temperature rise error of bridge wire.

Table 1 :
Test results of electromagnetic efect of EED under continuous wave.