Cylindrical copper wire array explosions were carried out in de-ionized water, sodium polytungstate solution, nitromethane, and polyester in order to obtain high energy density conditions in the vicinity of implosion using the generated converging shock waves. The use of different materials in which the array is immersed can contribute to this goal with higher density resulting in higher shock velocities and possible combustion. The generated shock waves were captured by a framing and a streak camera, and shock velocities were calculated and compared. The pressure behind the shock front was calculated using the known hydrodynamic relations (for water, polytungstate, and polyester) and compared to two-dimensional hydrodynamic simulations coupled with the equations of state (for water and polyester). It was shown that despite lower shock wave velocity in polytungstate solution than in water, the pressures generated are similar in both materials. In polyester, both shock velocities and generated pressures are 2–4 times higher than in water. It was also shown that it is possible to carry out these explosions in a solid which has several advantages compared to liquids, such as not relying on waterproof systems and easier transportation.

The electrically driven explosion of wires is of great interest to the high energy density physics community for both basic research studies including investigations of equations of state (EOS),1 conductivity models,2 and hydrodynamic instabilities3 and practical applications such as the production of nanopowders and fracking.4,5 While many experiments are performed exploding wires in a vacuum or in air, exploding wires in water offers several advantages—the water prevents the formation of surface plasma on the wires early in time, while water's low compressibility prevents the rapid expansion of the wire material. Together, these effects prevent the formation of low resistance paths through the wire material until relatively late in time, significantly increasing the efficiency of energy transfer from a pulsed power generator to the wires. Given its low compressibility, when the wires do explode into the gas phase and start to ionize, strong shock waves are launched into the surrounding water.6 If the wires are exploded in a cylindrical, spherical, or superspherical geometry,7 shock waves from adjacent wires will merge, and convergence can produce extreme densities and pressures on axis,8–10 ideal for warm dense matter studies.

Seeking to explore the effects of different media on wire explosion, a recent series of studies at the Technion have been performed with single wires and spherical wire arrays in glycerol.11–13 Again the insulating properties of glycerol and its low compressibility meant that the wires exploded in a similar manner to when the experiments were performed in water—however, the velocity of the generated shock waves was ∼20% higher than in water, and the resulting pressure in the vicinity of implosion was predicted to be approximately two times greater. In addition, evidence was found that the combustion of glycerol contributed to the energy of the converging shock. In the work carried out by Han et al., discrete pressure probes were used as diagnostic tools for single wire explosions covered by energetic materials and immersed in solid powders.8,9 The explosions in these materials showed lengthened shock wave duration and the generation of a second shock, probably due to the detonation of the material. The explosion in powders showed that the shock waves that were generated could not easily pass through the air/powder interface.

In this paper, we aim to further explore the production of shock waves in insulating media—particularly examining the effects of density and compressibility through the use of sodium polytungstate solution, a high density liquid with similar compressibility to water, and by embedding the wires in polyester resin which set as a solid with significantly lower compressibility. We also explore the effects of combustion through the use of nitromethane. Table I summarizes the different material properties. Providing that it could be used as a media, solidifying polyester resin also presents two long term advantages for research—it could enable the use of a cartridge based loading system, removing the need for liquid handling within the pulsed power generator, and it could support the production of far more complex wire geometries than at present, which have to be loaded in situ.

TABLE I.

Material properties in which the wire array was exploded.

MaterialDensity (kg/m3)Speed of sound (m/s)Impedance (Pa × s/m)Heat of combustion (J/kg)
Water 1000 1500 1.5 × 106 … 
Sodium polytungstate solution (85%) 3000 1600 4.8 × 106 … 
Polyester 1380 2400 2.1 × 106 ∼24 × 106 
Nitromethane 1140 1130 1.3 × 106 11 × 106 
Glycerol 1260 1920 2.4 × 106 18 × 106 
MaterialDensity (kg/m3)Speed of sound (m/s)Impedance (Pa × s/m)Heat of combustion (J/kg)
Water 1000 1500 1.5 × 106 … 
Sodium polytungstate solution (85%) 3000 1600 4.8 × 106 … 
Polyester 1380 2400 2.1 × 106 ∼24 × 106 
Nitromethane 1140 1130 1.3 × 106 11 × 106 
Glycerol 1260 1920 2.4 × 106 18 × 106 

The structure of the remainder of this paper is as follows: In Sec. II, the experimental setup is described. In Sec. III, the results of the experiment are presented. In Sec. III A, the current and voltage measurements are shown along with the calculated power and energy deposition, and the differences between the materials are discussed. In Sec. III B, the framing and streak shadowgraphy results are shown with the plots of shock wave trajectories. In Sec. IV, estimations of pressures in the vicinity of implosion are presented using hydrodynamic simulations and analytical calculations. Finally, conclusions are provided in Sec. V.

The experiments were carried out at the Mega-Ampère-Compression-and-Hydrodynamics (MACH) facility at Imperial College London. MACH is a compact pulsed power generator that was designed to produce up to 2 MA currents with ∼450 ns rise times when connected to a low inductance (<5 nH) transmission line and load. MACH is configured as a set of 40 parallel capacitors in series with 20 low inductance switches that are connected via a radial feed. In its simplest form, this can be represented as a lumped 6 μF capacitance in series with an inductance of ∼20 nH and a resistance of 15 mΩ.

In the present experiment, the capacitors were charged to 60 kV and discharged through a 10 mm diameter cylindrical copper wire array consisting of 60 wires of 125 μm diameter and 50 mm length each, with an inductance of ∼10 nH. The wire initial diameters were calculated using the current action integral10 to obtain the fastest and most efficient explosion of the wires. Prior to the wire array explosions, copper rods of either 2 mm or 10 mm were used as short circuit loads for calibrations of voltage and current probes. The current through and voltage across the wires were measured using two B-dot and two D-dot probes placed 90° apart from each other and at a distance of 15 cm from the center. The diagram of the experimental setup is presented in Fig. 1 and an external view of the wire array in Fig. 2. The setup was improved since the previous cylindrical array experiments11 by using smaller array holders and an acrylic tube to hold the material in which the array was immersed. This was done to reduce the load's inductance and simplify the loading process.

FIG. 1.

Experimental setup. Blue arrows indicate the direction of current flow. B-dot and D-dot probes were fitted into the indicated holes with more of each in at 90° angle.

FIG. 1.

Experimental setup. Blue arrows indicate the direction of current flow. B-dot and D-dot probes were fitted into the indicated holes with more of each in at 90° angle.

Close modal
FIG. 2.

Wire array picture inside the acrylic tube stretched between stainless steel electrodes.

FIG. 2.

Wire array picture inside the acrylic tube stretched between stainless steel electrodes.

Close modal

The array was immersed in either de-ionized water, sodium polytungstate solution, nitromethane, or polyester. The polytungstate solution was supplied by Sigma-Aldrich, with the formula Na6O39W12, a concentration of 85% in water, and a molecular weight of 2968 g/mol. The liquids were poured through the hole in the electrode shown in Fig. 2. The polyester resin, initially in liquid form, was mixed with a catalyst and then degassed in a vacuum chamber, and the explosion was carried out approximately 24 h after waiting for it to set and be in solid form. No bubbles remained on the surface of the wires.

Laser shadowgraphy was used to capture the dynamics of the generated shock waves. A beam of 532 nm, 6.5 W laser was coupled to a single-mode optical fiber and then collimated into a ∼15 mm diameter beam before being fed through the array. The beam was then relayed to an optical table and then split to an Invisible Vision framing camera with twelve 1024 × 1024 pixel frames with an exposure of 10 ns and a Kentech 40 mm optical streak camera backed with a digital single lens reflex camera. Calibration of timing was done using a high-speed light emitting diode pulser and of magnification using test objects placed at the midpoint of the array. A detailed diagram of the optical path can be found in Ref. 11.

Typical waveforms of current, resistive voltage, power, and energy are presented in Fig. 3. The resistive voltage was calculated as VResistive=VtotalLdI/dt, where L is the inductance of the system from the point of the voltage measurement and I is the current through the load. The total inductance of the system was measured for a short circuit load and found to be ∼35 nH. The inductance from the point of voltage measurement with an exploding wire array load was found to be ∼12 nH. Figure 3(a) includes also the current measured with a short circuit load (10 mm copper rod) for comparison.

FIG. 3.

Waveforms of measured (a) current and (b) resistive voltage and calculated (c) power and (d) energy deposition.

FIG. 3.

Waveforms of measured (a) current and (b) resistive voltage and calculated (c) power and (d) energy deposition.

Close modal

The peaks at the start of the resistive voltage waveforms (near t =0) are partially because of noisy D-dot probes in the beginning (<100 ns) of the discharge corresponding to the switch closing and possible initial nonuniformity in the current distribution among wires because of nonperfect wire contacts with the electrodes.

Except for the explosion in polyester, the current waveforms are aperiodic, where most of the stored energy transfers to the Ohmic heating of the wire instead of oscillating back and forth between the wires and the capacitors as a lightly damped circuit. The polyester waveform decays fast after the current peak, then slowly drops to zero, and becomes periodic. The peaks in the resistive voltage waveforms coincide with the rapid drop in current which corresponds to the solid/liquid to liquid/gas phase transition where the resistivity rapidly rises. In polyester, a plateau is seen in the voltage waveform. Polyester's different behaviors of current and resistive voltage after peak current can be explained by a breakdown accompanied by a relatively low resistance plasma formation that occurred during the shot along the surface of the wire. This breakdown, however, occurs after the peak in current and thus has small influence on the generated shock waves.

The energy deposited into the wire array [see Fig. 3(d)] during the first 2.5 μs is smaller as compared to the stored energy of ∼10.8 kJ. The important period of energy deposition is up to the fast drop in current where the shock wave is launched into the surrounding material. One can see that the energy is best coupled to the array until this time in the following order: polyester, polytungstate solution, nitromethane, and de-ionized water. These differences in energy deposition can be explained by the different expansion rates of the wires in different materials influencing the change in resistance, which results in different heating rates (slower expansion leads to higher energy deposition due to larger resistance). The expansion rate is expected to be the slowest in polyester due to its lower compressibility. For the liquids, the wires are expected to expand the slowest in the polytungstate solution, then in nitromethane, and finally in water due to the higher densities of the polytungstate solution (∼3 g/cm3) and nitromethane (∼1.14 g/cm3).

FIG. 4.

Shadow images of the converging shock wave in water. Times are with respect to the beginning of the current rise.

FIG. 4.

Shadow images of the converging shock wave in water. Times are with respect to the beginning of the current rise.

Close modal

The shadow images of the converging shock waves are presented for water in Fig. 4 and a streak image for polytungstate solution in Fig. 5. One can see a high azimuthal uniformity of shock wave convergence. Similar framing and streak images were obtained for the rest of the materials except for nitromethane. Unfortunately, the laser shutters malfunctioned during the explosion in nitromethane, and the experiment was not repeated because of the great damage caused by the chemical explosion of the material. A dashed line was added to the streak image to highlight the shock trajectory, and two phases are clearly seen, an initial slow phase and a final fast phase. According to earlier experiments, these two phases are a result of two different waves. The first is a sound wave generated by the wires during solid-liquid-vapour phase transitions, and the second is a shock wave, which was launched later in time and overtook the sound wave, which was generated by the wire explosion.

FIG. 5.

Streak image of the converging shock wave in polytungstate solution. The dashed line is to highlight the shock trajectory. The image turns black near the end of the streak (at ∼1.9 μs) because this is the end of the camera's aperture.

FIG. 5.

Streak image of the converging shock wave in polytungstate solution. The dashed line is to highlight the shock trajectory. The image turns black near the end of the streak (at ∼1.9 μs) because this is the end of the camera's aperture.

Close modal
FIG. 6.

Shock wave velocities (d) and positions for (a) water, (b) polytungstate solution, and (c) polyester. Squares in (a)–(c) are from framing images, and lines are from streak images.

FIG. 6.

Shock wave velocities (d) and positions for (a) water, (b) polytungstate solution, and (c) polyester. Squares in (a)–(c) are from framing images, and lines are from streak images.

Close modal

The shock trajectories along with the current waveforms for both framing (squares) and streak images (line) are presented in Figs. 6(a)–6(c), and shock velocities are presented in Fig. 6(d). For comparison, the sound velocities in water and polyester are ∼1.5 km/s and ∼2.4 km/s, respectively, and the sound velocity in the polytungstate solution used in this experiment is ∼1.6 km/s.12 It is seen that the shock wave in polyester reaches the highest velocity, while the lowest velocity is in polytungstate solution. The result for polyester is expected, contrary to the result in the polytungstate solution which was expected to have higher shock velocity than water due to higher density.

To estimate the pressure behind the shock front, the following relation was used, which is derived from the Hugoniot relations under the assumptions of a perfect gas with constant specific heats and strong shocks:13 

p=2ρ0us2γ+1,
(1)

where p is the pressure behind the shock front, ρ0 is the density at normal conditions, us is the shock velocity, and γ is the adiabatic index. To justify the use of this equation in our conditions, we first look at the relation often used in the study of shock physics for solids and liquids13 

p=Aρρ0n1,
(2)

where ρ is the density behind the shock front and A and n are constants obtained experimentally for each material. For strong shocks, where p1p0, Eq. (2) suggests that pρn, similar to the case of a perfect gas with constant specific heats where pργ from which Eq. (1) is derived. Thus, Eq. (1) is a good approximation for strong shocks in solids and liquids while using n instead of γ. The value of n for water is usually assumed to be n78.13 The value of n for polyester was found by fitting to EOS data14 and found to be n1.76. The value for metals is often taken to be n=4;13 therefore, the value for the polytungstate solution was assumed to be n47 (between the value for metals and the value for water).

As another estimate, a two-dimensional (2D) hydrodynamic simulation, coupled with EOSs, was run for water and polyester14 since we do not have EOS tables for polytungstate solution. The input to the simulation was the power calculated from the measured current and resistive voltage. A detailed description of the simulation algorithm can be found in Ref. 15. The pressure at ∼100 μm radius for water and polyester is presented in Fig. 7.

FIG. 7.

Pressure at ∼100 μm radius for polyester and water, calculated by 2D hydrodynamic simulation.

FIG. 7.

Pressure at ∼100 μm radius for polyester and water, calculated by 2D hydrodynamic simulation.

Close modal

Since the pressures are estimated at slightly different radii, the self-similar equation P1P0r0/r10.62,16 where P0 is the pressure at r0 and P1 is the pressure at r1, was used to estimate the pressures at the same radius of 100 μm to make comparison easier. The results are summarized in Table II.

TABLE II.

Theoretical and simulation pressure estimates at a distance of 100 μm from the origin of implosion.

pTheoretical (GPa)pSimulation (GPa)
Water 8.3–11.4 14.4 
Polytungstate solution 8.1–15.7 … 
Polyester 45 32.4 
pTheoretical (GPa)pSimulation (GPa)
Water 8.3–11.4 14.4 
Polytungstate solution 8.1–15.7 … 
Polyester 45 32.4 

It can be seen that there is reasonable agreement between the theoretical and simulation results for water. The small discrepancy (≤30%) can be explained by the simulation not taking into account some of the current flowing through the water and not going into the exploding wires. The difference (also ≤30%) between the theoretical and simulation values for polyester is larger and may be due to the polyester used in the experiment is not exactly the same as the one in the EOS tables. It can also be seen that water and polytungstate solution have very similar values.17–21 The higher density of the polytungstate solution compensates for the low shock velocity and allows for the generation of similar pressures. It is clear however that the pressure in polyester is 2–4 times higher than in water and polytungstate solution.

Electrical wire explosions have been carried out in water, polytungstate solution, nitromethane, and polyester. The shadowgraphy framing and streak images (except for nitromethane) of the generated shock were used to obtain shock trajectories. The shock wave velocities were used to calculate the pressure behind the shock waves and compared to 2D dimensional hydrodynamic simulations coupled with EOSs for the case of water and polyester.

The results showed that in polytungstate solution, the shock velocity generated is lower than that in de-ionized water, unlike the results with glycerol in earlier experiments. The pressure, however, is similar in both materials.

The breakdown in polyester after the peak in current showed that wire explosions in a solid are possible for the generation of shock waves having advantages over the use of liquids such as different wire shapes and easy transport. In addition, higher pressures are generated in the vicinity of implosion.

While there are no imaging results for the explosion in nitromethane, the current and voltage waveforms showed that there was no breakdown during the explosion. This suggests that this material can be used in the future, preferably with better setups that use disposable parts.

This research was funded by the EPSRC, First Light Fusion Ltd., U.S. Department of Energy under Cooperative Agreement Nos. DE-NA0003764 and DE-SC0018088 and Sandia National Laboratories.

1.
D.
Sheftman
and
Y. E.
Krasik
,
Phys. Plasmas
17
,
112702
(
2010
).
2.
A. W.
DeSilva
and
J. D.
Katsouros
,
Phys. Rev. E
59
,
3774
(
1999
).
3.
V. I.
Oreshkin
,
Phys. Plasmas
15
,
092103
(
2008
).
4.
Y. A.
Kotov
,
J. Nanopart. Res.
5
,
539
(
2003
).
5.
B.
Liu
,
D.
Wang
, and
Y.
Guo
,
Phys. Lett. A
382
,
49
(
2018
).
6.
A.
Grinenko
,
A.
Sayapin
,
V. T.
Gurovich
,
S.
Efimov
,
J.
Felsteiner
, and
Y. E.
Krasik
,
J. Appl. Phys.
97
,
023303
(
2005
).
7.
D.
Yanuka
,
H. E.
Zinowits
,
O.
Antonov
,
S.
Efimov
,
A.
Virozub
, and
Y. E.
Krasik
,
Phys. Plasmas
23
,
072704
(
2016
).
8.
R.
Han
,
H.
Zhou
,
Q.
Liu
,
J.
Wu
,
Y.
Jing
,
Y.
Chao
,
Y.
Zhang
, and
A.
Qiu
,
IEEE Trans. Plasma Sci.
43
,
3999
(
2015
).
9.
R.
Han
,
J.
Wu
,
W.
Ding
,
H.
Zhou
,
A.
Qiu
, and
Y.
Wang
,
Phys. Plasmas
24
,
113515
(
2017
).
10.
V. I.
Oreshkin
,
S. A.
Barengol'ts
, and
S. A.
Chaikovsky
,
Tech. Phys.
52
,
642
(
2007
).
11.
S. N.
Bland
,
Y. E.
Krasik
,
D.
Yanuka
,
R.
Gardner
,
J.
MacDonald
,
A.
Virozub
,
S.
Efimov
,
S.
Gleizer
, and
N.
Chaturvedi
,
Phys. Plasmas
24
,
082702
(
2017
).
12.
R.
Sadeghi
,
R.
Golabiazar
, and
M.
Ziaii
,
J. Chem. Eng. Data
55
,
125
(
2010
).
13.
Y. B.
Zel'dovich
and
Y. P.
Raizer
,
Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena
(
Academic Press
,
New York, London
,
1966
).
14.
S. P.
Lyon
and
J. D.
Johnson
,
SESAME: The Los Alamos National Laboratory Equation of State Database
(LANL Rep. LA UR-92-3407,
1992
).
15.
M.
Kozlov
,
V. T.
Gurovich
, and
Y. E.
Krasik
,
Phys. Plasmas
20
,
112701
(
2013
).
16.
G.
Bazalitski
,
V. T.
Gurovich
,
A.
Fedotov-Gefen
,
S.
Efimov
, and
Y. E.
Krasik
,
Shock Waves
21
,
321
(
2011
).
17.
A.
Fedotov-Gefen
,
S.
Efimov
,
L.
Gilburd
,
G.
Bazalitski
,
V. T.
Gurovich
, and
Y. E.
Krasik
,
Phys. Plasmas
18
,
062701
(
2011
).
18.
O.
Antonov
,
S.
Efimov
,
D.
Yanuka
,
M.
Kozlov
,
V. T.
Gurovich
, and
Y. E.
Krasik
,
Appl. Phys. Lett.
102
,
124104
(
2013
).
19.
D.
Yanuka
,
A.
Rososhek
, and
Y. E.
Krasik
,
Phys. Plasmas
24
,
053512
(
2017
).
20.
A.
Rososhek
,
S.
Efimov
,
M.
Nitishinski
,
D.
Yanuka
,
S. V.
Tewari
,
V. T.
Gurovich
,
K.
Khishchenko
, and
Y. E.
Krasik
,
Phys. Plasmas
24
,
122705
(
2017
).
21.
A.
Rososhek
,
S.
Efimov
,
S. V.
Tewari
,
D.
Yanuka
,
K.
Khishchenko
, and
Y. E.
Krasik
,
Phys. Plasmas
25
,
062709
(
2018
).