This paper presents a simple but quite accurate numerical model for analyzing electrical explosion of copper wires in water. The numerical model solves a circuit equation coupled with one-dimensional magneto-hydrodynamic (MHD) equations with the help of appropriate wide-range equation of state (EOS) and electrical conductivity for copper. The MHD equations are formulated in a Lagrangian form to identify the interface between the wire and surrounding water clearly. A quotidian EOS (QEOS) that is known as the simplest form of EOS is utilized to build wide-range EOS for copper. In the QEOS, we consider the liquid-vapor phase transition, which is critical in analyzing the wire explosion system. For the electrical conductivity of copper, a semi-empirical set of equations covering from solid state to partially ionized plasma state are employed. Experimental validation has been performed with copper wires of various diameters, which are exploded by a microsecond timescale pulsed capacitive discharge. The simulation results show excellent agreements with the experimental results in terms of temporal motions of a plasma channel boundary and a shock front as well as current and voltage waveforms. It is found that the wire explodes (vaporizes) along the liquid branch of a binodal curve irrespective of wire dimension and operating voltage. After the explosion, the wire becomes a plasma state right away or after the current pause (dwell), depending on the operating conditions. It is worth noting that such a peculiar characteristic of wire explosion, i.e., current pause and restrike, is well simulated with the present numerical model. In particular, it is shown that the wire cools down along the vapor branch of the binodal curve during the current dwell, due to a significant difference of thermodynamic characteristics across the binodal curve. The influence of radiation for studying nonideal plasmas with a wire explosion technique and a physical process for shock wave formation by an exploding wire is discussed as well.
We explain that the classical integral expression of the average electron-ion momentum transfer cross section is of limited applicability to dense plasmas without correcting the cutoff screening radius approximation, and that the Zollweg-Liebermann model appears practically useful to reproduce the experimental data with mathematical simplicity.Zaghloul claims [1] that Zollweg and Liebermann's fitting formula [2] of the electron-ion collision cross section is unacceptably inaccurate and should not be used to calculate the transport properties of nonideal plasmas [3], because it fails to recover the exact values of the classical analytic expression of the energy-averaged electron-ion momentum transfer cross-section integral. Instead, Zaghloul proposed a new analytic formula that accurately fits the classical integral expression.As Zaghloul indicated in the Comment, the Zollweg-Liebermann fit indeed yields much higher cross-section values than predicted by the classical cross-section integral expression by ϳ100% in its proposed range of applicability. However, it should be noted that this classical integral expression has been derived based on the assumption of finite cutoff screening radius defined by the Debye shielding length D in a binary collision model, and can only serve as a rough estimation in most practical cases since its validity is limited by a restrictive condition ⌳ӷ1, where ⌳ is the Coulomb logarithm defined as the ratio of the Debye length to the average impact parameter b 0 [4]. In particular, when the plasma density is high, this classical expression tends to yield substantially underestimated values of electron-ion collision cross section because the Debye length rapidly decreases and the number of electrons within a Debye sphere becomes too small to shield out the ion charge effectively. Therefore, in order to obtain physically meaningful crosssection values in a dense plasma regime, one should take into account the effect of enhanced screening radius.Some authors have attempted to present detailed descriptions of the effective screening radius or effective collision frequency in nonideal plasmas [5,6], but, for simplicity, our previous calculation of the electrical conductivity utilized the fitting formula ln͑1 + 1.4⌳ 2 ͒ 1/2 given by Zollweg and Liebermann. Although a question may remain about the derivation of this formula, it is interesting to note that the fitting factor used in the Zollweg-Liebermann model is found to be consistent with the physical consideration of enhanced screening radius in nonideal plasmas, though its available parameter range is restricted to a narrow region. In addition, their modifying the Coulomb logarithm to have its minimum value limited by the interionic distance + = ͑ 4 3 n + ͒ −1/3 permits a description of plasmas at extremely high density. We also noticed that Zollweg and Liebermann's original paper showed a reasonable agreement of their calculations with experimental data available at that time. Comparisons with other theoretical models revealed no unaccept...
A practical approach has been implemented to calculate the ionization balance and electrical conductivity of warm dense aluminum plasma with the Coulomb coupling effect taken into account. The correction term for ionization potential is formulated with a number of basic dimensionless parameters that characterize nonideal plasma and incorporated with the fitted formulas of excess free energy given by Tanaka, Mitake, and Ichimaru [Phys. Rev. A 32, 1896 (1985)] and Chabrier and Potekhin [Phys. Rev. E 58, 4941 (1998)] to determine the ionization balance in an equilibrium state. The calculated degree of ionization of aluminum plasma exhibits a sudden increase near the solid density approximately 1 g/cm(3) at temperatures of a few eV, which effectively demonstrates the pressure-induced ionization. The electrical conductivity is evaluated in a partially ionized plasma regime based on a linear mixture rule that takes into account both the electron-ion and electron-neutral collisions and then the computed results are compared with available data from recent experiments. It is shown that the calculation well reproduces the overall trend of measured electrical conductivity of nonideal aluminum plasma accounting for the metal-insulator transition.
Monodispersed bimetallic Pt–Sn/SBA-16 catalysts prepared by coimpregnation technique and microwave-drying method showed enhanced catalytic activities for selective dehydrogenation of n-dodecane to its corresponding mono-olefins and preferential oxidation (PROX) of CO in the presence of excess H2.
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