Exploding Aluminum Wire Expansion Rate
With 1-4.5 kA Per Wire
D.B. Sinars, T.A. Shelkovenkoa), S.A. Pikuz a),
J.B. Greenly and D.A. Hammerb)
Laboratory of Plasma Studies, Cornell University, Ithaca, NY 14853
X-ray backlighter images (radiographs) of current-induced explosions of 12.7-25 µm diam Al wires have been used to determine the expansion rate and internal structure of the dense wire cores. The current rises to 1-4.5 kA per wire in 350 ns, but voltage and current measurements show that the energy driving the explosion is deposited resistively during the first 40-50 ns, when the current is only a few hundred amperes per wire. A voltage collapse then occurs as a result of plasma formation around the wire, effectively terminating the energy deposition in the wire core. High-resolution radiographs obtained over the next 150-200 ns show the expanding wire cores to have significant axial stratification and foam-like structures with ~10 µm scale lengths over most of the wire length before they disappear in the expansion process. The expansion rate of the portion of the wire cores that is dense enough to be detected by radiography is 1.4-2 µm/ns commencing approximately 25 ns after the moment of the voltage collapse. (The sensitivity limit is equivalent to 0.2 µm of solid density Al.) By 250 ns after the start of the current pulse, the detectable wire core diameter is 250 µm, but it contains only about 30% of the initial wire material.
Introduction
Recent success in achieving extremely high energy density z-pinch implosions using Al, Ti and W wire arrays on the Z accelerator at Sandia National Laboratories, Albuquerque,,, has generated great interest in their use as an x-ray source for inertial confinement fusion. The implosion phase of these z-pinch experiments is preceded by a wire expansion and plasma formation phase initiated by a 50-100 ns current ramp from 0-1 kA/wire that precedes the main current pulse. The experiments reported here were undertaken to investigate the effect of a simulated prepulse current on the state of individual Al wires.
In comparison with W, Al has a much lower mass density, melting point and boiling point. Evidently as a consequence of these (and, perhaps other) properties, the rate of expansion reported here for Al wires is substantially greater than that previously reported for W wires under the same conditions. This conclusion is drawn by comparing radiographs obtained of the exploding Al and W wires as a function of time after the start of the current pulse. In the case of W, the bulk of the material remains in the condensed (liquid) state and the wire core expands at a rate of the order of 0.1 µm/ns. By contrast, we report here that a substantial fraction of the Al wires appears to be vaporized in 100-150 ns, resulting in a wire core expansion rate of more than 1 µm/ns. The expansion rate depends strongly on the energy deposited in the wire before plasma forms around it. Using the same technique that we previously used with W wires, we have also obtained calibrated density measurements of the material in the residual Al wire cores as they expand. On the basis of these measurements, we estimate that more than half of the initial wire material had expanded sufficiently to be below our detection limit by about 250 ns after the start of the current pulse.
The qualitative features of the experimental results reported here are similar to results reported in the late 1950’s by W.G. Chace, and by Fansler and Shear in 1964, except that those authors used larger diameter wires (100-625 µm versus our 12.7-25 µm), and applied a microsecond time scale current pulse to the wires in air at atmospheric pressure. Although our experiments were performed in vacuum with a factor of ten smaller length and time scales, our radiographs of 12.7- and 25-µm Al wires exhibit many of the same structural characteristics as were reported by Chace and by Fansler and Shear.
In the remainder of this paper, we first describe the experimental apparatus used for these wire explosion experiments with up to 4.5 kA per wire. We then present a series of radiographs to illustrate the various stages of Al wire explosion and expansion as a function of time for single wires and for 2 or 3 wires adjacent to each other. From these and similar radiographs, we infer wire core expansion rates. Measurements of the voltage and current applied to the wires enable us to calculate the energy deposited in the wires prior to plasma formation around them, and it is this quantity which we believe correlates with the wire expansion rate.
Description of Experiment
In order to determine the expansion rate of exploding Al wires under pulsed current conditions similar to the prepulse on the Z-accelerator (i.e. - ~1 kA/wire), we built the LC1 pulser. It consists of a low inductance 75-nF capacitor typically charged to 15 kV, a triggered gas switch, and a 50-W (RG-8) cable to deliver the pulse to the wire load. When driving a relatively low inductance short circuit load instead of fine wires, this pulser produces a damped sinusoidal current pulse having a 350-ns quarter period rise time, an amplitude of 4.5 kA, and an e-fold damping time of 4.25 µs. However, we are concerned here with only the first 500 ns, i.e. – less than a half-cycle. A typical oscillogram of the full current pulse and the first 500 ns are shown in Figs. 1a and 1b, respectively. Current in the circuit was measured with a Rogowski coil, and a current shunt monitor was located at the wire load. Voltage was measured with a resistive monitor in parallel with the wire load and connected to the same electrodes.
The Al wire explosions were radiographed as a function of time after the start of the current pulse using Mo wire X pinches for direct x-ray backlighting, as described by Shelkovenko et al. In brief, Mo-wire X pinches are found experimentally to produce bright x-ray sources in the 2.5-10 keV x-ray energy range. The spectrum of a Mo X pinch when the radiation is filtered by a 12.5-µm Ti foil consists of free-bound continuum and several L-shell lines, and the size of the source is submicron.
The experimental setup used to obtain the radiographs is shown in Fig. 2. The current for the two parallel X pinches shown in . Since two X pinches were used at a time, we usually obtained two separate radiographs of the same Al wire explosion. We obtained the relative timing of the X-pinch radiation bursts by monitoring them using fast response time diamond photoconducting detectors (PCDs) and a 5 GS/s digitizing oscilloscope (Tektronix 684B). The time resolution of the PCD detector system routinely used for this purpose was about 0.5 ns, and it recorded X-pinch x-ray bursts lasting from 0.6 to 2 ns. In a special series of tests using a faster PCD and digitizer, pulses shorter than 0.4 ns were recorded. By using different wire diameters in the two X pinches (ranging from 17.5 µm to 30 µm), the time between the initial radiation bursts from them could be varied from near 0 (for the same size wires) to about 30 ns.
A sandwich of 3 x-ray-sensitive films was placed in a shielded camera behind a 12.5-µm Ti filter to record the radiographs, as shown in Fig. 2c. Aluminum step wedges were deposited on the Ti filter. The step wedges, consisting of known thicknesses of Al ranging from 0.1-2 µm, were used to calibrate the gray scale of the film to the amount of Al (gm/cm2) in the path of the x rays on each pulse. Thus, the areal density of the exploding Al wire was obtained by comparing the gray scale of different portions of the image with the step wedge gray scale on each film, as was previously done in W wire experiments. Unless otherwise noted, the radiographs shown in the following figures were obtained on the first film. The exposure on this film is predominantly due to the softer component (2.5-5 keV) of the Mo X-pinch x rays that pass through the Ti filter. The transmission of the 12.5-µm Ti filter as a function of energy is shown in .
The spatial resolution of the method depends upon several factors: the source-object-film arrangement, the size of the bright x-ray source (because we do not use a pinhole) in the energy range that passes through the Ti filter, and the specifications of the films taking into account the spectral range of the x rays. After scanning the films with a 2700 dpi Nikon LS2000 scanner, the effective spatial resolution in these experiments was 2-3 µm.
Results and Discussion
The experiments reported here involved up to three 12.7- and 25-µm Al wires as the load for the LC1 pulser. By varying the trigger timing between the LC1 and XP pulsers, we recorded radiographs of the exploding wires at times ranging from 50 to 500 ns after the start of the LC1 current pulse. The spacing between wires was varied from 0.4 to 1.0 mm. The radiographs shown in Figure 4 presents radiographs of three different two-wire explosions taken 110, 154 and 170 ns after the start of the LC1 current waveform in Fig. 1. These three radiographs illustrate the expansion of the Al wire cores as a function of time. Clearly there is no sign of the mm scale length "sausage-like" instability that is present in high current Al wire explosion plasmas,. However, the wires do not expand uniformly along the wire, showing both long scale length variation and small-scale structure. The latter is reminiscent of the structure reported elsewhere in explosions of ~1 mm wires by high current pulsers on the µs time scale,. The non-uniform expansion rate along the wire is believed to be due to non-uniform formation of coronal plasma around the wires, especially near the ends, where the contact is important. At the top of the radiographs the unexploded wires can be seen, providing a size reference.
Figures 5 and Figure 6 shows details of one wire in a 12.7-µm pair indicating that by 90 ns, the wire core has taken on a foam-like appearance over most of its length. There appear to be ~10 µm diameter bubbles both in the wire interior and at the surface. This is similar to structure we observed at later times in W wire explosions.
Horizontal (perpendicular to the wire axis) gaps have also developed (see Figs. 6a and c) by 90 ns and become more prominent during the next 100 ns, as can be seen in Fig. 4. The radiograph in Fig. 4c, which is greatly expanded in Fig. 4d, illustrates horizontal stratification extending over a large fraction of the wire length. Figure 6b indicates that this structure begins to develop as early as the more prominent gaps, such as the one shown in Fig. 6c. A three-wire array radiographed at 190 ns is shown in Figs. 7a-c. It had slightly less current per wire but slightly more time to expand (190 ns vs. 170 ns) than the pair in Fig. 4c, but it shows very similar structure near its ends.
Thus, in less than 100 ns, wires driven by less than 1 kA/wire expand by a factor of up to 5 in diameter and develop a foam-like structure, which is believed to be a liquid-vapor combination based upon energy considerations to be discussed later. Stratification develops and gaps open up toward the end of that period. By 150 ns the stratification begins to disappear in the middle of the wire and a smooth radial profile develops. Stratification survives to 175-200 ns only near the electrodes, where expansion (to 100-150 µm in Fig. 4c) is less than that near the middle of the wires (about 250 µm in Fig. 4c). By contrast, only a portion of the left-most wire in the three-wire array shown in Fig. 7a has lost its structure by 190 ns, which would seem to indicate the importance of the current per wire as well as the time. However, as we shall discuss later, it is almost certainly the energy deposited per wire, rather than the current per wire, that determines the development of the wire morphology and expansion rate.
Expanded vapor/plasma columns without visible structure have formed by 250 ns at 2 kA per wire, as shown in Fig. 8a. Expansion continues (e.g. – Fig. 8b at 340 ns) so that by 470 ns (Fig. 8c), the residual wire cores have intersected each other everywhere except at the ends. Figure 9 shows a greatly expanded image of the lower end of the right wire in Fig. 8c, demonstrating that structure is still visible at the ends. The wire core end is close to 100 µm in diameter at this moment in time and the bubbles in the foam-like material appear to be larger than in Fig. 6.
The Al density in the wire explosions was estimated using Al step wedges by the same method previously described for W wires. The step wedges and some areal density estimates for radiographs at two different times are shown in Figs. 10 and 11 at 244 and 418 ns, respectively. As noted earlier, the Al step wedges enable the gray scale of the wire image on the film to be related to the gm/cm2 of Al through which the backlighter x rays have had to pass. The areal density of the wire core can be estimated using this calibrated gray scale. Our minimum sensitivity is > (0.4-0.5)x10-4 g/cm2 (equivalent to > 0.12 µm of Al), because we cannot resolve the thinnest layer (0.11 µm) in the step wedge on these images. Estimating the volume density requires an estimate of the wire core thickness. For Fig. 10, it is probably reasonable to assume the wire cores are still cylindrically symmetric. This is not likely to be the case in Fig. 11, however, because material from the two wires has merged.
Using the method described in Ref. , we estimate the mass per unit length in the wire core on the left side of Fig. 10 to be (0.9-1.0)x10-6 g/cm, depending upon the axial position. The right wire core is in the range (0.9-1.1)x10-6 gm/cm. The estimated absolute error in these linear density measurements is ±25%. The initial wire was 3.4x10- 6 g/cm. Thus, most of the original mass of both wires must be in the coronal plasma, which is not visible in our radiographs. Taking the visible wire core diameters to be about 170 µm from Fig. 10, and assuming 30% of the wire material is uniformly filling that diameter, the average mass density is 0.4x10-2 gm/cm3 and the Al density is 1020/cm3. We do not know the fractional ionization of this material.
The same sort of analysis can be performed for the radiograph in Fig. 11 even though the wire cores have merged. The detectable total mass per unit length of the pair of wires is estimated to be 1.6x10-6 g/cm, which is only 20% of the original mass of the two wires. This corresponds to an average Al mass density of about 0.2x10-3 g/cm3 and number density of about 0.5x1019/cm3, assuming 1-mm thickness by 1-mm width.
Figure 12 summarizes the 12.7-µm Al wire core expansion results obtained in these studies, including data from many radiographs not presented here, in the form of a plot of core diameter as a function of time. Four different sets of Al wire data are plotted. They correspond to one-, two-, and three-wire loads, plus a set of anomalous one-wire data which we discuss shortly. The error bars shown reflect the uncertainty in measuring the wire core diameter, which is more difficult as the wire core expands. Each point represents the maximum diameter measured in a single radiograph. In two- and three- wire tests, the maximum of any of the wires was plotted. For the two wire experiments, the maximum diameter was usually about the same for both wires, as seen in Figs 3, 4 and 8. For the three wire tests, there was more variation, as is evident in Fig. 7a. Since at most 2 radiographs were obtained in each pulse, the graph presents data obtained over many pulses. As stated earlier, the current pulse shown in Fig. 1 is shared among all the wires used in a test.
Assuming that the wire expansion is reasonably reproducible from pulse to pulse, we fitted the one- and two-wire data to straight lines using the error size as a weighting parameter. These data indicate that wire expansion is very slow (at most 0.04 µm/ns, and perhaps zero) for the first 75 ± 25 ns of the LC1 current pulse. After this delay time, the expansion rate of the core diameter reaches 2.0± 0.1 µm/ns for single 12.7-µm wires and 1.4± 0.1µm/ns for two-wire experiments. We emphasize, however, that the wire sizes that we plot are not the diameters of 100% of the wire material. Rather, we are plotting the detectable diameter of the dense wire core. As we have noted earlier, by 250 ns, this detectable dense core contains only about 30% of the original wire mass.
In order to understand the wire expansion data, we developed the capability to measure the voltage and current across the test wire(s) with reasonable accuracy during the first 100 ns of the LC1 current pulse. Figure 13 shows two examples of current and voltage data for single wire tests. The solid line curves are from pulse 1588, represented in Fig. 12 by data at 165 and 181 ns. The dotted curve is for pulse 1596, the highest of the anomalous points shown near 140 ns in Fig. 12. (The majority of the points in Fig. 12 were obtained before the current and voltage monitors were in place.) The initial current increase is limited by the inductance of the circuit (including the wire(s) but not dominated by them). As the resistance of the wires increases due to heating (the resistivity of Al increases by a factor of 12-15 between room temperature and the melting point), a resistive voltage of 8-9 kV develops across the wire(s). As a result, the rate of increase of the current (dI/dt) decreases (or even becomes negative), increasing again only when the voltage collapses. The latter occurs, we believe, as a result of plasma formation around the wires, as we discuss in the Conclusion section. Once a low-resistance plasma is available to carry current, the current can increase at a circuit-inductance-limited rate, and essentially none of the current will continue to flow in the high-resistance path represented by the superheated liquid metal core (> 75 W , ignoring the effects of vapor bubble formation, for a 12.7-µm initial wire diameter).
The energy deposited in the wires as a function of time is also shown in Fig. 13, and was obtained by integrating the product of the current and voltage over time. We estimate that a 10-mm long, 12.7-µm diameter Al wire requires only 6.2 mJ to reach the vaporization temperature, and 45 mJ to vaporize all of it. In pulse 1588, approximately 25 mJ was deposited in the wire in about 33 ns. After that time the voltage collapsed and the energy plot no longer measures the energy deposition in the wire core because of current shunting by plasma. This energy is enough to superheat the material (i.e. – to heat the liquid Al to above its boiling point, but not to vaporize all of it). Though enough energy is deposited to boil some of the metal, a lack of nucleation sites evidently delays the onset of boiling. When vapor bubble formation does occur, it appears to proceed very rapidly, leading to explosive expansion of the wire core. Chace came to a similar conclusion in trying to explain why wires expanded slowly before expanding rapidly in his microsecond time scale experiments. We believe that none of the experiments plotted in Fig. 12 approached an energy deposition of 45 mJ before voltage collapse except for the anomalous data, which lie far from the curves generated in the remaining series of single wire experiments.
The anomalous points in Fig. 12 resulted from three consecutive pulses. The current, voltage and energy waveforms from the first one, pulse 1596, are shown in Fig. 13. These three tests were performed after another series of wire explosion experiments investigating the behavior of oil-coated wires. In that test series, experiments with W, Ag and other wire materials coated with an insulator, including oil-coated wires, showed that insulating coatings delayed the voltage collapse, resulting in greater energy deposition in the wire core and more rapid expansion. The results in the three anomalous pulses are similar to those seen when we intentionally coated wires, suggesting that the wires in the three anomalous tests in Fig. 12 were carried out contaminated with residual oil. The increased energy deposition and expansion rate was greatest for pulse 1596, and decreased markedly in the next two. The current, voltage, and energy data in Fig. 13 imply that it is the energy deposition, which depends upon the current per wire during the first 30-50 ns of the current pulse, that determines the wire core expansion rate. Similar comparisons with other wire materials support this hypothesis, and further research into this effect is in progress.
Conclusions
From the results and calculations presented in this paper, we have concluded that fine Al wires subjected to current pulses of up to 4.5 kA per wire with a 350-ns quarter period rise time explode and expand at a rate which is determined by the energy deposition in the first 50 ns. The wires heat resistively to the melting point in less than 20 ns, and, in just a few more ns, to the vaporization temperature. Thus, material evaporates from the surface of the wire at the same time an 8-9 kV resistive voltage develops as a result of increasing wire resistivity. The increasing electric field in the vapor around the wire leads to local electric discharges, apparently first near the wire/electrode contact points. Eventually a discharge stretches from one electrode to the other along the wire, and virtually all of the current is carried by the plasma surrounding the wire core. The step changes in wire expansion along the wire, as exemplified by the radiographs in Figs. 6a and 7b are indicative of the discharge’s developing nonuniformly, thereby shunting current by different sections of the wire core at different times.
Although a substantial fraction of the liquid metal Al in the wire core is heated beyond the vaporization temperature by the energy deposited during the initial resistive heating phase of the wire explosion, vapor bubble formation requires nucleation to take place. It appears that this process may take 20-30 ns based upon the data plotted in Fig. 12. After this delay time, the rapid expansion rate of the wire core, and its foam-like appearance, implies that vapor bubbles develop rapidly throughout the wire core. The resulting high pressure impulsively accelerates the metal/vapor residual wire core to an expansion rate of 1.4-2 µm/ns in a time of the order of 10 ns or less. An internal pressure of 108 – 109 Pa or more is suggested, with pressure relief occurring as soon as the vapor can vent through the wire core surface. Evidently this process requires only of the order of 10 ns since the wire expansion rate appears to be constant just a few tens of ns after the energy is deposited in the wire.
By contrast, W wire expansion appears to be subject to a much longer delay time, and the expansion rate is slower (~0.1 µm/ns) once it begins. In addition, the axial uniformity of Al wire expansion is greater than it is with W, perhaps reflecting the importance of desorption of nonuniformly adsorbed impurities from the wire surface for W. As a final point of comparison of Al with W, Figs. 10 and 11 indicate that the Al wire explosion completely eliminates all structure in the residual wire core after 250-400ns, whereas W retains complex structure well into the µs time scale.
The increasing resistivity of Al with temperature assures a thermal instability, which could be the explanation for the observed cross-wire stratification and gaps shown, for example, in Figs. 6-8. This conclusion was drawn by Chace and by Fansler et al. for their longer pulse heavier wire experiments in which similar horizontal stratification was observed.
Because Al wires expand so rapidly, it is possible that the prepulse current on Sandia’s Z accelerator produces nearly continuous Al vapor in a cylindrical shell by the time the main pulse arrives, and that this explains recently achieved high x-ray emission rates with Al. The current per wire would have to be only 300 A during the energy deposition phase of the wire explosion (i.e. – for perhaps 30 ns at the beginning of the prepulse). This could also be applicable to the experiments performed with Al on the Saturn accelerator.
Acknowledgments
We wish to thank Drs. Keith Matzen, Tom Sanford and Rick Spielman of Sandia National Laboratories, Albuquerque, for their continuing interest in these experiments and for many valuable discussions. This research was supported by Sandia Contracts BD-9356 and BF-6410, and Department of Energy grant number DE-FG03-98DP00217.
Figure Captions