Modified Transceiver Antenna for NQR Detection of Explosive Objects in Demining Conditions

Abstract

This paper presents the conceptual stages of the simulation and development of a modified transceiver antenna for a high-power pulsed nuclear quadrupole resonance (NQR) detector of explosives containing the ¹⁴N isotope. At a frequency of 4.645 MHz, better characteristics are obtained using a nine-turn coil shaped as half of a Fermat spiral with an outer radius of 75 mm. Using a COMSOL Multiphysics numerical parametric simulation and a materials browser, it was possible to calculate a physical system with parameters as close to reality as possible. According to the results of the experimental studies of the radio frequency (RF) energy, the proposed antenna features an increase in the working area compared to a similar antenna, the topology of the conductive coil of which has the form of an Archimedean spiral. The resulting diagrams of the distribution of the magnetic induction also indicate that the topology of the electromagnetic (EM) field does not depend on the orientation of the sample under study relative to the axis of the radial symmetry observed in square–rectangular planar antennas.

1. Introduction

One of the key features of the development of our civilization is the protection of people’s lives. However, recently, an increase in military conflicts and terrorist acts has occurred. Sometimes, such dangerous situations can be prevented by using novel equipment for detecting explosive objects [1,2,3,4].

Despite the intensive development of science and technology, EM metal detectors, the first prototypes of which were used during the Second World War, are still the main devices for detecting explosive objects. Metal detectors of this type have a number of disadvantages. Due to the fact that the EM signal reflected from the anti-personnel mine is much weaker, the sapper must increase the sensitivity of the detector. However, at higher sensitivities, many other metal objects, such as nails and hull debris, interfere with the detector. Unfortunately, the next step is the most difficult, since it is necessary to separate the signals of real explosive devices from “false alarms”. The sapper performs a very delicate extraction with a pointed stick to classify the source of the reflected signal, which could be a landmine, a forgery, or simply a rusty nail. In this sense, while the search for mines is quite simple, separating them from other objects is difficult and extremely dangerous [1]. Another significant disadvantage of EM metal detectors is their inability to detect explosive objects in non-metallic containers (hand luggage, envelopes, plastic containers, etc.) [2].

An alternative method for detecting explosives is the use of highly sensitive vapor sensors. However, the evaporation of explosives used in landmines is rather weak. Furthermore, modern mines are produced with a hermetically packed explosive in a polymer case. Since the vapors and particles of explosives are quite sticky, the infiltration of explosives through the case and then through the soil is slow and inefficient. Studies have shown that under field conditions, even highly sensitive vapor sensors may not detect vapor plumes from mines [5].

A basis for the development of promising hardware and software tools for the detection of explosives is the idea of using the pulse NQR method to observe the free induction decay of the ¹⁴N isotope [2,6,7,8]. Based on the analysis and with regard to the obvious advantages of the method (such as its non-destructive effect, the possibility of studying inhomogeneous mixtures, and rapid analysis without preliminary sample preparation), it was found that the development of hardware and software for detecting hazardous substances based on NQR is more appropriate than other methods [9,10].

This paper presents a simulation and an experimental prototype of a modified transceiver antenna with an extended working area for detecting explosive objects using the NQR method in demining conditions.

2. Methods of Geometric and Spatial Simulation of a Modified Antenna

2.1. Statement of the Research Problem

In most cases, the transceiver antenna of the NQR explosive detector is a spiral RF coil operating in the near EM field [11,12]. In order to adapt to the functional requirements of demining, the size of the coil is chosen in proportion to the size of explosive object. In the case of NQR observation, it is important to design the coil geometry with regard to the highest possible signal-to-noise ratio (SNR) of the detector. This scientific problem was considered in detail in [13]. The problem mostly depends on the noise level of the detector’s receiving path and, above all, on the quality of the coil. To analytically estimate the SNR of NQR detectors operating in the HF and VHF frequency bands, we can apply the expression [14]:

$$\mathrm{SNR}=\frac{1}{8}\cdot {\left(\frac{{\omega }^3\cdot \eta \cdot Q\cdot V_S}{2\cdot {\mu }_0\cdot k\cdot T\cdot N_F\cdot \Delta F}\cdot \frac{T_2}{T_1}\right)}^{1/2}\cdot \frac{{\chi }_0}{\gamma }$$

(1)

where η is the energy-transfer coefficient, Q is the quality factor, V_S is the volume of the sample, T₁ and T₂ are the relaxation-time constants, µ₀ is the permeability, k is the Boltzmann constant, T is the absolute temperature, N_F is the noise figure for the detector’s receiving path preamplifier, ΔF is the detector’s receiving-path bandwidth, χ₀ is the magnetic susceptibility, ω is the angular frequency of the resonance, and γ is the gyromagnetic ratio.

The parameter η is defined as the ratio of magnetic energy stored in the sample to magnetic energy stored in the antenna [14]. It also depends on the homogeneity of magnetic induction (no more than 15%). This is especially important when using the pulse method for detecting resonant signals, where the maximum level of the free-induction decay signal largely depends on the magnetic induction in the antenna during excitation [15].

Improving the homogeneity of the EM field is especially important for detecting low-level responses from substances containing nitrogen atoms (¹⁴N). Therefore, when choosing the configuration of the coil and the approach to its manufacture, the quality parameter ηQ, taking into account the homogeneity of the EM field, is crucial.

2.2. Substantiation of Geometry and Development of the Spiral-Coil Model in Comsol Multiphysics

To simulate three-dimensional fields, the finite-element method has several applications [16,17,18]. The EM field distribution near the proposed NQR detector antenna was calculated using the analytical capabilities of COMSOL Multiphysics software, which offers wide functionality for the implementation and study of models of physical fields [19].

To improve the EM field distribution in the working area of the antenna, it is necessary to decrease the distance between the turns of the flat coil with increase in distance from its geometric center. The conclusion about the reduction in the interturn distance is made on the basis of an analogy with respect to the law of inverted squares. The solution of this problem is possible by using the Fermat spiral expression to construct the coil geometry. Fermat spiral is a type of Archimedean spiral [20]. However, it differs from the usual Archimedean spiral in that the distance between adjacent turns in the former spiral is always the same, and this pattern is not preserved in Fermat spiral. General view of the equation of a plane curve in polar coordinates is as follows:

$$r^2=a^2\theta$$

(2)

where r is the radial coordinate, a is the angle of polar inclination between the tangent to the curve and the corresponding polar circle, and θ is the azimuth.

Since for any given positive value of θ there are two values of r equal in modulus but opposite in sign

$$r=\pm a{\theta }^{1/2}$$

(3)

to calculate the geometry of the required coil shaped as half of Fermat spiral, we take into account a special case for r > 0.

The equations described above, converted from the polar to Cartesian coordinates, were adapted to synthesize a numerical model of the coil geometry in COMSOL Multiphysics.

To adapt to the functional requirements of demining, the size of the coil was chosen to be proportional to the size of the anti-personnel mine, resulting in a coil diameter of 150 mm. The number of turns was chosen according to the results of magnetic-field simulations; nine turns showed the best result for the given coil sizes. A spiral thickness of 3 mm was chosen, taking into account that the maximum current in the coil did not exceed 1.5 A. Other parameters were calculated according to the equations given in

Table 1. System of equations and parameters for simulation of coil geometry in COMSOL Multiphysics.

Description	Name	Expression	Value
Initial spiral radius	a1	9	9 mm
Final spiral radius	Af	75	75 mm
Spiral growth rate	b1	(af − a1)/(2 × pi × n1)	1.1671 r.u.
Updated growth rate	b2	(gap + thick)/(2 × pi)	1.1671 r.u.
Turn-to-turn distance	Distance	(af − a1)/n1	7.3333 r.u.
Gap distance	Gap	distance-thick	4.3333 r.u.
Number of turns	n1	9	9
Initial angle	Theta_0	0	0 deg
Final angle	Theta_f	(af − a1)/b1	56.549 deg
Thickness of the spiral	Thick	3	3 mm

.

For simulation by the finite-element method, a technique was used, which was considered in detail in [21]. The geometric model (calculation area) of the proposed antenna, obtained on the basis of its numerical model, is shown in Figure 1. Structurally, the antenna is a flat coil in the form of a parabolic spiral with the following parameters: outer radius, number of turns, winding pitch, geometry and material of conductive conductors, etc. This data, as well as information about the initial simulation conditions, are global top-level definitions in Model Builder. The geometry of the coil is represented by half of a Fermat spiral with a relative tolerance of 10⁻⁵, which is technologically easy to produce on a glass-fiber-epoxy printed-circuit-board laminate. We used FR-4-35/0–1.5 mm (at a frequency of 1 MHz, the typical dielectric constant is 4.5 and the dielectric loss angle tangent is 0.017) with a one-sided metal-coating 35 µm thick. At the ends of the flat coil, there are parallel rectangular contact pads, which serve to connect the lumped port (LP) excitation source with a characteristic impedance of 50 ohms and the capacitor of the parallel oscillatory circuit of the NQR detector input circle — lumped element (LE) (Figure 1). Copper with electrical conductivity 5.998 × 10⁻⁷ S/m and relative magnetic permeability 0.99999 was chosen as the material of conductive elements. A fixed capacitor was used to simplify the simulation. In the real experiment, a variable capacitor was used to fine-tune the input circuit of the NQR detector to the resonance frequency.

The bottom metal plate is the electromagnetic shield. In the experimental model, a steel sheet with dimensions of 220 mm × 190 mm and a thickness of 1 mm was used. In the future layout, the bottom of the metal case of the NQR detector antenna will serve as the shield.

In order to simulate perfect conditions for the absorption of electromagnetic radiation energy and prevent erroneous reflections, the geometrical model of the antenna is limited to an air cube with the following parameters: side equal to 400 mm, electrical conductivityequal to 0 S/m, relative magnetic permeability equal to 1, temperatureequal to 293.15 K and pressure equal to 1 atm.

Numerical simulation was carried out using the AC/DC and RF modules of the program [19]. Specifically, the calculation of the EM topology of the magnetic field was performed using the parameterized interfaces Magnetic Fields (mf) and Electric Currents in Shells (ecis). The response of the model, which is subjected to harmonic excitation in the operating-frequency range, was calculated using the parameterized interface Electromagnetic Waves, Frequency Domain (emw), and adaptive frequency scanning for more accurate frequency resolution. Wave Equation (4) describes the region of an air cube and the region of copper conductive elements:

$$\nabla \times {\mu }_r^{-1}\left(\nabla \times E\right)-k_0^2\left(E_r-\frac{j^{\sigma }}{\omega E_0}\right)E=0$$

(4)

For the electrical connection of LP and LE with the end terminals of the coil, lossless metal conductors were added, represented in the simulation stage of the boundary condition (5) of the perfect electrical conductor (PEC). Thus, the requirements for computing resources were significantly reduced:

$$n\times E=0$$

(5)

At the previous simulation stage, parameterized interfaces were adjusted and mesh sensitivity was analyzed (Figure 2).

The mesh step (Figure 3) was chosen as optimal, taking into account the fact that its increase leads to deterioration in the simulation accuracy, but its reduction leads to errors in fractional operations. Furthermore, reducing the mesh step requires a significant amount of hardware-computing resources. The optimal mesh parameters were established empirically: the largest element size equal to 200 mm, the smallest element sizeequal to 0.6 mm, the largest increment of the element sizeequal to 1.35 mm, the curvature factorequal to 0.3, and the narrow area resolutionequal to 0.85. These values were determined for the model under study in order to improve the simulation efficiency. The appearance of the parametric mesh superimposed on the geometric model of the spiral coil is shown in Figure 3a and an enlarged view of the mesh is shown in Figure 3b.

3. Discussion of Results

3.1. Analysis of Simulation Results

The simulation was performed on a workstation containing a HexaCore Intel Core i7-8700K microprocessor clocked at 4.3 GHz and 32 GB of DDR4 RAM. In order to compare the characteristics of the proposed antenna shaped as half of a Fermat spiral with an alternative classical Archimedean-spiral design, COMSOL Multiphysics also synthesized a numerical model of the geometry of the latter coil and tested both models using the parameterized mf, ecis, and emw interfaces. The electrical characteristics of the elements used in the study of the numerical models Fermat spiral coil and Archimedean spiral coil are given in

Table 2. Electrical characteristics of elements used in the study of numerical models of Fermat spiral coil and Archimedean spiral coil.

	Fermat Spiral Coil	Archimedean Spiral Coil
Coil inductance	L = 8.386 uH	L = 4.955 uH
Lumped element capacitance	C = 140 pF	C = 237 pF
Frequency	F = 4.645 MHz	F = 4.645 MHz
Characteristic impedance of resonant circuit	ρ = 244.745 ohms	ρ = 144.593 ohms
Coil resistance	R = 0.15983 ohms	R = 0.15983 ohms
Quality factor of resonant circuit	Q = 1531	Q = 905

.

The simulation was carried out around the ¹⁴N NQR frequency (4.645 MHz) in NaNO₂ [22]. This quadrupole core can serve as a kind of sensitivity marker for the NQR sensor of explosive objects, since it provides a weak signal of the free-induction-decay response, which was confirmed by our previous experimental studies. In order to investigate the frequency dependence of the impedance of a parallel oscillatory circuit with a resonance frequency of 4.645 MHz using the parametric simulation method, a capacitive lumped element was connected in parallel with the lumped port, the capacitance of which was determined individually for each coil from the following equation [23]:

$$C_t=\frac{r}{\sqrt{r{\omega }^2{Z}_0\left(L^2{\omega }^2+r^2-r{Z}_0\right)}}$$

(6)

where L is the antenna inductance, ω is the angular frequency of the resonance, Z₀ is the input resistance of the NQR detector, and r is the active resistance of the antenna.

In order to find resonant modes for two coils with different geometries at frequencies of 4.4–4.9 MHz, the study was begun with a resolution of 0.1 MHz. The lumped capacitive element placed parallel to the lumped port was used for tuning. More accurate resonant modes were found using frequency-swing control algorithms in steps of 5 kHz.

The processing of the results of the numerical simulation was carried out by the built-in COMSOL tools using the “Results” menu.

From the data obtained using the numerical simulation, multilayer models of the EM field isosurface were built in the vicinity of the conductive elements of the investigated coils (Figure 4 and Figure 5) [24]. The simulation took into account the limiting conditions that described the distribution of the EM field within the computational domain. In particular, Figure 5 shows the simulation results of the EM field at a frequency of 4.645 MHz for half of a Fermat spiral coil. It was established that for the modified coil (Figure 5) there was a larger area with increased uniformity of the EM field distribution than for the coil shaped as an Archimedean spiral (Figure 4). Moreover, for a more detailed study of the dimensions of the working area with a magnetic-induction inhomogeneity of no more than 15%, it was necessary to conduct an additional analysis of the results of the numerical simulation for individual sections of the computational domain.

In the study of both coils by numerical simulation, the dependences of the magnetic induction on the displacements along the radius vectors drawn parallel to the y-axis at distances of 20 mm and 40 mm from the XY plane were obtained (Figure 6). The analysis of these dependencies allows us to estimate the magnitude of the decrease in the intensity of the EM field radiation with increasing distance from the geometric center of the coils. It also explains how to place the sample under study. The dependences of the magnetic-induction distribution show that the zones of sufficient field homogeneity (10–15%) on both sides of the geometric center of the Archimedean spiral were ±18 mm and ±22 mm at distances from the XY plane of 20 mm and 40 mm, respectively, and, for the Fermat spiral of about 25 mm for the two cases. With the subsequent removal of the virtual sensor along the z axis for the modified coil, in contrast to the Archimedean spiral, there was no significant change in the radial dependence of the normalized magnetic induction.

As noted above, the inhomogeneity of the magnetic induction is not the only parameter that must be considered. Considering the expression for H₁ in [25], we can see that to obtain the maximum EM field strength in the area of the sample, it is necessary to minimize the volume of the coil, while, at the same time, the quality factor should be maximized in the signal-reception mode. In order to determine the quality factor of the coils and their subsequent coordination with the transmitting and receiving equipment, an additional analysis of the frequency dependences of the impedance of the elements of the oscillatory circuits used in the study of the numerical models was carried out (

Table 3. The results of analysis of the frequency dependences of the impedance of the elements of oscillatory circuits used in the study of the numerical models of Fermat spiral coil and Archimedean spiral coil.

Frequency, MHz	Archimedean Spiral Coil			Fermat Spiral Coil
	Inductive Reactance XL, ohms	Capacitive Reactance XC, ohms	Full Impedance |ZLC|, ohms	Inductive Reactance XL, ohms	Capacitive Reactance XC, ohms	Full Impedance |ZLC|, ohms
4.6100	143.52	−145.67i	9741.1	242.86	−246.60i	16,035
4.6150	143.68	−145.51i	11,407	243.13	−246.33i	18,689
4.6200	143.84	−145.35i	13,758	243.39	−246.07i	22,393
4.6250	143.99	−145.20i	17,324	243.65	−245.80i	27,920
4.6300	144.15	−145.04i	23,377	243.92	−245.53i	37,057
4.6350	144.30	−144.88i	35,908	244.18	−245.27i	55,051
4.6400	144.46	−144.73i	77,307	244.44	−245.00i	1.0691 × 105
4.6450	144.61	−144.57i	5.0980 × 105	244.71	−244.74i	1.8131 × 106
4.6500	144.77	−144.42i	59,373	244.97	−244.48i	1.2135 × 105
4.6550	144.92	−144.26i	31,538	245.23	−244.22i	58,741
4.6600	145.08	−144.11i	21,479	245.50	−243.95i	38,764
4.6650	145.24	−143.95i	16,289	245.76	−243.69i	28,934
4.6700	145.39	−143.80i	13,122	246.02	−243.43i	23,086
4.6750	145.55	−143.64i	10,988	246.29	−243.17i	19,208
4.6800	145.70	−143.49i	9452.2	246.55	−242.91i	16,448

).

The results obtained by simulating the frequency dependences of the lumped-port impedance for both coils in the frequency range 4.55–4.75 MHz are shown in Figure 7. Due to the near-doubling of the inductance (8.386 uH vs. 4.955 uH) and approximately the same active resistance, the quality factor of the modified coil increased by approximately 69%, which allowed us to improve the optimal conditions for receiving NQR signals.

3.2. Experimental Studies

Based on the results obtained using the computer simulations, experimental models of two transceiver antennas were constructed. These were structurally identical to the geometric models developed in the COMSOL Multiphysics program. The models were fabricated by chemical etching on FR-4-35/0–1.5-millimeter glass-fiber-epoxy laminate. Figure 8 shows photographs of the experimental layouts of the antennas, which were further investigated to verify the topology of the magnetic induction. The diameters of both spirals were 150 mm, with a conductor width of 3 mm, the distance between the centers of the turns of the Archimedean spiral antenna (Figure 8a) was 8.45 mm. The distance between the centers of the turns of the modified antenna (Figure 8b) was determined based on the numerical model of the coil geometry shaped as half of a Fermat spiral.

An equivalent scheme of the experimental setup for studying the topology of the magnetic induction is shown in Figure 8c. It consisted of a spiral antenna, an RF signal generator, and a voltmeter with a magnetic-loop antenna connected via an SMA connector, which acted as a scanning device of the EM field. Since the magnetic-loop antenna was in the zone of close-field interaction with the antenna under study, it was possible to detect the value of the electric current in the circuit of the latter, which was proportional to the magnetic induction in accordance with the Biot–Savart–Laplace law. To prevent a short circuit in the coil circuit, a resistor with a nominal resistance of 1 kohm was connected in series between the generator and the antenna under study.

To measure the topology of the field distribution, a two-coordinate device was used, which made it possible to move the magnetic-loop antenna with a step of 1 mm along two mutually perpendicular axes to control the longitudinal (B_X) and transverse (B_Y) components of the magnetic induction. The experimental studies were performed at a frequency of 4.645 MHz by scanning the field at distances of 20 mm and 40 mm from the surfaces of the studied antennas with a step of 5 mm along the spirals, and 10 mm outside them. The remaining experimental conditions were identical to those of the computer simulation.

Figure 9 shows the results of the experimental studies in the form of the relative distributions of the magnetic induction B₁(y)/B₁(0) for two antenna variants. In the case of a modified antenna, there was a more uniform distribution of magnetic induction along the radius of the spiral than in that of the Archimedean spiral, where the maximum values of the magnetic induction were localized in the center. Therefore, the zones of permissible field inhomogeneity on both sides of the geometric center of the antenna in the form of the Archimedean spiral were: ±14 mm and ±18 mm at distances from the XY plane of 20 mm and 40 mm, respectively. For the modified antenna, the figures were approximately ±29 mm for the two cases. As in the case of the computer simulation, further removal of the loop antenna from the modified coil along the z axis did not lead to a significant change in the radial dependence of the normalized magnetic induction. Therefore, for the proposed coil, in addition to increasing the working area, the dimension of this area does not significantly depend on the distance of the test sample (

Table 4. Comparison of the working areas of the investigated coils.

Investigation Type	Working Area of the Archimedean Spiral Coil	Working Area of the Fermat Spiral Coil	Ratio	Increase
Simulation, distance 20 mm	36 mm	50 mm	1.39	14 mm
Simulation, distance 40 mm	44 mm	50 mm	1.14	6 mm
Experimental, distance 20 mm	24 mm	58 mm	2.42	34 mm
Experimental, distance 40 mm	36 mm	58 mm	1.61	22 mm

).

4. Conclusions

According to the results of the analysis, the complex task of detection by the pulsed NQR method of weak signals of free-induction decay from the atoms contained in the vast majority of explosive substances (isotopes ¹⁴N, ³⁵Cl, ³⁷Cl) requires the solution of a number of problems, which, in particular, involve optimizing the design of the detector’s transceiver antenna. Summarizing the presented results, it is necessary to highlight the most important:

• A numerical model of the coil geometry was synthesized in COMSOL Multiphysics, which allowed the expansion of the working area compared to the classical version of the spiral coil. This was achieved by compensating for the weakening of the magnetic induction at the edges of the coil.
• The zones of sufficient field homogeneity (10–15%) on both sides of the geometric center of the coil shaped as half of a Fermat spiral were studied. It was established that the zones of permissible field inhomogeneity on both sides of the geometric center of the antenna in the form of the Archimedean spiral were ±14 mm and ±18 mm, at distances of 20 mm and 40 mm from its surface, respectively. For the modified antenna, these values were approximately ±29 mm for the two locations of the measuring sensor.
• The obtained magnetic-induction-distribution diagrams also showed that the volume of the working area did not significantly depend on the distance of the object of study, and the topology of the EM field did not depend on the orientation of the sample relative to the radial-symmetry axis observed in the planar antennas.
• The results obtained by simulating the frequency dependences of the lumped-port impedance indicate that, the near-doubling of the inductance, the quality factor of the modified coil increased from 905 to 1531, which contributed to an increase in the sensitivity of the input circuit of the radio-receiving path of the detector in the NQR signal-reception mode.

In general, the research confirmed that the obtained parameters of the proposed transceiver antenna meet the conditions of the task and allow its effective use in the development of portable, pulsed NQR detectors of explosives. In addition, the proposed antenna can also be used in medium-power wireless power-transmission systems.