Efficient and consistent methodology for the calculation of population densities, partition functions, and thermodynamic properties of ideal and weakly non-ideal multicomponent plasma mixtures in the P-T phase space
A set of nonideal Saha equations, for multicomponent plasma mixtures, can be derived from the conditions of the minimization of the free energy function in the ionization processes. Population densities derived from the solution of this set of equations subjected to electro-neutrality and conservation of nuclei are fully consistent with the thermodynamic properties derived from the same free energy function and, therefore, can be used to calculate these properties. Depending on the degree of complexity of the free energy function, nonideal Saha equations are obtained with different forms of nonideality corrections. In most practical situations, the problem of solving the resulting system of coupled nonlinear Saha equations, subjected to the above mentioned constraints, in the pressure-temperature (P-T) phase space, is found to be effectively a one-dimensional nonlinear problem i.e., solving a single transcendental equation. The methodology and algorithm presented herein are based on "the chemical picture," with all thermodynamic properties derived self-consistently from the free energy function, and on the mapping of the resulting set of governing equations into a one-variable zero-search. The algorithm is successful for most practical models for nonideality corrections to the free energy function, which are fully reflected in the derived nonideal Saha equations as lowering of ionization potentials, corrected equation of state, and truncated partition functions. The ease and efficiency of the introduced algorithm allows, with significant simplicity, the computations of population densities of all plasma species (neutral, ionized, and excited) up to maximum ionization states equal to the atomic numbers of the involved elements with minimal computational work. It also considers an extensive database of energy levels of the excited states. The algorithm is analytically known to be safe, fast, efficient, and solves the problem to the machine accuracy. It shows no numerical instabilities, no convergence problems, and no accuracy limitations or lack-of-change problems, which have been repeatedly reported in the literature. A nontrivial problem is worked out and presented in detail showing the effectiveness of the present methodology. For completeness, a criterion for the validity of the assumption of local thermodynamic equilibrium is applied to the results of the sample problem showing regions of the pressure-temperature phase space over which the assumption is valid.
A theoretical model for the physical processes in the confined high pressure discharges of electrothermal launchers
Different physical processes in confined high-pressure discharges are analyzed. The energy transport inside the discharge tube yields a radial temperature profile which has sharp gradients only near the tube walls. The regime at which such discharges can operate at a steady state is determined. For a given discharge ablation rate and plasma pressure, the tube length is limited. An analytical model is developed for confined high-pressure discharges operating in a quasi-steady-state in which the resulting plasma jet characteristics are steady at hydrodynamic timescales. This model allows the calculation of all the discharge parameters, such as ablation rate plasma temperature, resistivity, density and pressure as functions of the slowly varying current and the tube dimensions. The scaling laws obtained in this model are important for determining the impedance matching between the discharge and the power source and upgrading the discharge energy in electrothermal launchers to hypervelocities. Good agreement is obtained between the analytical model and experimental results at energies up to 100 kJ. >
Dissipation Loss Effects in Isolated and Coupled Transmission Lines
This paper describes a computer-aided analysis of dissipation losses in uniform isolated or coupled transmission lines for microwave and millimeter-wave integrated-circuit applications. The analysis employs a quasi-TEM model for isolated transmission lines and for the even- and odd-mode transmission lines associated with coupled-line structures. The conductor and dielectric losses are then related to equivalent charge density distributions, which are evaluated using a method-of-moments solution. The transmission lines treated by this analysis may contain any number of Iossy conductors and inhomogeneous dielectrics, consisting of any number of different homogeneous dielectric regions. A development is provided to explicitly relate the four-port terminal-electrical performance of directional couplers to evaluated even- and odd- mode loss coefficients. Examples of evaluated losses are presented in graphical form for isolated lines of inverted microstrip and trapped inverted microstrip and edge-coupled microstrip with a dielectric overlay. The analysis accuracy has been confirmed using microstrip and coplanar waveguide configurations. A comparison is made of the total loss characteristics for microstrip, coplanar waveguide, inverted microstrip, and trapped inverted microstrip. Calculations are compared with measurements for the coupled-line structure. Accuracy of the solution and suggested refinements are discussed. Five computer programs are documented.