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Excited state and steady state populations in high pressure plasma with heavy particle collisional ionization and electron-ion recombination
Single- and two-particle properties in a dense plasma are discussed in connection with their role in the mass action law for a partially ionized plasma. The two-particle-bound states are nearly density independent, while the continuum is essentially shifted. The single-particle states are damped, and their energy has a negative shift and a parabolic behavior for small momenta.
A computer program based on the theoretical work of Gyftopoulos, Steiner, and Levine on bimetallic systems and using a modified version of Wilkins' SIMCON subroutine SURFAS was written for the Univac 1108. This program, WFGSL, accepts the operating conditions and the physical parameters pertinent to the substrate and adsorbate, and outputs the field-free work function, electron current (Richardson equation), ion current (Saha equation), and fractional substrate coverage by the adsorbate. A brief description of the theory is presented together with a program description and listing. An application of the program to a bimetallic system of cesium (adsorbate) and rhenium (substrate) is also described.
Validity range of Saha equation for radiationless decay of high-density plasmas in magnetohydrodynamic power generation
The structure of a cylindrical blast wave with ionization at non-LTE conditions was calculated using equations previously developed by Wu and Fu (1970). The degree of ionization was predicted by a modified Saha equation. Temperature profiles show that the temperature at non-LTE conditions is lower than at LTE near the shock front. This corresponds to a higher degree of ionization for the non-LTE limit, which indicates that the neutral gas absorption is much more efficient at non-LTE than at the LTE limit. The decaying velocity under non-LTE is approximately 15% less than under LTE.
Presented here is a transcription of the lecture notes from Professor Allan N. Kaufman’s graduate statistical mechanics course Physics 212A and 212B at the University of California Berkeley from the 1972–1973 academic year. 212A addressed equilibrium statistical mechanics with topics: fundamentals (micro-canonical and sub-canonical ensembles, adiabatic law and action conservation, fluctuations, pressure, and virial theorem), classical fluids and other systems (equation of state, deviations from ideality, virial coefficients and van der Waals potential, canonical ensemble and partition function, quasistatic evolution, grand-canonical ensemble and partition function, chemical potential, simple model of a phase transition, quantum virial expansion, numerical simulation of equations of state, and phase transition), chemical equilibrium (systems with multiple species and chemical reactions, law of mass action, Saha equation, chemical equilibrium including ionization and excited states), and long-range interactions (including Coulomb, dipole, and gravitational interactions, Debye–Hückel theory, and shielding). 212B addressed nonequilibrium statistical mechanics with topics: fundamentals (definitions: realizations, moments, characteristic function, and discrete variables), Brownian motion (Langevin equation, fluctuation–dissipation theorem, spatial diffusion, Boltzmann’s H-theorem), Liouville and Klimontovich equations, Landau equation (derivation, elaboration, and H-theorem, and irreversibility), Markov processes and Fokker–Planck equation (derivations of the Fokker–Planck equation and a master equation), linear response and transport theory (linear Boltzmann equation, linear response theory of Kubo and Mori, relation of entropy production to electrical conductivity, transport relations and coefficients, normal mode solutions of the transport equations, sketch of a generalized Langevin equation method for transport theory), and an introduction to nonequilibrium quantum statistical mechanics.
The theory of dense hydrogenic plasmas beginning with the two component quantum grand partition function is reviewed. It is shown that ionization equilibrium and molecular dissociation equilibrium can be treated in the same manner with proper consideration of all two-body states. A quantum perturbation expansion is used to give an accurate calculation of the equation of state of the gas for any degree of dissociation and ionization. In this theory, the effective interaction between any two charges is the dynamic screened potential obtained from the plasma dielectric function. We make the static approximation; and we carry out detailed numerical calculations with the bound and scattering states of the Debye potential, using the Beth-Uhlenbeck form of the quantum second virial coefficient. We compare our results with calculations from the Saha equation.
Density of ionization from corrected Saha equation applied to dense aluminum plasmas
Statistical mechanics of partially ionized hydrogen plasma, deriving Saha equation to calculate ionization degree and potential for various electron densities and temperature
The effect of the calculation of the cluster integrals on three particles is analyzed and evaluated for a hydrogen plasma where a pairwise-additive hard sphere-Coulomb potential is assumed. The Mayer cluster integral method was used to calculate the Helmholtz free energy which was then applied to the calculation of the electron number density through an iterative technique using a corrected Saha equation. It is seen that the three particle integrals provide a substantial correction to the calculations in the low energy-high density region of the hydrogen plasma.
Transition probabilities for 14 lines of Fe II and 12 lines of Fe I in the wavelength region 2560-2737 A were measured by use of a shock tube and the hook method. Absolute oscillator strengths for resonance lines of Fe I reported by Banfield and Huber were used to determine the number density of neutral iron in the shock-heated gas. With the assumption of thermal equilibrium, the density of singly ionized iron atoms in this gas was then computed from the measured temperature and pressure with the aid of the Saha equation. Our results on the 12 strongest of the 13 lines belonging to the first ultraviolet multiplet of Fe II indicate that the multiplet f-value is larger by a factor of 2 than that derived from lifetime measurements by Assousa and Smith.
An experimental investigation is described in which measurements were made of plasma properties and other physical parameters upstream and downstream of the orifice plate of an operating mercury hollow cathode. These measurements included plasma property profiles, internal surface temperatures, internal pressure, and spectroscopic data of the external discharge. The results show the plume-to-spot mode transition to be characterized by significant changes in the plasma properties downstream of the cathode orifice, including the disappearance of an apparent electron free-fall region which is found to be present in the plume mode. The results also indicate the existence of a very dense plasma (10 to the 10th to 10 to the 14th electrons/cu cm) with steep electron density gradients in the region upstream of the orifice. The upstream data is found to correlate well with a modified form of the Saha equation. The related analysis indicates that the heavy particles approach thermal equilibrium with the electrons in the region of the orifice and that the ionization fraction in the orifice is very high - 80 to 100%.
Experiments showed that stray magnetic fields can adversely affect the capacity of a hollow cathode neutralizer to couple to an ion beam. Magnetic field strength at the neutralizer cathode orifice is a crucial factor influencing the coupling voltage. The effects of electrostatic accelerator grid aperture diameters on the ion current extraction capabilities were examined experimentally to describe the divergence, deflection, and current extraction capabilities of grids with the screen and accelerator apertures displaced relative to one another. Experiments performed in orificed, mercury hollow cathodes support the model of field enhanced thermionic electron mission from cathode inserts. Tests supported the validity of a thermal model of the cathode insert. A theoretical justification of a Saha equation model relating cathode plasma properties is presented. Experiments suggest that ion loss rates to discharge chamber walls can be controlled. A series of new discharge chamber magnetic field configurations were generated in the flexible magnetic field thruster and their effect on performance was examined. A technique used in the thruster to measure ion currents to discharge chamber walls is described. Using these ion currents the fraction of ions produced that are extracted from the discharge chamber and the energy cost of plasma ions are computed.
Many-body formulations of the equations of state are restated as a set of Saha-like equations. It is shown that the resulting equations are unique and convergent. These equations are similar to the usual Saha equations to the order of the Debye-Huckel theory. Higher order corrections, however, require a more general formulation. It is demonstrated that the positive free energy resulting from the interaction of unscreened particles in high orbits depletes the occupation of these states, without the introduction of shifted energy levels.
Discrepancy between observed ion production rate in cesium thermionic converter and Saha-Langmuir equation prediction suggests locality of ion formation
The study deals with the plasma behavior as applied to spacecraft propulsion from the perspective of obtaining better design and modeling capabilities. The general theory of spectroscopy is reviewed, and existing methods for converting emission-line intensities into such quantities as temperatures and densities are outlined. Attention is focused on the single-atomic-line and two-line radiance ratio methods, atomic Boltzmann plot, and species concentration. Electronic temperatures for a helium plasma are determined as a function of pressure and a gas-flow rate using these methods, and the concentrations of ions and electrons are predicted from the Saha-Eggert equations using the sets of temperatures obtained as a function of the gas-flow rate. It is observed that the atomic Boltzmann method produces more reliable results for the electronic temperature, while the results obtained from the single-line method reflect the electron temperatures accurately.
We present the framework and methodology for the new Los Alamos National Laboratory (LANL) G as chemical E quation O f S tate at H igher temperatures code (GEOSH) which aims to accurately model the behavior of chemically complex gaseous mixtures in equilibrium. Assuming the ideal gas approximation, GEOSH leverages the recursive nature of the Saha ionization and molecular equations in order to eliminate the molecular and ionic degrees of freedom, thereby reducing the problem size to the number of atomic species plus one for the free electrons if ions are included. This approach allows the chemical species, both molecular and ionic, of the mixture to be expressed in terms of the abundances of the elemental species. As a result, the GEOSH framework achieves a reduction in computational expense, increased processing speed, and the capability to efficiently model large-scale chemical networks. This report provides the necessary physical background and theoretical foundations for the GEOSH code, accompanied by benchmarking studies.
Ion production rate in cesium thermionic converter related to Saha-Langmuir surface ionization equation