Deok-Kyu Kim

Numerical model for electrical explosion of copper wires in water

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 simulat...

Lagrangian simulation of explosively driven magnetohydrodynamic generator

A series of time-dependent one-dimensional simulations has been carried out on the hydrodynamic behavior of argon and air plasmas in an explosively driven magnetohydrodynamic power generator. The thermodynamic properties of plasma gases are computed using equation-of-state data obtained from a detailed theoretical model. The plasma conductivities are given by a mixture rule, which comprises the fully and weakly ionized plasma approximations. The effects of the initial pressure and the magnetic field strength on the plasma behavior in the flow channel are examined over a moderate range of operating conditions, and then the computed results are compared with the experimental measurements, showing good agreement for the case of low magnetic Reynolds number.

Numerical simulation of exploding wires driven by pulsed capacitive discharge

Summary form only given. A time-transient simulation code for analyzing underwater wire explosion driven by a pulsed capacitive discharge is developed. It solves a circuit equation coupled with one-dimensional magneto-hydrodynamic equations with the help of appropriate wide-range equation of state (EOS) and electrical conductivity for copper. A modified quotidian EOS model1 is further improved to include the liquid-vapor phase transition which is critical for the generation of shock waves by wire explosion. For the electrical conductivity of copper, a semi-empirical set of equations covering from solid to strongly coupled, partially ionized plasma state2 is utilized. With an appropriate tuning of coefficients appeared in the equation set, an excellent agreement with the experimental results is obtained 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 strength of shock wave generated by wire explosion is greatly influenced by a diameter of the wire and the peak pressure is proportional to the current value at the time of voltage peak irrespective of operating conditions. The numerical model presented in this paper will be utilized not only to optimize the wire explosion system for generating strong shock waves, but also to investigate thermophysical and transport properties of non-ideal plasmas.

Simple mixed equation-of-state model of nonideal plasma for simulation of underwater wire explosion

Summary form only given. We present a mixed equation-of-state (EOS) model of nonideal plasma, which is given as a simple combination of the Thomas-Fermi-Dirac (TFD) theory, related ionization fitting formulae and ideal-gas EOS. The mixed EOS model is applied in one-dimensional simulations of under-water wire explosion for comprehensive predictions of the dynamic behaviors and property changes of a single metal wire that is electrically discharged in the water. The TFD part of the EOS model takes account of exchange interactions to give the zero-temperature pressure and energy of electrons at very high densities. The final EOS data at finite temperatures are obtained by adding the temperature-dependent ideal-gas EOS of ions and electrons to the zero-temperature values from the TFD part. Considering its simplicity, this EOS model is in reasonably good agreement with more sophisticated models and/or first-principles calculations as well as it guarantees smooth couplings with hydrodynamic codes. The results of wire explosion simulations are compared with experimental measurements to show the validity of the EOS model. Future applications of the mixed EOS model include modeling and simulations of Z-pinch experiments on a new pulsed-power driver named PRIMA (Pulsed Power Generator for Rapidly Increasing Mega-Ampere Current) which is being designed at ADD.

Hybrid model of chemical equilibrium equation of state for nonideal plasmas in underwater wire explosion simulation

Summary form only given. We present the equations of state (EOS) of metal plasmas in non-ideal regimes computed by a hybrid approach that combines the chemical equilibrium model with analytic formulae1 of free energy devised to accurately fit ab inito calculations. The correction term of ionization potential in the Saha equation is formularized explicitly with the analytic free energy functions to give iteratively converged solutions to the ionization balances.2 The EOS obtained by this hybrid approach is compared with results from other theoretical models, and then applied to a hydrodynamic simulation of underwater wire explosion.3 The validity and accuracy level for its practical applications are briefly discussed.

Simulation of exploding metal wire in under-water discharge experiments for warm dense matter study

Summary form only given. We present one-dimensional time-dependent simulation of exploding metal wire in under-water electric discharge experiments. Starting from the initial condition of solid wire at room temperature and taking relevant phase transitions into account, the simulation predicts the approximate onset time of wire explosion based on the ohmic heating power computed from measured current-voltage pulse profiles. The expanding boundaries of wire column and water shock-front are reproduced by the simulation and compared with the fast-frame camera images obtained in the experiments so that the validity of the employed equation-of-state model can be assessed. From the measured data of wire resistance and radius in corporation with calculated temperatures, the electrical conductivity of wire material is evaluated for the warm dense matter (WDM) conditions and compared with results given by other theoretical and experimental studies.1

MHD simulation of wire ablation and implosion in wire-array Z-pinch

We present magnetohydrodynamic (MHD) simulation of ablated tungsten wire in the wire-array Z-pinch on MAGPIE1 using the GORGON code2. The simulation is incorporated with theoretical models of equation-of-state and electrical conductivities for nonideal plasmas3 in addition to an astrophysical model for radiation cooling effects4. The dynamic behaviors of exploding wire plasma are demonstrated in a two-dimensional domain during the early stage of Z-pinch implosion. The computed profiles of electron density are compared with data measured by laser interferometer, which shows a rough agreement in terms of the order of magnitude. Possible reasons for the discrepancies are briefly discussed in relation with the employed theoretical models of plasma properties.

Simulation of ablating wire in wire array Z-pinch

Summary form only given. Ablation of a wire in the wire-array Z-pinch discharged on MAGPIE has been simulated in a two-dimensional domain of finer grid resolution using a magnetohydrodynamic code, GORGON. For accurate description of ohmic heating at high densities, an electrical conductivity model for nonideal plasma has been incorporated in the code. Emissions of line radiation as well as blackbody radiation are taken into account based on an astrophysical model in order to show the radiation cooling effect. Starting from the wire core assumed as warm dense plasma initially, the expansion and implosion dynamics of coronal plasma are demonstrated and basic plasma parameters are calculated as a function of time. Computed profiles of electron density are compared with data measured by laser interferometer at a certain point of time. The level of electron densities predicted by simulation appears reasonably compatible with measurements despite some discrepancies found in regions away from the initial wire core position. A few physical points are discussed regarding nonideal plasma and radiation emission models.

Electrical Conductivities of Nonideal Iron and Nickel Plasmas

Summary form only given. Electrical conductivities of iron and nickel plasmas are calculated using a nonideal plasma ionization balance model that takes into account the excess free energy due to strong Coulomb coupling between charged particles in the pressure- ionization regime. A linear mixture rule is utilized that takes account of both the electron-ion and electron-neutral collisions. The electrical conductivities calculated for partially ionized plasmas are in fair agreement with data measured in exploding wire discharge experiments and effectively demonstrate the insulator-metal transition near solid densities. A time-dependent one-dimensional MHD simulation is carried out for various metal plasmas including aluminum and copper and shocked water produced by under water explosion of metal wires. For comparison, hydrodynamic behaviors have been measured by a fast framing camera. Comparisons of the temporal behaviors of plasma boundaries and water shock propagations show reasonable agreements. In the early stages of discharge, the calculated electrical conductivities seem to effectively reproduce the measured conductivity behaviors.

Insulator-Metal Transition Simulation of Nonideal Plasmas

Summary form only given. The transport properties of dense plasmas, which are usually produced by strong shock wave compression or capillary discharge, exhibit nonideal characteristics, e.g., insulator-metal transition, that can not be described by classical theories. This paper presents a practical computational model to evaluate the ionization balances and electrical conductivities of a dense plasma in which the strong Coulomb interactions between ions and electrons taken into account. The correction term in the ionization potential expression is derived by adopting excess free energy fittings given by Chabrier-Potekhin [Phys. Rev. E 58, 4941 (1998)] and Tanaka-Mitake-Ichimaru [Phys. Rev. A 32, 1896 (1985)]. The calculated electrical conductivities of hot dense metal plasmas in their partially ionized regime show reasonable agreements with data measured in experiments including pressure-ionization phenomenon