High fidelity dynamic 3D characterization of in-flight exploding foil initiator flyers based on microscope photonic Doppler velocimetry

Exploding foil initiators (EFIs), also known as slapper initiators, were originally proposed by a researcher in the United States in 1976.¹ The device utilizes the electrical explosion of a metal bridge foil to propel a flyer to detonate low-sensitivity explosives. EFI stands out for its immunity to electromagnetic interference, precise timing capabilities, and stable pressure output, making it widely applicable in military applications. The performance of the EFI has a direct impact on the reliability of the entire system. The complete operational cycle of the EFI mainly includes three closely related processes: the electrical explosion of the metal bridge foil caused by the pulsed high current discharge, the acceleration of the flyer drive by the high-temperature and high-pressure plasma within the barrel, and the impact of the accelerated flyer on the explosive to achieve detonation. Focusing on these processes, researchers worldwide have conducted extensive studies in the areas of theory,² numerical simulation,³ and experiment.^4,5 The flyer, which serves as the intermediate carrier for energy conversion in these three processes, is influenced by a complex interplay of several factors, including the parameters of the discharge circuit, the bridge foil, the flyer itself, and the barrel. The morphology of the flyer, including integrity, planarity, velocity distribution, and thickness distribution, ultimately determines whether it can reliably initiate the explosive pellet and then detonate the subsequent explosive sequence.

In EFI theoretical research, the one-dimensional electrical Gurney theoretical model developed in the 1960s and 1970s effectively predicts the flyer velocity.⁶ Additionally, the one-dimensional Wakler and Wasley and James shock ignition criteria can evaluate the threshold of the initial explosive ignition by the flyer impact.^7,8 Since 2010, the three-dimensional magneto-hydrodynamic codes such as ALEGRA⁹ and ALE-MHD,¹⁰ along with commercial nonlinear finite element analysis software like AUTODYN and LS-DYNA, have been developed to provide information on flyer velocity, three-dimensional morphology, particle velocity, and pressure characteristics associated with impact-induced explosive ignition. Based on these advancements, researchers have further proposed a three-dimensional impact ignition criterion.¹¹ 

The continuous progress of simulation programs and the emergence of three-dimensional impact ignition criteria have necessitated the development of corresponding diagnostic techniques with two-dimensional and three-dimensional spatial resolution capabilities. Therefore, the experimental three-dimensional characterization of the flyer morphology inside the barrel and at the muzzle exit is paramount. This will provide valuable experimental data for comparison and verification with theoretical models and simulation results and will serve as a crucial basis for research work such as EFI optimization, margin assessment, and the establishment of the initiation criterion for the initial explosive.

In terms of experimental research, the imaging method remains the most intuitive approach for characterizing flyer morphology. As early as 1989, Boberg employed a streak camera to evaluate the shape of the flyer by recording the luminescence generated when the flyer struck the surface of the plexiglass.¹² In 2017, Bowden used high-speed shadowgraphy to investigate the morphology of the flyer.⁵ However, due to limitations inherent to the visible light technique, including its limited penetration characteristics and extended exposure time, the experimental outcomes were not as satisfactory as anticipated. Since 2016, Willey have been conducting phase-contrast imaging research utilizing x rays with superior penetrating power on the advanced photon source (APS), a third-generation synchrotron radiation light source facility.⁴ However, this method merely captures the integral projection of the flyer. Assuming a high degree of consistency in the EFI actuation process, the flyer is photographed from multiple angles, and the three-dimensional morphology is subsequently reconstructed through a computed tomography algorithm. X-ray phase-contrast computed tomography currently stands as the most effective and intuitive technique for capturing the morphology of the flyer. However, it is limited in certain ways. First, in order to resolve flyers constructed from low-density materials like polyimide, x rays with an energy level of approximately 10 keV must be selected. However, these x rays are insufficient to penetrate high-density metals or ceramic barrels found in real explosive initiator components. Consequently, the technique is primarily confined to the diagnosis of the flyer without barrels or those situated within thin-walled barrels crafted from low-density materials such as aluminum.¹³ Second, the spatial resolution of single-direction x-ray radiographic diagnosis is 1.4 μm; but due to an integral effect, it lacks resolution along the projection direction. Although combined with computed tomography, it has not achieved simultaneous multi-angle shooting. Instead, different projection angles were used in separate experimental shots, making it challenging to maintain temporal and spatial consistency between each shot. Consequently, the spatial resolution for the three-dimensional reconstruction of the flyer is limited to only 11.3 μm, which is inadequate for resolving the morphology of flyers with a thickness ranging from 25 to 100 μm. Third, working on large-scale facilities such as advanced photon sources involves relatively high experimental costs and limited experimental shots.

Visible light and x-ray imaging technology can indeed provide some morphology information about the flyer, but when it comes to measuring velocity, a key physical quantity in the diagnosis of exploding foil initiators, these techniques are limited in their ability to capture only the average velocity of the flyer at multiple instances. Continuous measurement of the flyer's velocity history, however, can only be achieved through laser velocimetry technology. From 1989 to 2007, researchers utilized techniques such as the velocity interferometer system for any reflector (VISAR)¹² and the Fabry–Perot interferometer (FP)^12,14 to assess the performance of various EFI components, yielding encouraging results during that period. The photonic Doppler velocimetry technology, which emerged in 2004, has gradually found its application in the research of exploding foil initiators.⁵ In 2007, Ralph Hodgin conducted a comprehensive analysis comparing the capabilities of the FP and photonic Doppler velocimetry (PDV) techniques in measuring flyer speed.¹⁴ PDV has become the most common velocity measurement method in the field of detonation wave and shock wave due to its portability, relatively low cost, no need for grinding the sample surface, and the unambiguous processing method that the speed is proportional to the signal frequency.¹⁵ They also presented experimental results obtained through single-point PDV measurements and outlined plans to redesign the PDV probe to enable simultaneous three-point measurements.

Building upon our extensive experience in laser velocimetry research, we have initiated diagnostic experiments on flyer velocity fields utilizing the line-imaging and framing plane-imaging velocity interferometer since 2014.¹⁶ This technique employs imaging measurements with a spatial resolution of approximately 5 μm. Its primary advantage lies in the intuitive representation of flyer characteristics through interference fringe images. Specifically, the line-imaging VISAR captures the velocity history of individual points along a designated line on the flyer's surface, while the frame-imaging VISAR reveals relative velocity differences across various points on the entire flyer surface at different moments. This comprehensive approach greatly facilitates the interpretation of flyer velocity characteristics both inside and outside the gun barrel as well as insights into the planarity of the flyer. Nevertheless, the VISAR measurement principle renders it susceptible to the reflection state of the flyer's surface and its tilt characteristics, which presents challenges in obtaining complete velocity measurements across the entire surface, particularly at the edges of the flyer.^16,17

Considering the greater tolerance of PDV technology to target surface conditions, a new method is proposed to achieve spatial resolution measurement of flyer velocity fields utilizing microscopic PDV, enabling precise characterization of the flyer morphology. To simulate the impact of the explosive pellet, a transparent window such as LiF is employed at the muzzle exit. Then, a velocity measurement probe, capable of emitting dense light spots, is employed to measure the velocity history at different positions on the flyer surface. By comparing and correlating these velocity history data, it is possible to obtain characteristics of the flyer's acceleration process within the gun barrel associated with spatial positions. Additionally, quantitative data on the flyer's integrity, planarity, velocity, and thickness during muzzle exit can be obtained. This approach enables a high-confidence characterization of the three-dimensional morphology of the real-structure exploding foil initiators flyer.

The EFI barrel typically has an inner diameter ranging from approximately 0.20 to 1.00 mm, which presents significant challenges for PDV in achieving high spatial resolution measurements of velocity fields within such a confined space. To address this issue, a microscopic PDV probe with in situ detection capability of light spot distribution has been designed. The optical path schematic is depicted in Fig. 1(a). A specific optical design ensures that each measurement channel's light spot is precisely focused on the surface of the flyer, with no overlap within the gun barrel's height. The interval between the light spots can be selected within the range of approximately 40–100 μm. This configuration allows for accurate and reliable velocity measurements, even in such a restricted environment. Concurrently, the target surface and the light spots are imaged onto a CCD camera, providing crucial position information for subsequent data interpretation, including velocity history. A typical light spot distribution schematic is shown in Fig. 1(b). Since the flyer is usually semi-transparent, we can see the bridge foil through the semi-transparent flyer. The spot spacing and non-overlapping height of the PDV probe can be tailored to match the specific velocity field diagnosis requirements of EFI components with varying size parameters. The in situ detection capability of the light spot distribution ensures precise illumination of areas of interest, such as the corners of the bridge foil, the edges of the bridge zone, or any holes present in the bridge foil.

As shown in Fig. 1(a), the transparent LiF window replaces the initial explosive at the gun barrel’s exit, enabling the simultaneous measurement of both the free surface velocity of the flyer as it traverses the barrel and the interface particle velocity when the flyer impacts the LiF window, leveraging the PDV technology. In the typical velocity spectrogram of the flyer, it can be observed that there is a significant jump when the flyer plate impacts the LiF window. By analyzing these spectrograms, we can extract the velocity profiles of the flyer's impact surface and rear surface within the barrel. These profiles are denoted as V_impact(x, y, t) and V_rear(x, y, t), respectively, and include the interface particle velocity V_particle(x, y, t). In addition, for each measurement point, the impact time [T_impact(x, y)], impact velocity [V_impact(x, y, T_impact)], and impact pulse width [τ(x, y)] can be determined, as illustrated in Fig. 2(a).

The apparent velocity of the rear surface, as represented on the spectrogram, requires correction using the modification coefficient of the flyer material to obtain the true rear surface velocity curve.¹⁸ By integrating the velocity curves of the front and rear surfaces and subtracting the results, the thickness change history of the flyer can be derived, as shown in Fig. 2(b). Furthermore, the impact pulse width, which is defined by the interface particle velocity, is intricately linked to the thickness of the flyer prior to impact, according to the theory of plane impact.¹⁹ Consequently, the thickness information derived from subtracting the integrals of the velocity curves can be cross-validated with the experimental impact pulse width.

If a sufficient number of measurement points, for example, 40–100 points are strategically arranged on the surface of the flyer, it becomes feasible to accurately measure the velocity history of both the free surface and the interface particles across various spatial positions. By conducting a thorough correlation analysis and interpretation of these data in both the time and space dimensions, valuable insights into the integrity and planarity of the flyer can be gained.

During the cutting acceleration process within the gun barrel, the morphology of the flyer can be determined as follows: Assuming an ideal signal-to-noise ratio at each measuring point, it becomes feasible to extract the velocity curves corresponding to both the impact surface and the rear surface. By integrating these velocity profiles, these two integral displacement of each measuring point can be accurately calculated. This information can then be used to reconstruct the shape of the impact surface and the thickness of the flyer inside the barrel.

The morphology of the flyer at the moment of impact with the LiF window can be characterized in the following ways: The integrity of the flyer, or its effective area, is indicated by the presence or absence of the valid signal from the measuring point at different spatial positions. The planarity of the flyer, referring to the shape of its impact surface, is determined by the time differences between the impacts of each measuring point on the transparent LiF window. Furthermore, the relative difference in the thickness of the flyer, specifically the thickness between the impact surface and the rear surface, is characterized by the pulse width of the impact of each measuring point on the LiF window.¹⁹ If the flyer remains intact without any signs of spalling or delamination, it becomes feasible to reconstruct its three-dimensional morphology at the moment of impact, as depicted in Fig. 3. Δt(x,y) signifies the time lag between the impact at the measuring point located at (x,y) and the initial impact. On the other hand, Z(x,y) represents the displacement calculated through velocity integration over this time interval, serving as an indicator of the flyer’s planarity. Finally, H(x,y) characterizes the thickness distribution of the flyer plate derived from the pulse width of particle velocity.²⁰ 

Given the distinctive characteristics of EFI, including its brief motion duration, which ranges from 100 to 500 ns and significant velocity variations, which span from 0 to 5.0 km/s, the PDV data processing program has undergone meticulous optimization through the prudent selection of processing parameters. When the signal-to-noise ratio of the interference signals recorded by the oscilloscope is approximately equal to 1, the PDV data processing software can achieve the following indicators^20,21: (1) An uncertainty of no more than 10 m/s for the flyer's free surface velocity during the slow-varying section; (2) an uncertainty of no more than 35 m/s for the particle velocity at the interface within the slow-varying section; and (3) an interpretation uncertainty of ≤0.5 ns for impact time and pulse width. It is noteworthy that this uncertainty diminishes when the interferometric signal-to-noise ratio exceeds 1, while it tends to increase when the ratio falls below 1.

The dimensions of the copper bridge foil of the transducer element used in the experiment are 0.45 × 0.45 mm², and the thickness of the polyimide flyer is 47 μm. As described in Sec. II A, a transparent LiF window was positioned at the exit of the gun barrel. Through this window, the outgoing light spot from the probe illuminated the surface of the flyer within the barrel. The distribution of the light spot was captured by a camera, resulting in the image shown in Fig. 4(a). Sixty-one measurement spots were arranged in an equilateral triangular pattern, maintaining a spot spacing of approximately 58 μm and a spot coverage diameter of at least 400 μm. Notably, the light spots did not overlap within the height range of the gun barrel, thus eliminating any crosstalk between the signals of adjacent measurement points. Figure 4(b) provides a visual representation of the light spot distribution within the actual gun barrel. It clearly depicts how all 61 light spots (with only 56 utilized for the PDV measurement) are distributed evenly across the surface of the bridge foil. Notably, the bridge foil exhibits a slight eccentricity within the gun barrel.

The PDV system utilized in the test is a wavelength-division time-division multiplexing PDV, designed and developed by Institute of Fluid Physics, China Academy of Engineering Physics. In conjunction with two 4-channel oscilloscopes, this sophisticated system is capable of accurately measuring the flyer velocity at 56 distinct channels, with a maximum velocity measurement capability of 5 km/s or greater.

The interference signals captured by the oscilloscope are processed by our optimized data processing program to generate velocity spectrograms corresponding to the spatial locations of the 56 measured spots depicted in Fig. 4(a). In order to obtain these velocity spectra of the flyer, the window width chosen for the windowed Fourier transform is 10.24 ns, with a non-overlapping interval of 0.24 ns. According to the conservative analysis of Eq. (2) in Ref. 20, the uncertainty of the flyer velocity is small than 6.1 m/s. As illustrated in Fig. 5, these spectrograms exhibit satisfactory signal-to-noise ratios, with each spectrogram displaying one or two distinct and clear ridges. The aforementioned ridges correspond to the velocity history of the free surface of the flyer and the particle velocity history during the impact of the flyer hitting the LiF window.

Extract the impact surface velocity curves (specifically, the one located below the two distinct ridges) for all measuring points depicted in Fig. 5 and compile them into a single diagram. According to Fig. 6(a), the difference between the velocity at different times and the average is within ±100 m/s. Additionally, Fig. 6(b) illustrates that the standard deviation of the velocity curve at each time remains mostly below 40 m/s. It is noteworthy that in Fig. 6(a), the velocity curves of all measuring points exhibit a downward trend in the final nanoseconds before impact. This trend is attributed to the limitations of the data processing method in regions of velocity mutation, rather than reflecting an actual physical process.

The displacement curve is derived through the integration of the velocity curve. Assuming that the angle between the motion direction of the flyer and the laser beam direction within the measurement area is 5°or less, which is typically the case, the error incurred in the displacement calculation through velocity integration remains within 0.5%. By extracting the displacements of each measurement point at corresponding time points and employing surface fitting techniques, we can reconstruct the evolution of the flyer impact surface shape within the gun barrel and its configuration upon striking the LiF window. Figure 7 illustrates the surface shapes captured at 40 ns intervals, spanning from 580 to 740 ns. The final image depicts the impact moment. The surface profiles consistently exhibit a pot-like structure with a raised center and depressed periphery, where the maximum deviation between the highest and lowest points is less than 10 μm. This flyer state aligns with the desired configuration sought by researchers.

Additionally, the impact time and impact pulse width of each measurement point can also be extracted from particle velocity spectrogram. When calculating the particle velocity spectrum, the windowed Fourier transform adopts a window width of 1.92 ns and a non-overlapping interval of 0.12 ns. Obviously, the window width of 1.92 ns will cause the widening of the rising or falling edge of the particle velocity. However, during data processing, an accuracy of less than 0.5 ns can be guaranteed by using 50% position of the rising or falling edge of the interface particle velocity as the basis for the impact time and impact pulse duration. Therefore, when the flyer plate velocity is lower than 4 km/s, the reconstruction uncertainty in the Z direction of the flyer is small than 2 μm. The surface shape and impact duration distribution at the impact moment can be obtained by surface fitting methods. It is noteworthy the surface shape also exhibits a pot-like structure, characterized by a raised center and depressed edges, with a height difference of less than 10 μm between the highest and lowest points. A comparison between Figs. 7(j) and 8(a) reveals a remarkable congruency between the surface shape at the impact moment obtained through velocity integration and the surface shape reconstructed based on the impact time.

Figure 5 illustrates the velocity spectrograms of each measurement point, which often reveal two distinct ridges. These correspond to the velocity profiles of the flyer’s impact surface and the rear surface with the bridge foil, respectively. It is evident that the velocity ridges obtained at the edges of the flyer, particularly the upper and lower edges, exhibit a greater degree of separation compared to those obtained at the central points. This indicates that the difference in integrated displacement between the two curves is smaller for the edge points, suggesting that the thickness of the flyer’s edges is thinner than that of the center. This qualitative observation is consistent with the pulse width being longer in the central region and shorter at the edges when the flyer impacts the LiF window in Fig. 8(b).

Utilizing the impact surface profile reconstructed at the impact moment and the thickness information of the flyer derived from the duration of the impact pulse, a three-dimensional representation of the flyer's morphology within an approximately 400 μm diameter region was successfully reconstructed. This reconstruction is depicted in Fig. 9. Assuming a consistent density throughout the flyer, Fig. 10 presents the integral projections of the flyer, both perpendicular to and along the direction of the current. When viewed perpendicular to the current direction, the flyer appears predominantly flat. However, when viewed along the current direction, a slight concave shape is observed in the center of the flyer. The integral projection results are generally consistent with the flyer's morphology captured through x-ray radiography in Ref. 4 when it exits the gun barrel and travels a short distance. As shown in Fig. 4(b), the spots arranged in an equilateral hexagonal pattern do not completely cover the entire surface of the flyer within the gun barrel, resulting in a certain degree of discrepancy between the current integral projection and the actual integral projection of the flyer. In future work, our objective is to develop a microscopic PDV probe capable of measuring approximately 90 points, thereby providing a comprehensive coverage of the surface of the flyer within the gun barrel. Furthermore, we intend to undertake joint diagnostic efforts with x-ray radiography techniques to procure more conclusive and convincing comparative results.

The introduction of an LiF window positioned behind the gun barrel has enabled the flyer's movement to no longer pose a threat to the velocity measurement probe. This has allowed for the use of microscopic PDV technology, which can be employed to carry out experiments at a rate of approximately 5–10 shots per hour. This has resulted in a significant enhancement of experimental efficiency and a reduction in experimental costs compared to x-ray radiography techniques that rely on large-scale light sources.

This paper presents a novel approach to three-dimensional morphology characterization of EFI flyers based on microscopic PDV velocity field measurement. Compared to x-ray imaging technology, this method offers nanosecond time resolution and micrometer spatial resolution for quantitative characterization of the three-dimensional morphology of the flyer inside and outside the gun barrel, without requiring any modification to the product structure (such as the gun barrel). The microscopic PDV technology, renowned for its high spatiotemporal resolution, particularly its capability for in situ detection of spot distribution, promises to be a powerful technical tool in investigating the action mechanism of EFI as well as assessing the impact of various factors like bridge foil eccentricity, bridge foil defects, and product aging on the flyer’s morphology. Moreover, the reconstructed three-dimensional morphology of the flyer at the precise moment of impact, based on the impact time and impact pulse width, is of significant value for the establishment of volume-based shock initiation criteria for initial explosive agents, such as HNS.

This work was supported by the National Natural Science Foundation of China (Grant No. 12072330).

The authors have no conflicts to disclose.

Shouxian Liu: Conceptualization (equal); Data curation (equal); Funding acquisition (equal); Investigation (equal); Methodology (lead); Software (equal); Visualization (equal); Writing – original draft (equal). Jianzhong Li: Conceptualization (equal); Investigation (equal); Methodology (supporting); Resources (equal). Binqiang Luo: Data curation (equal); Investigation (equal); Resources (equal); Validation (equal). Rongjie Shui: Data curation (equal); Resources (equal); Validation (equal). Jiangbo Lei: Conceptualization (equal); Resources (equal); Validation (equal). Wenbin Huang: Conceptualization (equal); Investigation (equal); Methodology (equal); Validation (equal). Xincai Zhao: Conceptualization (equal); Formal analysis (equal); Resources (equal). Jing Wang: Conceptualization (equal); Resources (equal); Validation (equal). Yan Ye: Conceptualization (equal); Resources (equal); Supervision (equal). Qixian Peng: Conceptualization (equal); Resources (equal). Liguo Zhu: Conceptualization (equal); Project administration (equal); Supervision (equal). Xianxu Zhen: Conceptualization (equal); Project administration (equal); Supervision (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.