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.
Validity criteria for local thermodynamic equilibrium in plasma spectroscopy.
We have solved the collisional-radiative equations for atomic hydrogen and hydrogenlike ions (of nuclear charges 2 and 26) in a plasma and derived their excited-state populations for a wide range of plasma temperatures and densities. The populations of the higher-lying levels are well described by the Saha-Boltzmann equation. We refer to such plasmas as being in partial local thermodynamic equilibrium (LTE), and it is the purpose of this paper to present expressions by which it is possible to predict the lowest principal quantum number that meets the criterion of being within 10% of its Saha-Boltzmann value. We treat the ionizing plasmas, the recombining plasmas, and the plasmas in ionization balance as three separate cases. These criteria are then extended to the ground state to cover plasmas in complete LTE. Finally we discuss briefly the effect of opacity on these results and the extent to which they may be used for non-hydrogen-like systems. Throughout the paper care is taken to present physical pictures to explain the numerical results and comparisons are made with LTE criteria derived using more qualitative arguments by other authors.
Effects of thyrotropin-releasing hormone and a thyrotropin releasing hormone analog on growth and selected plasma hormones in lambs.
An 8-wk growth trial was conducted to assess the effects of continuous infusion of thyrotropin-releasing hormone (TRH) and an active TRH analog less than Aad-His-Pro-NH2 (the less than Aad is L-pyro-alpha-aminoadipic acid) on growth trial performance, carcass composition and hormone profiles of growing lambs. Both drugs were infused at 600 micrograms X lamb -1 X d -1 with 16 lambs/treatment. Both TRH and less than Aad-His-Pro-NH2 decreased average daily gain (ADG; P less than .01) and increased feed conversion (FC; P less than .01) compared with saline infused controls. Average daily feed intake was not altered. Carcasses of lambs given TRH or less than Aad-His-Pro-NH2 contained fewer kilograms of moisture (P less than .05) and appeared to contain fewer kilograms of protein. Thyrotropin-releasing hormone and less than Aad-His-Pro-NH2 increased thyroid gland weights (P less than .05), but pituitary gland weights were not different. Plasma thyrotropin (TSH) concentrations were increased by both drugs compared with control lambs, peaking at 4 to 7 d after initiating infusion. However, by 14 d, TSH concentrations returned to control levels. Triiodothyronine (T3) and thyroxine (T4) were elevated by both drugs over the entire 8-wk trial, with peak levels reached at 10 d and maintained for the duration of the study. Both TRH and less than Aad-His-Pro-NH2 increased prolactin over the entire period. Growth hormone levels were not altered by either drug. The effects of less than Aad-His-Pro-NH2 infusion on growth trial performance, carcass composition and hormone profiles of growing lambs were very similar to TRH. The negative effects of TRH and less than Aad-His-Pro-NH2 infusion on ADG, FC and carcass protein appear to be the result of elevated T3 and T4 levels.