Mofreh R. Zaghloul

Algorithm 916: Computing the Faddeyeva and Voigt Functions

We present a MATLAB function for the numerical evaluation of the Faddeyeva function w(z). The function is based on a newly developed accurate algorithm. In addition to its higher accuracy, the software provides a flexible accuracy vs efficiency trade-off through a controlling parameter that may be used to reduce accuracy and computational time and vice versa. Verification of the flexibility, reliability, and superior accuracy of the algorithm is provided through comparison with standard algorithms available in other libraries and software packages.

Thermo-Physical Properties and Equilibrium Vapor-Composition of Lithium Fluoride-Beryllium Fluoride (2LiF/BeF2) Molten Salt

Abstract An assessment of Flibe thermo-physical properties relevant to the prompt x-rays ablation of the liquid wall is presented with emphasis given to the equilibrium vapor composition and vapor pressure. The available data sets for Flibe thermo-physical properties, which cover a very narrow range of temperature have been extended and adjusted to cover the whole range of the liquid phase and to assure consistency with the estimated critical constants. Investigation of the equilibrium vapor composition showed a contradiction with previously published results regarding the stability of the mixed dimmer LiBeF3. New results for the vapor composition and total vapor pressure of Flibe also have been presented, compared to previous results, and used to calculate the temperature-dependent latent heat of vaporization.

On the ionization equilibrium of hot hydrogen plasma and thermodynamic consistency of formulating finite internal partition functions

The problem of formulating a thermodynamically-consistent finite internal partition function (IPF) in nonideal hydrogen plasma systems is investigated and analyzed within the chemical picture revealing inaccuracies and inconsistencies buried in widely used formulations in the literature. The analysis carried out here, though performed for the simplest case of pure nonideal hydrogen plasma, it shows all specific features of the problem and is extendable to the general case of a complex multi-component plasma mixture. A criterion for the separability of the configurational component of the free energy is presented and an accurate and consistent formulation of the problem is introduced. The presented criterion and the introduced consistent formulation of the problem clear ambiguities in other formulations in the literature and provide a better understanding of the problem. An illustrative example is worked out showing simplicity and effectiveness of the proposed consistent formulation and the importance of terms, essential for thermodynamic consistency, which are commonly neglected by other authors in the literature.

A simple theoretical approach to calculate the electrical conductivity of nonideal copper plasma

A simple theoretical approach to calculate the electrical conductivity of partially ionized nonideal copper plasma is introduced. The densities of plasma species are calculated, to machine accuracy, including electronic excitation and allowing for high ionization states up to the atomic number of the element. Depression of ionization energies is taken into account using an interpolation formula that is valid over a wide range of densities. The formula yields the results of the Debye–Huckel and the ion-sphere models at the limiting boundaries of low and high densities, respectively. The nonideal Coulomb logarithm is represented by an analytic wide-range formula supplemented by a specially tailored cutoff parameter. Effects of excluding excited and high ionization states on the calculation of ionization equilibrium and electrical conductivity of copper are investigated and assessed. Computational results of the electrical conductivity are compared with results from other theoretical models and available exp...

Improved modelling of electrothermal plasma source with radiation transport

An improved one-dimensional, time-dependent model with radiation transport is developed and used to simulate the evolution and flow of Ohmically heated nonideal plasma in the capillary of an electrothermal (ET) plasma source operated in the ablation stabilized arc regime. The model uses the Ohmic input power, recovered from the experimentally measured impedance, as the sole driving force of the computations to circumvent depending on arguable theoretical models of the resistivity of nonideal plasma. A consistent model of the equation of state and thermodynamic functions of weakly nonideal multi-component plasma mixtures is implemented and used to calculate the thermodynamic properties of the ET plasma generated from the ablation of the capillary wall. The flow velocity at the bore exit is not allowed to exceed the local sound speed and no prior assumptions of choked-flow are made at the bore exit. The frequency-dependent and frequency-averaged opacities of the plasma have been calculated considering the basic atomic processes of photoionization, inverse bremsstrahlung, resonant photoabsorption as well as electron scattering. Radiation transport has been implemented by modelling the plasma column as a grey gas the emissivity of which is calculated using an effective beam length Leb. The radiative heat flux escaping the surface of the grey plasma column is used to calculate the rate of the ablated mass improving the temporal behaviour of the calculated plasma parameters. Particular attention is devoted to investigating the ablation process and the evaluation of the so-called heat of ablation. Computational results are presented and discussed.

On the calculation of equilibrium thermodynamic properties and the establishment of statistical-thermodynamically-consistent finite bound-state partition functions in nonideal multicomponent plasma mixtures within the chemical model

The problem of the calculation of equilibrium thermodynamic properties and the establishment of statistical-thermodynamically consistent finite bound-state partition functions in nonideal multicomponent plasma systems is revised within the chemical picture. The present exploration accompanied by the introduction of a generalized consistent formulation, in terms of the solution of the inverse problem, clears ambiguities and gives a better understanding of the problem on top of pointing out weaknesses and inaccuracies/inconsistencies buried in widely used models in literature.

IFE Liquid Wall Response to the Prompt X-Ray Energy Deposition: Investigation of Physical Processes and Assessment of Ablated Material

Abstract This paper considers the physical processes and material removal mechanisms associated with the energy deposition in an inertial fusion energy liquid wall from the prompt X-ray spectrum of an indirect-drive inertial fusion target. These are important as the ablated material could generate aerosol in the chamber, which without adequate chamber clearing could result in a chamber environment unsuitable for driver propagation and/or target injection. Simple computations were used to identify and characterize the important material removal mechanisms relevant to the energy deposition regime under consideration. Explosive boiling was found to be the most relevant thermal response mechanism due to the high heating rate from the X-ray photon energy deposition. Investigation showed that explosive boiling occurs when the material temperature approaches the critical temperature and has a threshold value that can be derived from the material equation of state or the rate of homogeneous nucleation. Another important mechanism is mechanical spall that can result when shock wave-induced local tensile stresses exceed the spall strength of the material. Both explosive boiling and mechanical spall occur upon crossing the thermodynamic stability border (spinodal curve) either through rapid heating or through overexpansion of the material. Relevant material properties of the candidate liquid wall materials needed to perform the present assessment are compiled, derived, and presented. A simple energy deposition volumetric analysis is used to estimate both thermally ablated and mechanically spalled regions of the liquid wall material. The choice of liquid/wall combination is found to play an important role in reducing or eliminating the occurrence of spall in the liquid wall.

Measurement of Electrical Conductivity of Weakly Nonideal Multicomponent Plasma Mixtures Generated From Dielectric Materials

Nonideal complex multicomponent plasmas generated from dielectric compound materials are of crucial importance to many critical technologies, and the need to measure and determine the electrical conductivity of these plasmas is imperative. In this paper, we present preliminary successful measurements of the electrical conductivity of weakly nonideal partially ionized complex plasma mixtures generated from dielectric materials. The complex multicomponent partially ionized vapors were generated using an electrothermal plasma source operated in the ablation-controlled arc regime, where the compound dielectric materials were used as the liner of the capillary wall serving as the source of plasma species. The measured discharge current was used in conjunction with the active or pure resistive part of the recorded discharge voltage to calculate the electrical conductivity as a function of time. A comprehensive 1-D time-dependent computer code with radiation transport, which uses the recovered ohmic input power as the only driving force of the computations, was used to report the corresponding plasma state. Measurements in the temperature range of 11000-16200 K and density range of 0.1-25 kg/m3 were performed, and the results were presented, discussed, and compared with theoretical predictions.

Inconsistency in Fermi’s probability of the quantum states

AbstractWe point out an important hidden inconsistency in Fermi’s probability of the quantum states that engendered inconsistent/inaccurate equations-of-state extensively used in the literature to model nonideal plasma systems. The importance of this amendment goes beyond rectifying our comprehension and foundation of an important physical problem to influencing contemporary research results.

Critical parameters, thermodynamic functions, and shock Hugoniot of aluminum fluid at high energy density

We present estimates of the critical properties, thermodynamic functions, and principal shock Hugoniot of hot dense aluminum fluid as predicted from a chemical model for the equation-of-state of hot dense, partially ionized and partially degenerate plasma. The essential features of strongly coupled plasma of metal vapors, such as multiple ionization, Coulomb interactions among charged particles, partial degeneracy, and intensive short range hard core repulsion are taken into consideration. Internal partition functions of neutral, excited, and multiply ionized species are carefully evaluated in a statistical-mechanically consistent way. Results predicted from the present model are presented, analyzed and compared with available experimental measurements and other predictions in the literature. A distinct feature of the predictions of the present model is the appearance of a third kink in the Hugoniot curve at a weaker shock strength which can be attributed to the successive ionization of the three electrons in the M shell.