# Neutral Copper Gas Resistivity Measurements by Means of an Exploding Wire in Air
## 2 Experiment and Physical Model Description  
Experiments were performed with the ALEX (_ALambre EXplosivo_, exploding wire in Spanish) system, shown schematically in Figure 1.  
ALEX is formed by two capacitors in parallel, 1.1 \(\upmu\)F each, connected to a high voltage source, maximum charging voltage 60 kV, which discharges the capacitors through a metallic wire surrounded by open air when the spark gap is closed by a high-voltage trigger pulse. In order to perform the measurements of the resistivity limits described here, it is necessary to know the radial expansion of the metallic gas. In this work, the radial expansion was obtained from direct shadowgraphy images recorded with a streak camera, a Hamamtsu C7700. Voltages from probes 2 and 3 and the Rogowski coil signal, along with the photodiode signal, were also recorded in an oscilloscope enclosed in a Faraday cage room. Voltage and Rogowski coil probes were designed, mounted, and calibrated (3% error) in the laboratory to the frequencies of interest in these experiments. The high-voltage trigger pulse was synchronized with the streak camera unit as depicted in Figure 1 with the use of a DG-535 delay generator. The photodiode signal was used to synchronize the streak camera photographs with the electrical signals with a precision of \(\pm\)20 ns. Copper wires with fixed length of 5.1 cm and diameter of 50 \(\upmu\)m were used in these experiments. As was already written, these parameters were chosen to ensure a long dark pause, \(\approx\)1 \(\upmu\)s, which allows for a better study of the metallic gas produced by the exploding wire. A typical result of the shadowgraphy streak images of the exploding wire with the associated voltage and current traces is shown in Figure 2, where the dark pause is clearly visible in either the image or the electrical traces. The first small peak of the current at 2 \(\upmu\)s corresponds to the transformation of the solid wire into liquid due to the Joule heating. The dark pause that begins when the current reduces its value is the next step of the exploding wire process in our experiments, and the moment when the gas forms from the liquid central core and expands is evidenced in the streak image by a dark radial expansion (the metallic gas absorbs the backlight). The later appearance of the plasma by neutral gas heating due to the electrical current is marked in the voltage signal by the negative slope; meanwhile, the presence of plasma at the expansion outer surface is marked by the maximum in the current signal. This plasma presence in the outer expansion surface is also in coincidence with the maximum illumination in the shadowgraphy image, as can be observed in Figure 2.  
Notice that the streak image is not able to resolve the structure of the gas expansion and its central liquid core, as only the external surface of the expansion is visible. Therefore, as is explained in the next section, only data of this external surface can be measured, independently of the initial energy of the exploding wire system. Figure 1: Exploding wire setup. PH1 signals the photodiode, C the capacitors bank, and L0 and R0 the lumped inductance and resistance of the setup, respectively. Figure 2: (**a**) Exploding wire shadow streak image; (**b**) Voltage(—) and current(—) signals for a copper wire. The dark pause is clearly seen in the streak image, the dark region that expands prior to the plasma formation, and in the current and voltage traces. At 7 μs, the whole wire has been ionized, as indicated by the maximum value of the current. Inset in (a) shows the beginning of the wire expansion, shortly after some vapor is formed. Charging voltage was 10 kV. Different charging voltages--10, 15, 18, 21 and 25 kV--were employed to ensure that measurements of the resistivity limits (later explained in this section) were independent of the initial electrical energies, and therefore of the dynamical behavior of the metallic wire [5].