IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 36, NO. 2, APRIL

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1 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 36, NO. 2, APRIL Underwater Electrical Wire Explosion and Its Applications Yakov E. Krasik, Member, IEEE, Alon Grinenko, Arkady Sayapin, Sergey Efimov, Alexander Fedotov, Viktor Z. Gurovich, and Vladimir I. Oreshkin Abstract Results of an investigation of underwater electrical wire explosions using high-power microsecond and nanosecond generators are reported. Different diagnostics, including electrical, optical, and spectroscopic, together with hydrodynamic and magnetohydrodynamic simulations, were used to characterize parameters of the discharge channel and generated strong shock waves. It was shown that the increase in the rate of the energy input into exploding wire allows one to increase wire temperature and amplitude of shock waves. Estimated energy deposition into Cu and Al wire material of up to 200 ev/atom was achieved. The spectroscopic analysis of the emitted radiation has unveiled no evidence for the formation of a shunting plasma channel. Analysis of the generated shock waves shows that 15% of the deposited energy is transferred into the mechanical energy of the water flow. Also, it was shown that converging shock waves formed by underwater explosion of cylindrical wire arrays can be used to achieve extremely high pressure at the axis of implosion. A pressure up to 0.25 Mbar at 0.1 mm distance from the axis of the implosion at a stored energy of 4 kj was demonstrated. A model explaining the nature of similarity parameters, which have been phenomenologically introduced in earlier research, was suggested. Index Terms Dense plasma, shock wave, wire explosion. I. INTRODUCTION THE SUBJECT of underwater electrical wire explosion (UEWE) has been under intense theoretical and experimental investigation for more than 50 years due to many important technical applications (thermonuclear fusion, solid-state and plasma-chemical physics, rockets, etc.) and sophisticated physical phenomena involved in this process [1] [5]. UEWE is accompanied by phase transitions of the wire material and water, that is, melting, evaporation, nonideal plasma (coupling parameter Γ 1) formation and generation of strong shock waves (SW) and light radiation fluxes [6], [7]. UEWE depends Manuscript received August 21, 2007; revised December 18, This work was supported in part by the Center for Absorption in Science, Ministry of Immigrant Absorption, State Israel, Israel Science Foundation Grant 1210/04 and Israel Ministry of Science Grant The work of V. Oreshkin was supported in part by the Russian Foundation for Basic Research Grant Y. E. Krasik, A. Sayapin, S. Efimov, A. Fedotov, and V. Z. Gurovich are with the Physics Department, Technion, Israel Institute of Technology, Haifa 32000, Israel ( fnkrasik@physics.technion.ac; saypin@physics.technion.ac.il; efimov@physics.technion.ac.il; alexphy@tx.technion.ac.il; gurovich@physics. technion.ac.il). A. Grinenko was with the Physics Department, Technion, Israel Institute of Technology, Haifa 32000, Israel. He is now with the Center for Fusion, Space and Astrophysics, Physics Department, University of Warwick, CV4 7AL Coventry, U.K. ( A.Greenenko@warwick.ac.uk). V. I. Oreshkin is with the Institute of High Current Electronics, Tomsk , Russia, and also with Tomsk Polytechnic University, Tomsk , Russia ( oreshkin@ovpe.hcei.tsc.ru). Digital Object Identifier /TPS on many parameters, which include wire properties such as wire diameter, length, and material, characteristics of the electrical circuit, and properties of the background medium. Uncertainty in time-dependent parameters, such as specific resistance, thermal conductivity, density, and temperature of the wire and water during phase transitions, makes it difficult to provide a selfconsistent description of UEWE [5]. The rapid progress in the Z-pinch approach [8], where efficient radial compression of an exploding cylindrical wire array in vacuum was achieved, has restored interest in the phenomenon of electrical wire explosion. The electrical explosion of the wire array determines the first stage of the Z-pinch evolution. This stage involves the deposition on a nanosecond (ns) timescale of a large amount of energy into wire material by Joule heating. In addition to the interest related to the Z-pinch approach, the dense and relatively low-temperature plasma that forms as a result of electrical wire explosion presents a perfect example of a nonideal plasma [1]. The subject of nonideal plasmas has been of continuous interest for basic research related to transport coefficients of materials and equations of state under extreme conditions [1], [5], [8] [13]. To increase the temperature of the plasma, the deposition of a larger energy density needs to be achieved. However, in the case of wire explosion in vacuum, early termination of energy deposition occurs because of the electrical breakdown in the vicinity of the wire surface in the vapors of desorbed gases and evaporated wire material [5]. This breakdown leads to the generation of a plasma shell, which intercepts a significant part of the current. Thus, special measures should be taken to suppress surface breakdown. A significant increase in energy deposition into a metal core prior to the plasma corona formation was demonstrated in experiments by Sarkisov et al. [14] [16]. It was shown that in the case of polyamide-coated W wire in vacuum, one obtains an anomalously high energy deposition 20 times the atomization enthalpy. Another method of increasing the energy deposition into the wire core was to prevent surface breakdown by placing exploding wires in breakdownimpeding environments, such as pressurized gas, water, or oil [5]. In the case of UEWE in the microsecond (µs) and nanosecond (ns) time scales, it was shown that high pressures generated in the water during the discharge might suppress the generation of the plasma shell [17] [20]. In fact, generation an ultrahigh pressure is a key issue in research related to high-energy physics [1]. The most advanced methods used to obtain ultrahigh pressure are Z-pinch, laser irradiation of a target, and chemical explosion. Using these methods, extremely high pressures of 10 MBar were achieved /$ IEEE

2 424 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 36, NO. 2, APRIL 2008 with initially stored energy of 1 MJ [8]. Generation ultrahigh pressure is also possible by creating cylindrical or spherical converging SWs [21], [22] by explosives detonation methods. In the experiments [23], in the focus of the spherically imploding detonation waves propagating in a stoichiometric propane oxygen mixture in a detonation chamber, an ion temperature of 10 8 K was observed. Experiments on electromagnetically driven cylindrical SW implosion in water have been reported [24]. In these experiments a 23-MJ capacitor Z- pinch facility was used to accelerate and implode electromagnetically the cylindrical metal liner or shell onto a coaxial and concentrically located thin target containing water. All of these experiments were carried out in a time scale of 10 5 s. Within this time scale numerous experiments of UEWE showed that the process of wire explosion is accompanied by the generation of SW, with pressures up to 30 kbar [3]. In the case of ns time scale UEWE, scaling laws show that a larger pressure can be achieved due to the increase in the rate of the energy deposition [25]. On the other hand, extensive experimental investigations of UEWE have shown a relatively large discrepancy in the estimations of the efficiencies of the energy transfer to SW (η) and of the radiated light flux (η γ ). For instance, in experiments described in [26] and [27], the estimated η was in the range of 50% 80%, and in experiments described in [6] and [28], the estimated range of η was 15% 35%. A similar uncertainty can be found in the measured values of η γ. For instance, in [29] the value of η γ is 25%, and in [6] and [30] its value is 10%. The discrepancies in η and η γ could be related to the experimental diagnostic methods used to obtain these parameters. Indeed, in most experiments, SW parameters were determined by using various pressure probes, which can give a significant overestimation of the pressure if special measures are not taken [31], [32]. In addition, these probes can only be placed at a distance of several centimeters from the discharge plasma channel (DPC) and cannot be used for direct measurement of the pressure on the surface of the DPC. In a number of experiments [26], [27], [33], [34], an optical observation of the SW and DPC was made using streak shadow photography, but no proper analysis of the obtained images has been performed. In addition, the traditional spectroscopic diagnostic methods in the visible range of light are difficult to apply to the UEWE process because of the opacity, and in the majority of the experiments a black-body spectrum has been assumed [6], [34]. In this paper, an analysis of the results of the investigation of UEWE using a high-power µs and ns generators are presented. Different diagnostics, including electrical, optical, and spectroscopic used to characterize parameters of the discharge channel and generated strong SW, are described. It will be shown that the increase in the rate of the energy input into exploding wire allows one to increase wire temperature and amplitude of SW as well. No evidence for the formation of a shunting plasma channel was observed opposite to the case of wire explosion in vacuum or gas. Analysis of the generated SW show that 15% of the deposited energy is transferred into the mechanical energy of the produced water flow. Also, it was shown that converging SW formed by underwater explosion of cylindrical wire arrays can be used to achieve extremely high pressure at the axis of implosion. A pressure of 0.2 ± 0.05 Mbar at 0.1 mm distance from the axis of the implosion at stored energy of 4 kj was demonstrated. II. SIMILARITY PARAMETERS In spite of the complexity of phenomena involved in UEWE, numerous experimental investigations have shown that this type of discharge obeys a certain similarity law [3], [35], [36]. That is, the identity of dimensionless current and voltage waveforms was shown in different discharges when three dimensionless combinations of various discharge setup parameters, called the similarity parameters, were identical. However, this empirical approach does not offer a physical explanation for the existence of the similarity of discharges. In [37] a model that provides a physical insight into the process of the underwater wire initiated discharge was suggested. The discharge current causes intense heating, melting, evaporation, and ionization of the wire material. It was assumed that prior to the wire explosion and plasma generation a decrease in the wire cross-sectional area due to radial uniform evaporation of the wire boundary determined the increase in the wire resistance. In this case, the dimensionless equations for the electrical circuit and wire resistance read as follows: d 2 u dτ 2 + P du 1r m dτ dr m dτ = P 2r 3 m ( du dτ + u =0 (1) ) 2. (2) Here, dimensionless voltage is u(t) =ϕ(t)/ϕ 0, where ϕ 0 is the initial charging potential; dimensionless time is τ = t/ LC, where L and C are the inductance and capacitance of the discharge circuit, respectively; dimensionless resistance is r m (t) =R m (t)/r 0m, where R om is the initial wire resistance; and R m (t) =l/σ(t)s(t) is the time dependent resistance of the wire having length l, conductivity σ(t), and cross-sectional area of S(t). In these equations appear two dimensionless parameters: P 1 l 1 σ 0 S 0 Z = R 0m and Z ( )( ) ( )( ) C ϕ 2 P 2 0 WE 2R0m Zλσ 0 ρ 0 S0 2 =, W m Z where W E is the electrically stored energy, and W m is the energy required for complete evaporation of the wire, S 0 is the initial wire cross sectional area, and Z = L/C is the characteristic wave impedance of the electrical circuit. The first similarity parameter gives the ratio between the initial wire resistance and the electrical circuit wave impedance. The second similarity parameter determines the rate of wire evaporation. Indeed, the increase (decrease) in R om or decrease (increase) in W m relative to Z and W E, respectively, increases (decreases) the evaporation rate. Obviously, given a set of two numbers P 1 and P 2, one uniquely determines the dependence of normalized voltage u(τ) and normalized current du(τ)/dτ solving (1) and (2). However, the same numerical values of P 1 and P 2 can be obtained for different experimental setups, which mean that

3 KRASIK et al.: UNDERWATER ELECTRICAL WIRE EXPLOSION AND ITS APPLICATIONS 425 Fig. 1. Fig. 2. Miscrosecond times scale UEWE setup. Nanosecond time scale UEWE setup. the same normalized current and voltage waveforms will be obtained for these different setups. A detailed analysis of this model, which also includes an electrical discharge in water and a two-stage discharge, i.e., a parallel discharge through the wire and water, reveals additional P 3 and P 4 similarity parameters appearing in consequent differential equations [37]. The third similarity parameter P 3 appears as a result of the assumption that the plasma channel conductivity is proportional to the energy dissipated in the channel. Experimental validation of similarity of the plasma stage of discharges to the same P 3 indicates that this is the main process in the evolution of plasma channel resistance. Finally, the fourth similarity parameter P 4 = P 1 /P 3 determines the ratio between the initial wire resistance and the typical resistance of water plasma channel. Thus, it was shown that the original similarity parameters, which were intelligently guessed and validated by experiments, appear naturally in differential equations, thus demonstrating the reason for the similarity of UEWE and pointing out the main processes that govern this process. III. EXPERIMENTAL SETUPS AND DIAGNOSTICS Experiments on the µs time scale of UEWE(see Fig.1) were carried out using a capacitor bank consisting of up to four Maxwell type capacitors of 2.7 µf each, connected in parallel and charged to 30 kv, resulting in a total stored energy of up to 4.5 kj [17]. This generator delivers to the exploding wire a current pulse with an amplitude up to 100 ka with a rise time of 2 µs (di/dt 50 A/ns). The investigation of ns time scale UEWE was carried out using a generator that produced a pulse with voltage and current amplitudes of 110 kv and 70 ka (di/dt 140A/ns), respectively, and a pulse duration of 100 ns [19] (see Fig. 2). The energy stored in the generator was < 700 J. High-voltage and grounded electrodes with a wire (of wire array) between them were placed inside the experimental chamber that was filled with water and had windows for optical observation. To measure current and voltage waveforms, a self-integrated Rogowsky coil and an active voltage divider were used, respectively. The inductive voltage drop L w (di/dt) was eliminated using a calibrated B-dot loop, and the I(dL w /dt) term was eliminated using the streak image of the discharge channel. The time and space evolution of the discharge channel and generated SW was obtained as shadow images using either frame or streak photography by a 4Quick05A fast frame and VICO- 300 UV streak cameras, respectively. In these experiments, back lightning was produced by either flash lamp (Compact plus 1200) or dc green laser or/and pulsed Nd:YAG (Ekspla NL301) laser. The time- and space-resolved radiation spectrum was recorded using a 250-mm Chromex imaging spectrometer coupled with a 4Quick05A camera. Also, part of the radiation from the discharge channel was analyzed using a fast calibrated photodiode (OPHIR FPS-10) coupled with narrow band interference filters in UV and the visible range of light. Parameters of the SW were recorded initially using different electromechanical pressure probes (quartz, carbon based), and commercially available PCB-119A02 and PCB-138A38 gauges produced by PCB Piezotronics Inc., New York [31], [32] placed at different distances from the exploding wire, and the time-of-flight method using CA-1136 gauges produced by Dynasen Inc. The main disadvantages of using these probes are related to limited bandwidth ( 10 7 Hz), the necessity of eliminating electromagnetic noise, and placing these probes at a finite distance from the exploding wire. It was shown, for instance, that in the case of PCB gauges one should make a special mathematical processing based on energy conservation requirements and Fourier analysis to reconstruct the waveform of the pressure generated by UEWE [31]. In the case of carbonbased gauges, there is another problem related to the hysteresis effect and the necessity of carefully calibrating these gauges. The main problem concerning quartz gauges is that this gauge was destroyed in each shot. Finally, the time-of-flight (TOF) method can be used to estimate the SW amplitude, but one should take special care to decrease the error in the gauges positioning [32]. Thus, the parameters of the generated SW were obtained using optical methods based on shadow images of SW using either a 4Quick05A camera operating in single or multiframe mode or a streak VISO 300 UV camera and shearing interferometry, one-dimensional (1-D) hydrodynamic calculations and shadow images of the expanding discharge channel. In addition, a shearing interferometry in combination with hydrodynamic calculation and ray simulation based on the Eikonal approach was exploited to reconstruct the generated water flow pressure profile. This method allowed us to estimate the energy transferred from the discharge to the water flow. IV. MICRO- AND NANOSECOND TIME SCALE UEWE A. Microsecond Time Scale Wire Explosion Using a µs-timescale setup (see Fig. 1), an aperiodical discharge was obtained with a Cu wire 85 mm long and 0.5 mm in diameter. Typical waveforms of the discharge current and resistive voltage and shadow streak images of the discharge channel and SW

4 426 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 36, NO. 2, APRIL 2008 Fig. 5. Current and voltage waveforms obtained from the aperiodic discharge using 85-mm-long 510-µm diameter Cu wire and 5.4-µF 30-kV charged capacitors. Experimental data are shown by the solid lines; numerical MHD calculations are shown by the dashed lines. Fig. 3. (a) Typical waveforms of the discharge current and resistive voltage. (b) Streak shadow images of the exploding Cu wire and SW. Fig. 4. Pressure distribution at different times. Here, (r r DP C ) is the radial distance with respect to the DPC boundary having radius r DP C (t). are shown in Fig. 3(a) and (b), respectively. A hydrodynamic approach of analysis of UEWE and experimentally obtained trajectory of the DPC boundary were used to determine the pressure at the boundaries of the DPC and SW. The calculated SW trajectory was compared with the experimental one [see Fig. 3(b)]. The space distribution of the pressure at different times obtained using hydrodynamic simulations is shown in Fig. 4. This analysis showed that the efficiency of electrical energy deposition into the mechanical energy of the fluid is 25%, which is 400 J. The maximal pressure obtained at the DPC boundary was Pa. Because 25% of the input energy was transferred to the fluid, one can conclude that 75% of the energy delivered to the DPC is transferred into the radiation. For the Cu wire used, the energy per particle can be roughly estimated, resulting in an average temperature of 7 ev. Here, let us note that spectroscopical data of the spectrum radiated by the DPC showed the presence of Cu III ions, which indicates plasma electrons with energy 20.3 ev. These high-energy electrons can exist at the tail of the Maxwellian electron energy distribution having density 20 times less than the density of electrons with average temperature of 7 ev. Parameters of the DPC generated during UEWE were determined obtained using a 1-D magnetohydrodynamic (MHD) calculation and experimental results obtained from the discharge Fig. 6. Numerically calculated pressure and temperature profiles inside the DC after the onset of separation of DC and shock wave generated in water. employing Cu wire. The main difficulty in this calculation was to obtain the correct transport parameters of DPC for a large range of density and temperature values varying in both space and time. A wide range semiempirical conductivity model [4] was successfully applied in numerical calculations and good agreement with a set of experimental data was obtained (see Fig. 5). This conductivity was used to determine the temperature of the DPC using experimental data (electrical and optical measurements) and assuming uniform spatial distribution of DPC plasma parameters. Examples of the numerically calculated pressure and temperature profiles inside the DPC are shown in Fig. 6. It was shown that this method is applicable only at relatively late times of the discharge when the separation of DPC and SW occurred. At that time the error in the estimated temperature can be ascribed to the nonuniformity of the DPC, which is demonstrated by numerical calculation. B. Nanosecond Time Scale Wire Explosion The experimental setup shown in Fig. 2 was used in ns timescale UEWE experiments. Explosions of wires of different lengths (20 80 mm), diameters ( µm), and materials (Cu, Al) were studied. Similarly to µs time scale experiments, the main data were obtained with aperiodical discharge when all

5 KRASIK et al.: UNDERWATER ELECTRICAL WIRE EXPLOSION AND ITS APPLICATIONS 427 Fig. 7. Experimental (solid) and simulated MHD (dashed) current, voltage and DC boundary. Explosion of Cu wire ( 100 µm,l w = 100 mm). Fig. 9. Streak camera shadow image of the exploding wire and SW. Cu wire ( 100 µm,l w = 100 mm). The traces with the observed DPC boundary and the SW extracted from the streak image are represented by the solid line. Fig. 8. Dependence of the average deposited electrical energy per atom on the wire diameter for different wire lengths and material. the stored energy was delivered to the load (see Fig. 7). It was shown that in the ns time scale of UEWE one should take the skin effect into account, which results in an increase in average resistance of the wire as compared with µs timescaleuewe. The dependence of the deposited energy per atom versus the wire diameter is shown in Fig. 8. One can see that the maximum estimated value of average deposited energy per atom for the Cu wire (25 mm long and 50 µm in diameter) reaches 200 ev/atom, which is almost 10 times larger than the best results obtained in experiments with wire explosion in vacuum [16]. Taking into account that the enthalpy of atomization of Cu is 3.5 ev/atom, one obtains an overheating value of 60. Hence, one can see that the water medium plays a crucial role in the increase in the energy deposition per atom. Using a streak image of the expanding DPC and the SW (see Fig. 9) and hydrodynamic numerical simulations, the maximal value of the pressure p max at the DPC boundary was estimated. It was found that the value of p max depends almost linearly on deposited energy per unit wire length [see Fig. 10(a)]. A similar linear dependence of p max was obtained versus the parameter Π: Π= ρ 0 /l w (dp/dt) max. Here, ρ 0 is the initial density of the wire material, and P is the electrical power of the discharge. This parameter is obtained from the combination of the discharge parameters and has the dimensionality of the pressure. Finally, it was shown that the deposited energy per unit length increases almost linearly as a function of Π [see Fig. 10(b)], which allows one to expect an increase in overheating value with the increase in rate of power deposition into the wire. To estimate the parameters of the compressed water flow generated by ns time scale UEWE, a novel diagnostic method was developed [38]. The method combines a time-resolved shadowgraph and shearing interferometry techniques with hydrodynamic calculations. In the present experiments, simultaneously with the interferometric image, the shadowgraph and Schlieren images of the DPC and the generated SW were obtained. That is, the evolution of the radial dimensions of the DPC was used in hydrodynamic calculations of the fluid flow parameters distribution [18]. The calculated density profiles of the compressed fluid at different times of the discharge were translated to the profiles of the refraction index. These profiles were employed in the simulation of ray trajectory, which is governed by the Eikonal equation [39] and which was used to calculate the expected interferograms. The latter were then compared with the experimentally obtained interferograms. Calculated and obtained shearing interferograms are shown in Fig. 11. The good agreement of the predicted and the measured interferograms points to the adequacy of the calculated distribution of the compressed fluid s density and pressure. Thus, the combination of the hydrodynamic calculation with the interferometric and shadowgraph imaging enables an accurate estimate of the radial distribution of the density and pressure of the compressed fluid between the SW and the DC. It was found that the efficiency of transformation of the electrical energy dissipated in the exploding wire discharge channel to the mechanical energy of the compressed water flow is <15%. Analysis of the data concerning light radiated from the DPC showed that the radiation occurs in two pulses [19]. The first pulse, 200 ns long, corresponds to the wire explosion and starts with the onset of wire expansion as was shown by analysis of the streak shadow images of the DPC. A secondary light emission pulse, characterized by light intensity several times larger than the first light pulse, starts after a delay, whose value depends on the wire material, and it continues for tens of microseconds. A similar temporal behavior of light emission was observed in vacuum explosion of wires by Sarkisov et al. [40] where it was suggested that the second long-duration light emission is related to microparticle-type radiation. It was found that the intensity of the first and second radiation pulses increases almost linearly with an increase of input energy per atom. Conventional spectroscopic methods based on spectral line analysis are not applicable to deducing DPC parameters because of the opacity and intense spectral line broadening caused by the high-density DPC. Nevertheless, given the high density

6 428 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 36, NO. 2, APRIL 2008 Fig. 10. (a) Maximum pressure at the DPC boundary vs. total electrically deposited energy per unit length; (1) Cu wire, l w =50mm, 200 µm; (2) Cu wire, l w =50mm, 50 µm; (3) Cu wire, l w = 100 mm, 50 µm; (4) Cu wire, l w = 100 mm, 100 µm; (5) Al wire, l w =50mm, 127 µm; (6) Cu wire, l w =50mm, 100 µm; (7) Cu wire, l w =25mm, 100 µm. (b) Total electrically deposited energy per unit wire length vs. the similarity parameter Π. Designation numbers are the same as in (a). Fig. 11. Experimental (lower) and calculated (upper) shearing interferogram obtained in the case of the 100-mm-long100-µm in diameter Cu wire explosion at time delay of 0.4µs from the onset of the discharge current. of the DPC and its high opacity, it was speculated that the radiation is black body (BB), and the DPC surface temperature T was estimated within a framework of this assumption in spite of the fact that it does not seems to hold for all regimes of UEWE and for all wavelength ranges [19]. Also, because the Roseland path is λ 3, one can suppose the relevance of the BB approximation at long wavelength range to be reasonable. To measure the time-resolved BB spectral distribution, light emission in the visible spectral range has been sampled by interference filters, and the optical system was calibrated in situ, using a known light source. Furthermore, two methods have been used to deduce T. The first consisted of finding two parameters of the Planck equation, i.e., the amplitude and the temperature that should best fit the measured intensity at several wavelengths at each time step. A second method to deduce T was based on the measured absolute intensity at a single wavelength. An example of an intensity I ex (λ n,t) measured by the photodiode during the explosion of a Cu wire ( 100 µm,l w = 100 mm) is shown in Fig. 12. One can see that the peak of the radiation spectrum occurs at λ 400 nm, which, according to Wien s displacement law with T = 250 [ev nm]/λ, givest 0.6 ev. However, the fullwidth half-maximum (FWHM) of this distribution is 200 nm, whereas the FWHM of the Planck distribution corresponding to 0.6 ev is 550 nm. Therefore, an attempt to fit the full range of the sampled spectrum, including the UV range, by a BB curve results in an error of at least 50%. Fig. 12. Sampled spectrum of radiation from Cu wire ( 100 µm,l w = 100 mm). Fig. 13. Typical waveform of the current and temperature of the DPC surface during the explosion of Cu wire ( 100 µm,l w = 100 mm). The temperature estimated by the method of fitting of the observed visible spectrum to the BB intensity distribution is shown by the solid line with error bars. The temperature deduced from the absolute intensity at 410, 486, 488, 514.5, 532, 550, and 656 nm, respectively, is shown in the thick gray curve. A plot of the DPC temperature during the explosion of a Cu ( 100 µm,l w = 100 mm) wire evaluated by these two methods and omitting the UV range is shown in Fig. 13. One can see a good agreement between the DPC temperatures calculated according to the BB fit and according to the absolute intensity radiated within an isolated wavelength range. It was found that deviation from the BB approximation increases significantly for wires l w =50mm long (see Fig. 14). In these explosions, the values of T are clustered into two groups. The first group corresponds to a maximum DPC value of T 4.5 ev calculated

7 KRASIK et al.: UNDERWATER ELECTRICAL WIRE EXPLOSION AND ITS APPLICATIONS 429 Fig. 14. Typical waveform of the current and temperature of the DPC surface during the explosion of Cu wire ( 100 µm,l w =50mm). The temperature deduced from the absolute intensity at 410, 486, and 488 nm, respectively, is shown in the thick dark-gray curve. The temperature deduced from the absolute intensity at 514.5, 532, 550, and 656 nm, respectively, is shown in the thick light-gray curve. from the absolute intensity of radiation measured at the 410-nm, 486-nm, and 488-nm wavelengths, respectively, and the second group corresponds to a maximum value of T 7 ev calculated at the nm, 532-nm, 550-nm, and 656-nm wavelengths, respectively. At present, we do not know the reason of this discrepancy in temperature estimates. However, this discrepancy agrees well with our assumption that BB approximation can be used mostly in the long wavelength range. In the shorter wavelength range, the plasma becomes partially transparent, and therefore one is forced to decrease the effective temperature to fit the data using BB approximation. The estimated value of T gives an extremely intense radiation flux power of 10 MW/cm 2. In addition, a correlation was found between T and p max of the DPC. That is, the maximum pressure on the DPC boundary for a Cu wire (l w =50mm) is p max Pa and for a Cu wire (l w = 100 mm) p max Pa. The estimated temperatures for these two cases are 5 9 and 2.2 ev, respectively. One-dimensional MHD simulations of ns time scale UEWE s were carried out similarly to the case of µs time scale UEWE. Electrical conductivity of the DPC material was evaluated by the adjustable semiempirical method described in [4]. The two fitting parameters in this model are the value of conductivity at the critical point σ cr and a parameter α which determines the dependence of conductivity as a function of T at solid density. The conductivity found using this approach is strongly dependent on the state of the matter. That is, in the metallic part of the phase space the conductivity decreases with an increase in T, whereas in the plasma part of the phase space the conductivity increases. The conductivity dependence in the metallic and fluid phases is critical for correct calculation of the initial stage of the wire explosion. The semiempirical model described in [4] allows the specific conductivity σ(δ, T ) to be calculated, where δ = ρ/ρ 0 is the relative density, and ρ 0 is the normal density. The model is applicable in the metallic and fluid phases of the material for δ δ cr and T<3T cr, where δ cr and T cr are the density and temperature at the critical point. In these calculations, a fitting parameter α was introduced. The variation of α in the relatively small range of causes the change in the value of σ cr and, respectively, allows one to tune the delay between the calculated voltage and the current pulses to be similar to the delay that was observed in the experiments (see Fig. 7). Thus, these simulations showed that in the frame of this semiempirical model it is possible that the conductivity of the wire material depends on current density and current rise rate, which determine instantaneous thermodynamic variables such as temperature and density. This statement certainly deprives conductivity of its desired universality, which implies that it cannot be used in predicting a large range of experimental results. However, one can suppose that the conductivity of the material cannot be determined independently of the discharge parameters such as current density j, electrical power, and electrical power deposition rate when typical times of variation of these parameters become comparable with relaxation times characterizing the material. For example, in the case of the Cu wire (R w =50 µm,l w = 100 mm) explosion, typical lattice relaxation time can be estimated as R w /c s 14 ns, where c s =3.75 mm/µs is the sound velocity in the copper at normal conditions, whereas typical discharge current rise time I/ I 30 ns. Because these typical times are of the same order of magnitude, one can assume the influence of the current time variation on lattice vibration and, therefore, on the value of σ. Another comparison worth making regards the ratio of the average velocity of current carrying electrons u and sound velocity. Assuming uniform cross-sectional current density distribution, the maximal value of the average electron current velocity u(t) is calculated as u(t) I(t) πr 2 wn e e cm/s 0.11c s where n e is the density of electrons above the Fermi level, and e is the electron charge. When taking skin effect into account, the value of u can take values of the same order of magnitude as c s. This again points to the necessity of considering a more complex time-dependent model of conductivity. Despite the fact that the universal values of conductivities, which would give a satisfactory agreement with a large set of experimental results are absent, the MHD computation implying the described approach of calculation of conductivity can be regarded as a numerical experiment. When combined with the real experiment, it can be used to retrieve data inaccessible by experimental diagnostics, or otherwise confirm independently obtained experimental data. On the other hand, this approach may be regarded as an indirect way of computing conductivity, which takes into account the mentioned parameters such as j and di/dt. Simulations using appropriate conductivity values demonstrate good quantitative and qualitative agreement with electrical and optical diagnostics of fast explosions of Cu wires. An example of the calculated temporal evolution of temperature and pressure of the DPC and surrounding water for Cu wire explosion is shown in Fig. 15. Here, the plasma water interface can be identified in Fig. 14(a) at the radius where the temperature (in the scale of electron volts) drops to almost zero. One can see that the maximum value of pressure inside the DPC reaches Pa, which is above the critical pressure for Cu.

8 430 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 36, NO. 2, APRIL 2008 Fig. 16. Trajectory of the phase state of a thin layer adjacent to the surface of the heating wire with a radius of 150 µm for different heating rates of the wire. (a) Linear temperature growth. (b) Quadratic temperature growth. Fig. 15. Simulated cross-sectional distributions of (a) temperature, (b) pressure at different times of a Cu wire ( 100 µm,l w = 100 mm) explosion. Thus, one can expect that when the magnetic pressure drops and an explosion occurs, the wire material transforms into a gas plasma state skipping the quasi-stable states. V. P LASMA SHELL FORMATION It was reported [19] that using ns time scale UEWE the energy deposited into Cu or Al wire material can be up to 200 ev/atom. However, this estimate of the deposited energy was based on the assumption that the major part of the current flows inside the exploded wire material and that no shunting plasma shell forms around the exploding wire. To prove this assumption, additional time- and space-resolved spectroscopic measurements, using visible spectrometer coupled with a fastframing camera, were carried out [20], [41]. In the case of a shunting plasma shell formation in the vicinity of the DPC, the hydrogen H α and H β spectral lines as well as the intense O I and O II spectral lines would be observed at the beginning of this process [42]. A careful search for these spectral lines in the range of ns with respect to the beginning of the discharge current, with a frame time step of 1 2 ns, revealed no evidence of their existence. This negative result strongly indicates the absence of shunting plasma channel formation during ns timescale UEWE within the limit of a spatial resolution of 20 µm/pixel. Therefore, if this plasma shell does exist, it should be less than 20 µm wide. However, in this case, because of its large resistance, the plasma shell would be able to conduct only an insignificant current and thus cannot cause energy deposition into the discharge channel to be terminated. The absence of the shunting channel was explained by the results of a computer simulation of the heating process of water and the subsequent generation of acoustic flow by heating a wire submerged in water presented in [41]. The calculation was performed to obtain a trajectory of the phase state of a thin water layer adjacent to the surface of the wire during its heating. Vaporization can occur if the curve of the phase state crosses the saturation curve from the liquid to the vapor part or approaches it. In Fig. 16 the phase state trajectory in the p T plane of the layer adjacent to the 150-µm radius wire is shown for different linear and quadratic heating rates. The temperature increase in the wire was determined by T w = T 0 + (390 C)(t/t max ) n where T w is the temperature of the wire, t max is the maximum heating time parameter, and n is the power coefficient that, together with t max, determines the temperature growth rate. One can see that this trajectory is contained in the liquid part of the phase diagram, when heating of the wire to a temperature of 420 C is achieved in less than 500 ns. In the case of the wire explosions described in [17] [19] this condition was fulfilled, and therefore the question why no evidence for the shunting water discharge was observed in [20] is answered. Presented results also indicate that when more powerful generators with higher achievable wire heating rates than those used in [17] and [19] are employed, no vaporization of the water would occur due to thermal conductivity either. Here, let us note that 1-D MHD calculation, which accounts for radiation transport, showed that for a current amplitude > 1 MA the UEWE is accompanied by the formation a hot narrow plasma channel (several tens of electron volts) in the surrounding water [43]. This channel is formed due to an intense flux of photons with energy > 13.6 ev radiated by the exploding wire. It was found that this plasma shell catches up to 30% of the discharge current. However, intense radiation interchange between the water plasma channel and the DPC causes a strong heating effect of the wire material. As a result, the

9 KRASIK et al.: UNDERWATER ELECTRICAL WIRE EXPLOSION AND ITS APPLICATIONS 431 Fig. 18. Shadow streak image of the converging cylindrical SW for a 12 Cu wire zigzag array of 200 mm i.d. and 20 mm long. The Cu wire diameter 0.2 mm. Fig. 17. Zigzag wire array. thermodynamic parameters of the exploding wire plasma, i.e., pressure and temperature, remain the same as in the idealized case of the wire explosion in vacuum. Taking into account that the realistic wire electrical explosion in vacuum is accompanied by strata formation, breakdown of the adsorbed gases along the wire surface and fast wire plasma expansion, it is reasonable to make a statement about the evident advantages of UEWE that allow higher thermodynamic plasma parameters to be reached. Fig. 19. Time-of-flight and pressure of the SW as a function of its distance from the axis calculated by the Whitham model and 1-D hydrodynamic calculation for the case of the total time of flight of 1.8 µs. VI. UNDERWATER EXPLOSION OF THE CYLINDRICAL WIRE ARRAYS The process of wire explosion is accompanied by the generation of SW, and the efficiency of the stored energy transfer to the SW is 15%. Thus, converging SW can be used to generate high pressure at the axis of convergence and to deliver energy with high density to the target located in that place. Indeed, in [44] it was shown that the established converging cumulative water flow is self similar, in spite of the complexity of the implied equations of state. It was shown that the pressure at the front of the SW located at radius R c can be expressed as the function of total energy E t delivered to the water flow and R 0 as the initial self-similar SW radius at which the motion of the water flow can be considered self-similar as: p c E T R (5 2/α) 0 Rc 2 2/α and p c E T R (4 2/α) 0 for spherical and cylindrical geometry, respectively. Here, α is a self-similarity parameter equal to 0.6 and 0.75 in the spherical and cylindrical case, respectively. In [45] and [46], results of experiments and hydrodynamic calculations concerning converging SW generated by underwater electrical explosion of wire array using µs and ns time scale generators, respectively, were presented. In µs time scale experiments four Cu wires each 0.2 mm in diameter and 70 mm long, connected in parallel, were used. Each of the four wires is bent into three zigzags contributing three parallel sections. Four such zigzags connected in parallel and warped around result in a total array of 12 parallel wires 25 mm long and either 10 or 20 mm in diameter (see Fig. 17). R 2 2/α c Fig Experimental setup for ns time scale underwater explosion of cylindrical wire array. A typical streak image of the converging SW is shown in Fig. 18. The measured TOF of the SW was used to estimate the SW front pressure using three independent methods. That is, the method based on the Whitham approach [47], and 1-D and 2-D hydrodynamic calculations. The results of all three methods satisfactorily agree, i.e., it was demonstrated that even at a preliminary stored energy of a few kilojoules, a pressure reaches 0.2 ± 0.05 Mbar at 0.1 mm distance from the axis of a converging cylindrical SW, whereas initially generated SW pressure in the vicinity of the exploding wire is 0.05 Mbar [45] (see Fig. 19). In ns time scale experiments [46] an up to 24-Cu-wire cylindrical array having a diameter of 10 mm was used (see Fig. 20). The Cu wire diameter and length were of 23 µm and 25 mm, respectively. Three typical overlaid shadow frames (each frame duration is of 2 ns) of SW obtained with a

10 432 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 36, NO. 2, APRIL 2008 TABLE I IMPLOSION SETUP PARAMETERS: R sh THE INITIAL EXTERNAL RADIUS OF THE WATER BOUNDARY SHELL; R t THE INITIAL RADIUS OF THE DT TARGET; E T THE TOTAL ENERGY DEPOSITED BY THE EXTERNAL SOURCE INTO THE WATER FLOW; E in THE MAXIMUM INTERNAL ENERGY OF THE TARGET; Y THE TOTAL YIELD; η THE REACTION EFFICIENCY RATIO.DTREACTION YIELD CALCULATED FOR VARIOUS IMPLOSION PARAMETERS:1)R sh =7.5 mm, R t =0.25 mm, E T =31.2 kj; 2) R sh =5.0 mm, R t =0.25 mm, E T =10.8 kj; 3) R sh =7.5 mm, R t =0.5 mm, E T =36.5 kj; 4) R sh =5.0 mm, R t =0.5 mm, E T =10.2 kj Fig. 21. Three framing shadowgraphs of the SWs generated by (a) 10- and (b) 20-wire array underwater electrical explosions. The calculated SW front is shown by a white line. The frame time was 2 ns. and the time delays of the consecutive frames relative to the beginning of the discharge current were 300, 620, and 930 ns, respectively. 4Quick05 camera are shown in Fig. 21. The shadowgraphs demonstrate the transition of the SW front from the form dictated by individual multiple wire explosions to the cylindrical front. These experiments also showed that the use of a cylindrically converging SW allows one to obtain 10-fold increase in pressure ( 30 kbar at the distance of 0.1 mm from the axis) as compared with the SW pressure at the same distance from the individual exploding Cu wire, 100 µm diameter and 100 mm length. One of the most important questions concerning the efficiency of the application of multiwire array wire explosion for the generation of converging cylindrical SW is the damping of the SW instabilities inherited during the creation of the SW by multiple wires. Recent experimental results and results of 2-D simulations [46] show that in the case of the cylindrical implosion in the water medium the cylindrical symmetry of the converging SW may be obtained within times of flight of the SW as demonstrated in Fig. 21. VII. APPLICATION OF CONVERGING SW FOR IGNITION OF A SMALL DT TARGET A simplified analysis of the generation of the implosion in a water medium and the following interaction of the generated flow with a DT mixture target has been presented in [44]. In the considered model, such effects as electronic, molecular, and radiative heat transfer were neglected. The possible growth of two-dimensional instabilities was similarly not considered. These effects can play a crucial role in calculating the DT reaction yield and can significantly reduce the present estimation. On the other hand, the bremsstrahlung radiation was allowed to escape the system completely, as well as the energetic neutrons and α-particles, which can be used to ignite a heavy cryogenic layer of the target, as in the laser inertial confinement fusion (ICF) scheme [48]. Thus, it is understood that a more sophisticated calculation, which will include the aforementioned processes, is strongly required. Nevertheless, the carried-out simulations indicated that the target ignition by converging water SW can be considered to be a promising method for ICF. The most obvious demonstrated advantage of the proposed scheme is the inertial confinement of a hot target material by a massive compressed water flow. The main parameters of the simulated processes are summarized in Table I [44]. One can see that, by deposition of a number of kilojoules, a yield of can be achieved in a time scale of a few nanoseconds. In the last column of the table, the reaction efficiency ratio defined as the ratio of the total energy produced by the DT reactions to the maximal internal energy E in of the target achieved during the compression process, i.e., η = Y 17.6 MeV/E in, is shown. The maximum estimated value of η is 200; however, the total efficiency, i.e., Y 17.6 MeV/E T,is<1% in this case. The latter is due to the relatively low efficiency of the energy transfer from the water flow to the considered simplified target which is in our case E in /E T < %. VIII. CONCLUSION A review of recent experimental and simulations results concerning UEWE was presented. A model providing a physical insight into the process of the UEWE was suggested. Different electrical, optical, and spectroscopic diagnostics were developed to estimate the temperature of the DPC and the pressure of the generated SW. Using the obtained experimental data and hydrodynamic and MHD simulations coupled with equation of state parameters of the DPC and the generated water flow in µs and ns time scale of UEWE were studied. It was demonstrated that by increasing the power deposition rate, the input energy density can be substantially increased as well as the pressure of the generated SWs. It was shown that up to 200 ev/atom can be achieved in the case of Cu and Al wire explosions. The spectroscopic analysis of the emitted radiation has unveiled no evidence for the formation of a shunting plasma channel, opposite to the case of wire explosion in vacuum or gas. Optical methods combined with hydrodynamic calculations allowed us to estimate a 15% efficiency of energy transition from the DPC to the generated water flow. Temporally and spectrally resolved measurements showed that for an ns time scale aperiodical UEWE, the DPC can be considered as a source of BB radiation. Also, the MHD simulations carried out in ns time scale UEWEs indicate that it is possible that the conductivity of the wire material depends on current density and/or current rise time.

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12 434 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 36, NO. 2, APRIL 2008 Yakov E. Krasik (M 99) received the M.Sc. degree and the Ph.D. degree in physics from Tomsk Polytechnic Institute, Tomsk, Russia, in 1976 and 1980, respectively. From 1980 to 1991, he was with the Nuclear Research Institute, Tomsk. From 1991 to 1996 he was with the Weizmann Institute of Science, Rehovot, Israel. Since 1997, he has been with the Physics Department, Technion, Israel Institute of Technology, Haifa, Israel, where he is currently an Associated Professor. His main research interests are related to pulsed current-carrying plasmas. Alexander Fedotov received the B.Sc. degree in physics from the Physics Department, Technion, Israel Institute of Technology, Haifa, Israel in He is currently working toward the M.Sc. degree in the Pulsed Power and Plasma Laboratory, Physics Department, Technion, carrying out research on underwater electrical wire explosions. Alon Grinenko received the M.Sc. degree in electrical engineering and the Ph.D. degree in physics from the Technion, Israel Institute of Technology, Haifa, Israel, in 2002 and 2006, respectively. Since 2007, he has been with the Center for Fusion, Space and Astrophysics, Physics Department, University of Warwick, Coventry, U.K., as a Postdoctoral Research Fellow. His main research interests include plasma current carrying plasma and laser interaction with targets. Arkady Sayapin received the M.Sc. degree in radiophysics from the Tomsk State University, Tomsk, Russia, in 1972 and the Ph.D. degree in particle accelerators from Tomsk Polytechnic Institute, Tomsk, in From 1972 to 1989, he was with the Nuclear Research Institute, Tomsk. Since 2002, he has been with the Physics Department, Technion, Israel Institute of Technology, Haifa, Israel, where he is currently a Senior Research Scientist. His main research interests are related with microwaves generation, active plasma cathodes, and electrical wire explosion. Viktor Z. Gurovich received the M.Sc. degree in physics and mathematics from Kyrgyz University, Bishkek, Kyrgyzstan, in 1961 and the Ph.D. degree and the Doctor degree in physics and mathematics from Moscow State University, Moscow, Russia, 1966 and 1982, respectively. From 1968 to 1971 he was with the Novosibirsk Physics Institute, Novosibirsk, Russia. From 1971 to 2002, he was with the Kyrgyz Academy of Science, Bishkek, Kyrgyzstan. Since 2002, he has been with the Physics Department, Technion, Israel Institute of Technology, Haifa, Israel, where he is currently a Senior Research Scientist. His main research interests are related with cosmology, nonlinear gravitation, plasma physics, and relativistic gas. Sergey Efimov received the M.Sc. degree and the Ph.D. degree in physics from the Kharkov Polytechnical Institute, Kharkov, Ukraine, in 1987 and 1996, respectively. From 1986 to 1996, he was with the Kharkov Institute of Physics and Technology, Kharkov. Since 2002, he has been with the Physics Department, Technion, Israel Institute of Technology, Haifa, Israel, where he is currently a Senior Research Scientist. His main research interests are related with underwater electrical wire explosion and particle accelerators. Vladimir I. Oreshkin received the M.Sc. degree in physics from Tomsk Polytechnic Institute, Tomsk, Russia, in 1983, the Ph.D. degree in physics from the Tomsk State University, Tomsk, and the D.Sc. degree in physics and mathematics from the Institute of High Current Electronics, Tomsk, in Since 1978, he has been with the Institute of High Current Electronics, where he is currently a Senior Physicist, and since 2006, he has also been a Professor with Tomsk Polytechnic University, Tomsk. His main research interests are related to high-density pulsed current carrying.