Ionization Balance In Plasmas Research Articles

Plasma ionization balance in chemical-picture and average-atom models.

We propose an approximate method to calculate ion partition functions in the context of the chemical-picture representation of plasmas as an interacting mixture of various ions and free electrons under the local-thermodynamic-equilibrium conditions. The method uses the superconfiguration approach and implies that the first-order corrections to the energies of excited electron configurations due to the electron-electron interaction may be replaced by a similar first-order correction to the energy of the basic configuration of an ion with the same number of bound electrons. The method enables one to significantly speed up the calculations and generally provides quite accurate results. Using the method proposed, plasma ionization balance and average ion charges calculated on the base of the chemical-picture representation show a good agreement with the relevant average-atom data. For the case of weak electron-ion nonideality, we provide approximate relations between the chemical-picture and average-atom values of the average ion charge, chemical potential, and plasma-density depression of ionization potential.

Ionization Balance in Low-Temperature Plasmas with Nanosized Dust

Ionization mechanisms in the low-temperature thermal plasma, which contains alkali metal atoms as ionizable component and nanosized dust grains, are studied. In such a plasma, electrons are captured by dust grains, because the work function of grains depends on their sizes, and the electron adsorption rate is more than the thermionic emission rate for nanosized grains. Accordingly, an increase of the dust grain number leads to a decrease in the volume ionization and recombination rates, because they depend on the number density of electrons. At the same time, the role of surface processes in the plasma ionization balance is increased, because the total grain surface is increased. The approximate calculation techniques for low and high grain number densities are proposed. The criterions for approximate calculations are specified.

Electron emission from particles strongly affects the electron energy distribution in dusty plasmas

The electron energy distribution of a low-temperature dusty plasma has been measured via a Langmuir probe. An unexpected broad peak at energy in the 2–4 V range has been observed. This can be theoretically reproduced for a sufficiently large electron emission rate from the nanoparticles dispersed in the plasma. A careful analysis of the nanoparticle energy balance, using measured values of nanoparticle concentration and plasma density, confirms that particles are sufficiently hot under the conditions of this study to rapidly inject electrons into the plasma via field-assisted thermionic emission. This work suggests that the presence of dust affects the plasma ionization balance more deeply than previously thought.

Suppression of Dielectronic Recombination at Finite Densities

Density-dependent effective dielectronic recombination rate coefficients are determined in order to explore finite-density effects on the ionization balance of plasmas.

SUPPRESSION OF DIELECTRONIC RECOMBINATION DUE TO FINITE DENSITY EFFECTS

We have developed a general model for determining density-dependent effective dielectronic recombination (DR) rate coefficients in order to explore finite-density effects on the ionization balance of plasmas. Our model consists of multiplying by a suppression factor those highly-accurate total zero-density DR rate coefficients which have been produced from state-of-the-art theoretical calculations and which have been benchmarked by experiment. The suppression factor is based-upon earlier detailed collision-radiative calculations which were made for a wide range of ions at various densities and temperatures, but used a simplified treatment of DR. A general suppression formula is then developed as a function of isoelectronic sequence, charge, density, and temperature. These density-dependent effective DR rate coefficients are then used in the plasma simulation code Cloudy to compute ionization balance curves for both collisionally ionized and photoionized plasmas at very low (ne = 1 cm^-3) and finite (ne=10^10 cm^-3) densities. We find that the denser case is significantly more ionized due to suppression of DR, warranting further studies of density effects on DR by detailed collisional-radiative calculations which utilize state-of-the-art partial DR rate coefficients. This is expected to impact the predictions of the ionization balance in denser cosmic gases such as those found in nova and supernova shells, accretion disks, and the broad emission line regions in active galactic nuclei.

Plasma ionization and resistivity models for low-, mid- and higher-atomic number plasmas and their applications to radiative properties of z-pinches

The LTE Saha–Boltzmann plasma ionization balance model and the Braginskii plasma electric resistance model are compared with the results by a suite of codes based on the average-atom model, which is a quantum-mechanical version of the Temperature Dependent Thomas–Fermi Theory. The analysis is focused on low-Z Al, mid-Z Cu and higher-Z Mo plasmas over broad ranges of electron temperature Te and electron number density ne. Calculations of mean ion charge by these two LTE models are compared to the results produced by non-LTE atomic kinetic codes. The applicability of the LTE and non-LTE models to the description of the radiative properties of highly-radiating z-pinch plasmas is also discussed. Two different approaches to the calculation of plasma resistance and their effects on line radiation mechanisms are analyzed.

Theoretical studies on dielectronic recombination of neonlike gold and its effects on plasma ionization balance and radiation energy

The dielectronic recombination (DR) of neonlike gold ions is investigated employing the flexible atomic code based on the relativistic configuration interaction method, and its influence on the ionization balance and radiation energy in high-temperature plasma is also studied. The total resonance strength for LMM configuration complex is in a good agreement with the experimental measurement and other theoretical works. The DR rate coefficients are calculated and compared with the three-body recombination and radiative recombination rate coefficients. The DR process is the dominant recombination mechanism of Ne-like gold ions for plasma with temperature Te≥6.5 keV and density ne≤2×1022 cm-3, which is close to the condition of X-ray conversion region in the inertial confinement fusion. Moreover, the DR satellite spectra of LMM, LMN and LMO resonances are simulated, and compared with the intensities of the corresponding resonance lines induced by the electron impact excitation. The intensity ratio of the satellite line 3D’ $[(2p^{5}_{3/2}3d_{3/2}3d_{5/2})_{J=5/2}$ – $(2p^{6}3d_{3/2})_{ J=3/2}]$ and the resonance line 3D $[(2p^{5}_{3/2}3d_{5/2})_{J=1}$ – $(2p^{6})_{J=0}]$ is given, which can be applied for diagnostics of plasma temperature.

X-Ray Scattering Measurements of Radiative Heating and Cooling Dynamics

Spectrally and time-resolved x-ray scattering is used to extract the temperature and charge state evolution in a near solid density carbon foam driven by a supersonic soft x-ray heat wave. The measurements show a rapid heating of the foam material (approximately 200 eV/ns) followed by a similarly fast decline in the electron temperature as the foam cools. The results are compared to an analytic power balance model and to results from radiation-hydrodynamics simulations. Finally, the combination of charge state and temperature extracted from this known density isochorically heated plasma is used to distinguish between dense plasma ionization balance models.

Electrical Conductivities of Nonideal Iron and Nickel Plasmas

AbstractElectrical 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 couplings between charged particles in the pressure‐ionization regime. 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. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A Dynamic Conductance Model of Fluorescent Lamp for Electronic Ballast Design Simulation

A Spice-compatible dynamic conductance model of a fluorescent lamp for use in electronic ballast simulation is presented. The time-dependent conductance of the fluorescent lamp is derived from a plasma ionization balance equation that uses simplified descriptions of the physical processes within the lamp as its basis. The model has been designed to enable user-defined lamp radius, length, buffer gas pressure and cold-spot temperature as input parameters thus representing a valuable tool for ballast simulations. Simulation results are compared to experimental measurements and satisfactory agreement is achieved.

Ionization equilibrium and equation of state in strongly coupled plasmas

Calculation of the physical properties of reacting plasmas depends on knowing the state of ionization and/or the state occupation numbers. Simple methods have often been used to estimate ionization balance in plasmas, but they are not adequate for understanding a variety of new experimental and observational measurements. Theoretical methods to determine the ionization state of partially ionized plasmas must confront the effects of density on bound states and strong ion coupling. These methods can be separated into two categories. Chemical picture methods consider the system to be composed of distinct chemical species. Consequently, it is necessary to assert the effect of the plasma environment on internal states of these species. On the other hand, physical picture methods view the plasma in terms of its fundamental constituents; i.e., electrons and nuclei, so that plasma effects on bound states are a basic component of the theory. A discussion of some work representative of both of these philosophies will be given. Some comparisons between theories and with recent helioseismic observations and shock experiments will also be given.

Effect of excited states on the ionization balance in plasmas via the enhancement of ionization and recombination rate coefficients.

The effect of excited states on the effective ionization and recombination rate coefficients for the ground states was investigated analytically and by computer simulation. The calculation was done for carbon ions. The results using carbon ions show (1) the contribution from excited states to ionization rate coefficients becomes significant even at an electron density as low as 10(15) cm(-3) and saturated from around N(e) approximately 10(20) cm(-3); (2) the lower the electron temperature, the larger the contribution; (3) in the case of recombination rate coefficients, there is still a non-negligible contribution from excited states even at a very low electron density of 10(10) cm(-3), where the contribution has been considered negligible; (4) this contribution to the recombination rate coefficients increases linearly with the electron density; (5) the enhancements of the ionization and recombination rate coefficients increase as N(e) increases and are saturated to the same value at higher densities; (6) there exists a region of temperature and density where the recombination is effectively hindered. Some of the behaviors of the ionization and recombination rate coefficients in the extreme regions of a very low and high electron density were analytically understood. The calculated ionization and recombination rate coefficients for carbon ions, including the effect of excited states, were used in a one-dimensional magnetohydrodynamic code for the calculation of the ionization balance of carbon ions in a Z-pinch carbon plasma and the gain of C VI H(alpha) (18.2 nm) line. The significant change in the evolution of the ionization balance was observed. The rapid depletion of C VII ions by the increased recombination rate reduces the gain significantly by a factor of approximately 3 compared to the case where the contribution from excited states was neglected. Such calculations can be done for other ions. The characteristics found for carbon ions are generic and applicable to other ions.

The electronic structure of dense plasmas

The electronic structure of a dense plasma is considered within the context of a single electron interacting with an effective, time-independent potential. This potential consists of many screened ions which represent strong scattering sites. The strong, short range nature of the screened potentials significantly alters the plasma's electronic structure by introducing shape resonance effects. Additionally, the correlations between scattering sites can give rise to modifications analogous to band structure in crystalline matter. To lowest order these effects manifest themselves as a lowered continuum, while higher order terms generate structure in the density of states. These density-of-state modifications can alter rates of particular atomic transitions as well as change a plasma's ionization balance.

Soft-x-ray amplification in a laser-produced strontium plasma.

Amplification of soft x rays in Sr (Z=38) plasmas produced by second-harmonic laser irradiation of exploding foil targets is studied. Gains of 4.4 and 4.0 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, respectively, have been measured for the 164.1- and 166.5-\AA{} J=2 to 1 transitions in Ne-like Sr at laser intensities of 1.3\ifmmode\times\else\texttimes\fi{}${10}^{14}$ W/${\mathrm{cm}}^{2}$. Numerous x-ray and soft-x-ray transitions were identified in order to demonstrate typical spectra from x-ray laser plasmas and infer information regarding the plasma ionization balance. The J=0 to 1 transition at 159.8 \AA{}, analogous to the well-known Se J=0 to 1 line at 182.4 \AA{}, was not definitively observed due to a wavelength overlap with a Na-like Sr line. Two other J=0 to 1 transitions of interest at 84.9 and 133.0 \AA{} were not observed. Reduced gain on the J=2 to 1 lasing lines was seen for several shots taken at a lower pump laser intensity of 7.0\ifmmode\times\else\texttimes\fi{}${10}^{13}$ W/${\mathrm{cm}}^{2}$. Possible reasons for this are considered. The results of this work imply the feasibility of a high-output-power cavity geometry Ne-like Sr x-ray laser operating at 164.1 and 166.5 \AA{}.