We evaluate the energy conversion efficiency of an electrical exploding foil accelerator that accelerates a thin dielectric foil (called the flyer) to more than 1 km/s, which is propelled by electrically exploded bridge material. The effective flyer mass ejected from the accelerator is estimated by impulse measurements obtained using a gravity pendulum as well as by time-resolving flyer velocity measurements obtained using a photonic Doppler velocimetry system. For two different bridge sizes (0.2 and 0.4 mm), the flyer velocity and impulse increase with the input energy at the bridge section. The maximum flyer velocity and impulse, that is, 4.0 km/s and 67 µN s, respectively, are obtained by supplying 0.33 J of input energy. Upon increasing the input energy, the effective flyer mass also increases and exceeds the designed-bridge mass for both bridge sizes. The energy conversion efficiency from input electrical energy to flyer kinetic energy is calculated based on the effective flyer mass, velocity, and input energy. Both bridge sizes show comparable efficiencies: 27% and 30% for 0.2 and 0.4 mm bridges, respectively. The efficiency increases with increasing specific input energy at least up to 15 MJ/kg for the 0.4 mm bridge, whereas the efficiency of the 0.2 mm bridge above 30 MJ/kg decreases. This is owing to the excessively high input energy density in the 0.2 mm bridge, which causes the effective flyer mass to increase by including surrounding materials. These results indicate that the specific input energy should be optimized for obtaining maximum efficiency.
An electrical exploding foil accelerator is a unique small-scale device for accelerating a thin dielectric foil to high velocities (∼20 km/s1). Owing to developments and adaptations for high-energy sources, it has become increasingly useful for high-pressure and initiation devices2,3 compared to other pulsed-power sources such as lasers and charged particle beams. Generally, an exploding foil accelerator comprises three layers: a substrate, a conductive layer with a small conversion section (often referred to as the “bridge”), and a dielectric flyer. Although the construction of an exploding foil accelerator itself is simple, its flyer acceleration mechanisms are complicated, and clarifying the entire process remains challenging because of the small size (typically of the order of 0.1 mm) and time scales (the flyer acceleration completes within several hundred nanoseconds). The flyer terminal velocity of a given material and/or electrical configuration and the conversion efficiency of input energy to material acceleration are essential considerations.4 Gurney5 developed an analytical model for estimating the initial velocity. Subsequently, several studies have modified the original Gurney model to improve its accuracy6,7 with experimental validation.8 Rigorous modeling of the flyer acceleration by bridge explosion typically involves the use of a hydrocode with detonation equations.9,10 The development of time-resolving velocimetry techniques, such as the velocity interferometer system for any reflector (VISAR)11 and photonic Doppler velocimetry (PDV),12 has facilitated direct comparison of the numerical results and experimental data. In contrast, few studies have quantitatively investigated the energy conversion efficiency of the flyer acceleration process.4 Because the effective mass ejected by the bridge explosion is of the same order as the designed-bridge mass (order of 10−9 kg), precisely measuring the difference in mass before and after ignition and correspondingly the kinetic energy of the flyer is exceedingly difficult.13 In this study, we estimate the effective mass indirectly based on a combination of the impulse produced by the flyer upon impact with a target and flyer velocity measurements. For the impulse measurement, we use a gravity pendulum-type impulse stand, which is typically used in space propulsion research.14 Combining this measurement with the velocity measurement obtained using a PDV system, the correlation between the specific input energy and flyer kinetic energy for two different bridge sizes is described and discussed with respect to the input electrical energy.
II. EXPERIMENTAL APPARATUS AND PROCEDURE
A. Electrical exploding foil device and flyer velocity measurement
Figures 1(a) and 1(b) present the schematics of the flyer assembly and experimental setup for the flyer velocity measurement with its electrical circuit, respectively. The device comprised three layers: a 25-μm-thick substrate layer (polyimide), a 9-μm-thick conductive layer (copper), and a 25-μm-thick flyer (polyimide). In addition, a 300-nm-thick aluminum reflection layer was deposited on the flyer. The conductive layer included a converged square-shaped section (“bridge”), with a side length of lb (0.2 or 0.4 mm). The designed-bridge mass (mb) for lb = 0.2 and 0.4 mm was 4.7 × 10−9 and 1.9 × 10−8 kg, respectively. The device was mounted on a mount plate supported by the XY, Z, and gonio stages and pressed using a presser plate with a visualization window (4 mm height and 6 mm width). The electrical circuit for device initiation is depicted in Fig. 1. The device was parallelly connected, and the capacitor was charged by the high-voltage DC power supply. After the condenser was charged by the power supply, the switch was turned on to serially connect the device for flyer initiation. The discharge current and voltage were measured using a voltage probe (THDP0100, Tektronix, Inc.) and two Rogowski coils (CWT UM/30 B/1/80, Power Electronic Measurements Ltd.). The flyer velocity was measured using a commercial modular PDV system (VH17, IDIL Fibres Optiques) with a band-pass filter (TBF-1550-1.0-FCAPC, Newport Corporation) having a center wavelength of 1550 nm and a bandwidth of 0.8 nm. A PDV probe with an outer diameter of 3.2 mm and a working distance of 50 mm was set in the PDV probe holder with two gauge pins for adjusting the probe center with respect to the bridge center. The distance between the probe head and bridge surfaces was 8 mm, which was within the probe working distance. To record the discharge current, discharge voltage, and PDV signal, two oscilloscopes (1 and 2) were used: oscilloscope 1 (MDO4024C, Tektronix, Inc.), with a sampling rate of 1.25 GHz, recorded the discharge current and voltage of the condenser, whereas oscilloscope 2 (SDA 820Zi-B, Teledyne LeCroy), with a sampling rate of 80 GHz, recorded the discharge current and the PDV probe signal. In both recordings, the discharge current was used as the trigger signal.
An example plot of the time history of the discharge power (Pb, left axis) and flyer velocity (u, right axis) for lb = 0.4 mm is displayed in Fig. 2. The input power (Pb) was calculated based on the discharge voltage and current data. At t = 73 ns, Pb reached the maximum value of 8.1 MW and, simultaneously, the bridge section exploded (burst time)15 after which Pb gradually converged to zero. The input energy (Eb) to the bridge section is defined as the result of time integration of Pb,
For the operation condition shown in Fig. 2, Eb was calculated to be 0.33 J. When the bridge exploded, the flyer accelerated. The measured history of u (gray line) was fitted using a sixth-order polynomial approximation (blue line). The rise time of u was adjusted to the burst time in order to cancel out the internal time delay in the PDV system. The flyer velocity increased rapidly, and at t = 335 ns (262 ns after the burst time), a terminal velocity of 2.9 km/s was reached. The flyer terminal velocity was evaluated and used for estimating the effective bridge mass and related parameters as described below.
B. High-speed imaging
To verify the flyer velocity measurement by PDV, we performed flyer visualization using a shadowgraph imaging technique, as depicted in Fig. 3. In the shadowgraph method, a 50-Mfps high-speed camera (Ultra-8, Hadland Imaging, LLC) and a pulsed diode laser (Cavilux Smart, Cavitar) with a wavelength of 640 nm and an emission time of 20 ns that was used as the light source were activated with an appropriate delay time using a delay generator (DG645, Stanford Research Systems), which was triggered by the discharge current signal from the Rogowski coil. A band-pass filter (PB0640-060, Asahi Spectra Co., Ltd.), with a central wavelength of 640 nm and a bandwidth of 10 nm, was installed immediately in front of the high-speed camera to remove the emissions caused by bridge explosion, thereby improving the contrast and resolution of the experimental features. The flap angle of the bridge surface with respect to the laser light was adjusted using the gonio stage.
C. Impulse measurement
The impulse produced by the flyer impact was measured using a gravity pendulum-type impulse stand. Figure 4(a) illustrates the pendulum and bridge with its fixture. The pendulum comprised a 381-mm-long pendulum arm supported by two knife edges at the fulcrum, a 3D-printed flyer catcher, and an eddy current damper. The knife edges were made of stainless steel (ISO 4401-316-00-I), with a width of 10 mm and an apex angle of 60°. Each knife edge was mounted on a V-shaped groove with a full apex angle of 120°. Each groove was formed by two blocks of stainless steel (ISO: 4301-304-00-I) such that the bottom was not rounded. The eddy current damper included an aluminum plate, and a neodymium magnet dampened the pendulum oscillation. Figure 4(b) displays a magnified image of the flyer catcher with a 20-mm diameter inner hole, 6-mm height, and a 6-mm entrance hole. Because the flyer moved with the compressing atmospheric air, the flyer catcher included 16 exhaust holes, with a diameter of 1.0 mm each, set every 45° on the side-surface. The bridge was mounted on an L-shaped plate in front of the flyer catcher. The flyer catcher and bridge were set coaxially, and the distance between the flyer catcher entrance and bridge surface was set to 3.5 mm, where the accelerated flyer reaches the terminal velocity. A laser displacement sensor (LDS) (IL-030, Keyence Corporation), with a resolution of 1 µm, was used to measure the pendulum displacement, which was recorded using an oscilloscope (DL850E, Yokogawa Test & Measurement Corporation) at a sampling rate of 500 kHz, triggered by the discharge current.
Figure 5 depicts the time history plot of the pendulum displacement (red line) for lb = 0.2 mm and Eb = 0.33 J. The LDS signal was fitted using a dumping function (black dashed line) to calculate the envelope (black short-dash line). The fitted curve indicated that the natural oscillation period was 1.0 s, which was considerably larger than the timescale of bridge explosion (on the order of 100 ns). The pendulum was calibrated up to 97 µN s using an impact hammer (086E80, PCB Piezotronics, Inc.) supported by another knife edge, which is not shown in Fig. 4. The level of impact was varied by changing the angle of rise using metal washers, a pulley, an electromagnet, and a microstage. The impact point was the same as that of the flyer catcher. We applied the same calibration procedure described in Ref. 16. The calibration factor was 341 µN s/V and the regression correlation coefficient was 0.999. The uncertainty in the impulse measurement, which was caused by the repeatability and/or the curve fitting, was less than ±0.8 µN s, which was 1.2% of the minimum impulse value under the operation conditions.
III. RESULTS AND DISCUSSIONS
In Sec. III A, the experimental results of flyer velocity validated by high-speed imaging and impulse measurement are presented. All experiments were conducted under atmospheric pressure. The effective flyer mass and energy conservation efficiency were evaluated based on these results.
A. Flyer velocity and induced impulse characteristics
We measured the flyer velocities at different Eb values using high-speed imaging as well as PDV. Figure 6 shows the shadowgraph images of bridge explosion with lb = 0.2 mm and Eb = 0.33 J. All images were acquired perpendicular to the discharge current direction. The flyer was expected to be at the top of the particle cloud, which consisted of vaporized copper and polyimide flyer. However, unlike x-ray imaging,17 the shadowgraph imaging used in this study cannot visualize the internal structure of the particle cloud because the incident 640-nm light was reflected and/or refracted at the cloud. Figure 6 shows the corresponding projection profile of the cloud. When the bridge exploded, a hemispherical particle cloud was generated. The particle cloud expanded with time, maintaining a hemispherical shape, and the cloud radius (indicated by the white arrow in Fig. 6) gradually increased. In Ref. 17, detailed 3D in-flight flyer images, in which the flyer departs from the substrate, were reported; the radius of the flyer shape was consistent with that of our experiment. The cloud radius in each frame was estimated by counting the number of pixels, where a single pixel corresponded to 8.0 ± 0.05 µm, and calibrated using a glass-made reference scale. The estimated cloud radius in each frame is also depicted in Fig. 6, and based on the variation of the radius with time, the expansion speed of the cloud head was calculated to be 4.0 ± 0.15 km/s.
Figure 7(a) shows the flyer velocity (u) measured by the PDV system for different lb values. The input energy Eb was in the range of 0.15–0.33 J for lb = 0.2 mm and 0.13–0.33 J for lb = 0.4 mm. For both lb values, the measured u increased almost linearly with the increase in Eb, and at Eb = 0.33 J, u was measured to be 3.9 ± 0.1 and 2.9 ± 0.07 km/s for lb = 0.2 and 0.4 mm, respectively. The open symbols shown in Fig. 7(a) at Eb = 0.33 J were obtained through shadowgraph imaging. For the case with lb = 0.2 mm, the open and closed symbols overlapped. For both bridge sizes, the velocity measured through the PDV system agreed well with that of the shadowgraph imaging. The lb = 0.4 mm case exhibited a higher rate of increase in u with increasing Eb values; within the operating conditions, the velocity increase rates were 2.8 and 6.7 km/s/J for lb = 0.2 and 0.4 mm, respectively.
Figure 7(b) depicts the induced impulse (I) at the flyer catcher for different lb values. Overall, the measured impulse increased linearly with an increase in Eb. However, in contrast to the velocity values, a smaller bridge size resulted in a smaller impulse; at Eb = 0.33 J, I was measured to be 45 and 67 µN s for lb = 0.2 and 0.4 mm, respectively. The slope of the line from the origin represents the momentum-coupling coefficient (Cm ≡ I/Eb);14 hence, a higher Cm indicates more efficient energy conversion from the input electrical energy to the kinetic energy of the flyer. The maximum value of Cm was obtained at Eb = 0.33 J, and the values of Cm for lb = 0.2 and 0.4 mm were 136 and 200 µN s/J, respectively. The energy conversion efficiency is discussed in Sec. III B.
B. Energy conservation from the input electrical energy to the flyer kinetic energy
We estimated the flyer effective mass based on the u and I values measured in the aforementioned procedures and evaluated the energy conversion efficiency for conversion from the input electrical energy to flyer kinetic energy.
Figure 8 shows the dependence of the normalized flyer effective mass mb,eff/mb on Eb. The effective mass mb,eff was calculated using the relationship mb,eff = I/u. For both lb values, mb,eff/mb increased linearly with an increase in Eb and exceeded 1.0 at Eb = 0.15 J for lb = 0.2 mm and Eb = 0.26 J for lb = 0.4 mm. This indicates that the exploded area was larger than the designed-bridge area. Lei et al.18 presented several bridge images after explosion, where the exploded area increased with an increase in input energy and was larger than the designed-bridge area. In our experiment, the minimum distance (d) between the non-exploded electrodes was measured using a laser microscope (VK-X3000, Keyence Corporation). At Eb = 0.33 J, d/lb was found to be 3.8 for lb = 0.2 mm and 1.5 for lb = 0.4 mm, which is consistent with mb,eff/mb = 2.5 and 1.2 for lb = 0.2 and 0.4 mm, respectively.
Information on the input energy, effective flyer mass, and flyer velocity enabled the calculation of the energy conversion efficiency at the bridge section. Figure 9 displays the specific kinetic energy (u2/2) as a function of the specific input energy (Eb/mb,eff) for various lb values. The slope of the line from the origin represents the energy conversion efficiency [ηb ≡ (u2/2)/(Eb/mb,eff)]. For lb = 0.4 mm, Eb/mb,eff ranged from 9.4 to 15 MJ/kg, and u2/2 increased with the increase in Eb/mb,eff from 1.1 MJ/kg at Eb/mb,eff = 9.4 MJ/kg (ηb = 12%) to 4.3 MJ/kg at Eb/mb,eff = 15 MJ/kg (ηb = 30%). For lb = 0.2 mm, Eb/mb,eff and u2/2 were larger with comparable ηb; at Eb/mb,eff = 29 MJ/kg, u2/2 = 7.7 MJ/kg (ηb = 27%), whereas at Eb/mb,eff = 34 MJ/kg, u2/2 = 5.7 MJ/kg (ηb = 17%). Although both lb values exhibited comparable ηb, the Eb/mb,eff dependency of ηb exhibited contrasting behavior in the operation range examined. As shown in Fig. 8, the rates of increase in (mb,eff/mb)/Eb are 11 and 1.4 J−1 for lb = 0.2 and 0.4 mm, respectively. This result indicates that compared to the lb = 0.4 mm case, not only the designed-bridge area but also the surrounding materials exploded for the lb = 0.2 mm case owing to the excessively high input energy density. Therefore, Eb/mb,eff decreased with the increase in Eb. Thus, the quantitative evaluation of the effective flyer mass helped us infer that the specific input energy should be optimized in order to maximize the energy conversion efficiency.
In this study, we quantitatively investigated the energy conversion efficiency of an electrical exploding foil accelerator for two different bridge sizes (0.2 and 0.4 mm square) based on the flyer velocity and induced impulse measurements. For measuring the flyer velocity and impulse, a PDV system validated using high-speed imaging analysis and a gravity pendulum-type impulse stand, respectively, were used. With an increase in the input energy at the bridge section, the flyer velocity as well as the impulse increased almost linearly. The maximum flyer velocity was 3.9 km/s with an impulse of 45 µNs and 2.9 km/s with an impulse of 67 µNs for the 0.2 and 0.4 mm square bridges, respectively. The effective exploded-bridge mass calculated from the velocity and impulse data increased with input energy and was up to 2.5 times greater than that of the designed-bridge mass. The energy conversion efficiency from the electrical input energy to the flyer kinetic energy was evaluated based on the input energy, flyer velocity, and effective exploded bridge mass. Regardless of the bridge size, the maximum values of ηb were comparable (27% and 30% for the 0.2 and 0.4 mm square bridges, respectively), whereas the specific input energy dependency of the efficiency was contrasting. A higher specific input energy resulted in higher efficiency for the 0.4 mm bridge at least up to 15 MJ/kg, whereas the 0.2 mm bridge exhibited a contrasting dependency above 30 MJ/kg owing to the excessively high energy density; therefore, the effective flyer mass increased rapidly by including the surrounding materials. These results indicate that the specific input energy should be optimized for maximizing the efficiency and requires further investigation.
This research was supported by Japan Society for the Promotion of Science Grant-in-Aid for Early-Career Scientists Grant No. JP20K14950.
The data that support the findings of this study are available within the article.