# Neutral Copper Gas Resistivity Measurements by Means of an Exploding Wire in Air
## 1 Introduction  
In exploding wire experiments, a large current on the order of \(10^{3}\) A flows through a metallic wire, typically with a diameter of micrometers and centimeters length, causing the transformation of the metal into liquid, gas, and finally plasma by the fast heating due to the Joule effect [1]. It is a phenomenon long-known to science [2], and has subsequently been used in multiple scientific investigations [3; 4; 5]. Electrical energy absorbed by the exploding wire system until its transformation into plasma is a key characteristic in the further development of the phenomenon, as it influences the initial plasma state, prior to its last expansion [6]. Indeed, the state of an expanding wire in vacuum and its homogeneity are determined by the absorbed electrical energy [7] and the current rate [8]. Shortly after the beginning of the current discharge, when part of the wire material has become gas, its electrical conductivity is so small that the current is almost halted until further gas heating allows for the plasma formation [3; 9], provided that the wire is surrounded by a non-conducting medium, in order to avoid coronal plasma formation [10]. This current interruption is commonly known as dark pause. In experiments with a small current rate (under 20 A/ns) and with a wire of large enough mass, the dark pause becomes a very noticeable feature of the wire explosion. Plasma constitutive properties can be measured indirectly through the appropriate treatment of the electrical signals, for example, as in [11]. Among these properties, plasma electrical conductivity has been measured with an exploding wire setup for different materials and plasma conditions [12; 13; 14; 15]. Exploding wire setups had previously been used to confirm theoretical models of the conductivity in warm dense matter (WDM) studies [16], and to improve previous models [17]. Both models and experimental works have large error factors (at least a factor of two in the case of [PERSON] [18]) due to the difficulty of obtaining matter in clear and defined reproducible conditions, and due also to the problem of performing the measurements. These difficulties can be overcome with the use of more direct methods, such as the short pulsed laser used for the measurement of the resistivity of aluminum under solid density conditions and a broad range of temperatures [19]. As all those measurements and calculations are made in WDM conditions, more classical phases (e.g., a metallic neutral gas) have not been addressed. Specifically, in the classical limit, during the evolution from solid to plasma the wire must previously pass through a gas state that is reached during the dark pause. Usually, this pause is short and difficult to analyze, and therefore the measurement of the resistivity of the metallic gas--the main state during the dark pause--has not previously been conducted. Here we present the first measurements for the limits of neutral copper gas resistivity, using an exploding wire configuration, tailored such that the dark pause is long enough to allow for the measurement of the gas phase characteristics. Experimental parameters were chosen in order to explore the classical states of matter, in contrast with more usual exploding wire experiments that explore WDM conditions. The adequate conditions to this purpose requires: (a) a skin depth larger than the wire diameter; (b) a dark pause duration larger than 1 \(\upmu\)s; (c) a uniform discharge along the wire length without re-strikes or large instabilities; (d) a sufficient amount of mass so that the heating rate is not so fast; and (d) that the wire impedance is large enough to control the current discharge until the plasma formation.