Semiempirical wide-range conductivity model with exploding wire verification

Based on well-established physical relationships, a semiempirical set of equations dictating the electrical conductivity of dense, strongly coupled, partially ionized copper is presented. With the empirical coefficients, the model is tuned to experimental conductivity data obtained from exploding wire experiments [A. W. DeSilva and J. D. Katsouros, Phys. Rev. E 57, 5945 (1998)]. The result is a wide-range conductivity model, with demonstrated accuracy from room temperature-density conditions to 0.01 g/cm${}^3$ and 30 kK. Using magnetohydrodynamic simulation the ability to utilize the conductivity model for predictive simulations is demonstrated. A complete electrical conductivity dataset for copper has been made available to the public.

Figure 1

Empirically calculated conductivity isotherms versus mass density with comparison to QLMD [12], Kuhlbrodt and Redmer [9], Tkachenko and Fernández de Córdoba (TF) [22], Clérouin (QMD) [23], DeSilva (experimental) [11].

Figure 2

Experimental and MHD predicted voltage and current waveforms from capacitor discharge EW experiments with a 127-μm-diameter 18-cm-long copper wire in air at various initial capacitor voltages.

Figure 3

Conductivity contour plot (Ω${}^{-1}$ m${}^{-1}$) with temperature-density trajectories from EW experiments in Fig. 2 (solid lines), experimental conductivity data (triangles) [11], and QMD simulated data (circles) [23].