Collision-dominated Plasma Research Articles

Transformed two-fluid equations of low-pressure plasmas with non-vanishing ion temperature without the singularity at the ionic sound barrier and several methods to solve these equations numerically

The equations of the two-fluid model of low-pressure plasmas with warm ion gas are taken into consideration including collisions between charged particles and neutrals, the charge exchange, and the ionization. The basic equations contain a removable singularity at the ion sonic speed. These equations are ill-conditioned in the subsonic interval of the ion flux, but they are well-conditioned in the transsonic one. First, several transformations and auxiliary functions are introduced in order to eliminate the singularity at the ion sound speed. The resulting boundary value problem is numerically solved by a multi-shooting method for one of the versions of the transformed equations. Second, an improved one-fluid-model is well-conditioned wherein the space charge density is calculated additionally using the electric field and the Poisson equation. The numerical solution yields usable approximated results in the subsonic interval and suitable initial values for the solution of the two-fluid model in the transsonic interval. Third, the unknown functions are expanded as a power series in the relation of the ion temperature to the electron temperature. These equations can be numerically integrated throughout both intervals without serious difficulties. A set of parameters is given describing subsonic intervals extending over the whole plasma. Results obtained by means of the used methods confirm that Bohm's sheath criterion loses its meaning in collision-dominated plasmas. The scopes of application of the different methods are treated by means of examples.

Special Issue on Numerical Modelling of Low‐Temperature Plasmas for Various Applications – Part I: Review and Tutorial Papers on Numerical Modelling Approaches

Special Issue on Numerical Modelling of Low‐Temperature Plasmas for Various Applications – Part I: Review and Tutorial Papers on Numerical Modelling Approaches

Effect of DC magnetic field on atmospheric pressure argon plasma jet

In this work, external DC magnetic field effect on the atmospheric pressure plasma jet has been investigated, experimentally. The magnetic field has been produced using a Helmholtz coil configuration. It has been applied parallel and transverse to the jet flow. The strength of the DC magnetic field is 0–0.28 and 0–0.57 Tesla between the two coils in parallel and transverse applications, respectively. It has been shown that the plasma gas flow plays the main role in magneto-active collision-dominated plasma. The effect of plasma fluid velocity on the jet emission has been discussed, qualitatively. It has been observed that the external DC magnetic field has different trends in parallel and transverse applications. The measurements reveal that the plasma jet irradiance increases in parallel field, while it decreases in transverse field. The former has been attributed to increasing plasma number density and the latter to loss of plasma species that reduces the magneto-plasma jet irradiance and in turn shrinks plasma jet number density. As a result, the plasma fluid velocity is responsible for such trends though the magneto-active plasma remains isotropic.

Modelling penetration and plasma response of a dense neutral gas jet in a post-thermal quenched plasma

This paper is about the dynamics of gas jet injection and propagation into the cold, current quench (CQ) discharge following the thermal quench (TQ) phase of a disruption event. Understanding the processes involved in the interpenetration between a dense, fast-moving supersonic gas jet and a magnetized plasma is fundamental to the solution of the disruption mitigation problem using massive gas injection. An analytical model was developed that provides the penetration depth of the jet in the CQ discharge. The model developed incorporates the injector, the vacuum space between injector and plasma, and the low beta CQ plasma through which the jet penetrates. The radially moving gas stagnates at some point inside the plasma by formation of a ‘bottle shock’, resulting in a certain penetration depth. Consistent with experimental findings, it is shown that high fuelling efficiency >70% and good penetration beyond the q = 2 surface is possible in such plasma discharges, but in normal (unquenched) plasma discharges penetration of dense gas jets will be quite poor. The paper also sheds light on how the external plasma responds to allow interpenetration of perfectly insulating gas jet through a strong magnetic field B2/2μ0 ≫ ρu2. The paper also develops semi-analytical models for the response of the cold, high-current, collision-dominated plasma to the insertion of a dense neutral jet: the propagation of cooling waves out along the magnetic field lines, the heated and ionized surface layer which also expands outwards along the magnetic field lines, and the electrical breakdown of the neutral gas within the jet volume. Although good penetration in the ITER post-TQ discharge can be achieved, the plasma resistivity is only marginally enhanced. This may render repetitive gas inject ineffective, as the concept requires a sizable resistivity enhancement to initiate a current profile contraction, and resulting kink-tearing activity to suppress runaway avalanching.

Atomic process in high-temperature radiation field

The ratio of radiation energy density to matter energy density is an important parameter to distinguish the characteristic of atomic processes in plasma. Actoring to this parameter, atomic processes in plasma can be divided into two typical categories: collision-dominated and radiation-dominated. According to numerical simulation, atomic processes of these two categories have different characteristics. The LTE state can be quickly reached in the collision-dominated plasma. However in the radiation-dominated plasma, the temperature of bound electrons, the ionization degree, and the temperature of free electrons have different relaxation time scales. There is some kind of quasi-LTE state.

Doubly ionized ion emission in laser-induced breakdown spectroscopy in air

The emission from doubly ionized species in laser-induced plasmas has not been properly investigated before since most analytical measurements were made at relatively long delays. This work proves that doubly ionized species, such as boron (B) III and iron (Fe) III, can exist during the first 150-200 ns of the plasma lifetime in plasmas produced in air by typical lasers with irradiances of 10(9)-10(11) W/cm(2). The emission from these ions was detected using both the double- and single-pulse excitations. The sum of the second ionization potential and the energy of corresponding excited states is approximately 30 eV. The presence of doubly charged ions in the early plasma was additionally confirmed by computer simulations using a collision-dominated plasma model. The emission from doubly ionized species may be used for analytical purpose. For example, in the spectrum from a B-Fe ore, the B III analytical line at 206.6 nm is free from Fe spectral interference thus enabling the online laser-induced breakdown spectroscopy sorting of ores into three products with high, medium, and low B(2)O(3) contents.

Abel inversion applied to a transient laser induced plasma: implications from plasma modeling

We test the effects of non-uniformity, non-transparency, and non-stationarity of a laser-induced plasma on the results obtained by the Abel inversion method. The method is commonly used for obtaining spatially resolved emissivity of axially symmetric non-homogeneous radiating objects. Besides the axial symmetry, the plasma is assumed to be optically thin. As the method addresses a certain plasma state, the plasma is required to be stationary during measurements. It is difficult to satisfy the aforementioned conditions for transient laser induced plasmas. As such the plasmas are not stationary; they have steep gradients of thermodynamic parameters that rapidly vary during the plasma evolution. Therefore, any conclusion based on time-integrated measurements and the corresponding data processing should account for these effects. In this work, we use the collision-dominated plasma model to generate time- and spatially resolved synthetic spectra. The spectra are processed by executing the Abel inversion using two numerical algorithms. Thus obtained spatially resolved plasma parameters (emissivity, temperature, and number density) are compared with the exact parameters used to set up the model. In doing so, the accuracy of the Abel inversion method is assessed. Special attention is paid to the dynamic aspect of the expanding plasma and possible errors which result from time-integrated measurements.

Solid-state traveling-wave amplifiers and oscillators in the THz range: effect of electron collisions

Due to their high plasma frequencies, drifting semiconductor plasmas interacting with slow electromagnetic waves hold promise for terahertz amplifiers and oscillators. In these devices, the gain and the type of instabilities are influenced by electron collisions. To study the effect of collisions, we developed a two-wave model describing the interaction between drifting solid-state plasmas and electromagnetic waves. This paper analyzes the two-wave dispersion relation for representative examples. As the examples show, convective and absolute instabilities can occur at high and low collision frequencies depending on the relationship between the collision frequency and the coupling coefficient. Surprisingly, an absolute instability occurs when collision-dominated plasmas interact with backward waves. The model can be used to determine the potential of a particular configuration in a solid-state amplifier or oscillator.

Influence of local-field corrections on Thomson scattering in collision-dominated two-component plasmas

The dynamic structure factor, which determines the Thomson scattering spectrum, is calculated via an extended Mermin approach. It incorporates the dynamical collision frequency as well as the local-field correction factor. This allows to study systematically the impact of electron-ion collisions as well as electron-electron correlations due to degeneracy and short-range interaction on the characteristics of the Thomson scattering signal. As such, the plasmon dispersion and damping width is calculated for a two-component plasma, where the electron subsystem is completely degenerate. Strong deviations of the plasmon resonance position due to the electron-electron correlations are observed at increasing Brueckner parameters r(s). These results are of paramount importance for the interpretation of collective Thomson scattering spectra, as the determination of the free electron density from the plasmon resonance position requires a precise theory of the plasmon dispersion. Implications due to different approximations for the electron-electron correlation, i.e., different forms of the one-component local-field correction, are discussed.

Dust voids in collision-dominated plasmas with negative ions

Using fluid theory, the properties of voids in collision-dominated plasmas containing negative ions are studied. The profiles of the charged-particle densities in the void region are obtained. It is also shown that with an increase of the negative-ion concentration, the electric field, the ion drift velocity, the dust charge at the void edge, as well as the void size decrease.

Nonequilibrium Properties of Electrons in Oxygen Plasmas

Theoretical investigations of DC discharge plasmas in reactors with plane electrodes are presented. A multiterm method for the solution of the space-dependent Boltzmann equation of the electrons has been adopted and modified to analyze the behavior of the velocity distribution function and of relevant macroscopic properties of the electron component in oxygen discharge plasmas for a wide range of pressure and applied voltage. On the basis of the results, the main features of the kinetics of the electrons are discussed. In particular, the analysis shows drastic changes of the properties of the electron gas in the transition from the regime with almost negligible impact of collisions at lower pressure to the collision-dominated plasma at higher pressure. Regarding the multiterm method, it is found that the convergent solution of the Boltzmann equation of the electrons is generally obtained, where the conventionally used two-term approximation still gives fair results at lower applied voltages and pressures around 100 Pa, but a multiterm method with up to ten terms is required when decreasing the pressure by almost one order of magnitude.

Self‐consistent Magnetohydrodynamic Modeling of Current Sheet Structure and Heating Using Realistic Descriptions of Transport Processes

A magnetohydrodynamic (MHD) model of an electron-ion, collision-dominated plasma that includes the electrical conductivity and thermoelectric tensors in Ohm's law is used to generate current sheet solutions in parameter ranges that correspond to those of the solar transition region and lower corona. The model contains a prescribed sheared magnetic field with a characteristic length scale L. The characteristic sheet width is 2L, but it is found that the temperature has transition region or coronal values only within a diffusion region (DR) with a width several orders of magnitude smaller than 2L. The heating rate per unit mass and flow speed in the DR are orders of magnitude larger, and the density is orders of magnitude smaller than in the surrounding plasma. The heating rate per unit volume is a maximum in the DR and falls off steadily outside the DR. The Joule heating rate and current density each consist of a conduction component driven by the center-of-mass electric field and a thermoelectric component driven by the temperature gradient. It is found that these components largely cancel, leading to a total heating rate and current density orders of magnitude smaller than either of their components. This suggests that thermoelectric current drive is important in determining current sheet structure. The center-of-mass electric field that provides the energy to maintain the plasma in a steady state is almost entirely the convection electric field. The electron magnetization Me is the product of the electron cyclotron frequency and the electron-ion collision time. Nonzero values of Me cause the conductivity and thermoelectric tensors to be anisotropic. It is found that the large values of Me that occur in the DR increase the heating rates per unit volume and mass by several orders of magnitude and can change the sign of the heating rate per unit mass from negative to positive, corresponding to a change from a cooling process to a heating process. This suggests that electron magnetization, and hence anisotropic transport, is a major factor in current sheet heating.

Impact of Electron–Electron Collisions on the Spatial Electron Relaxation in Non-Isothermal Plasmas

The impact of electron–electron collisions on the spatial relaxation of electrons in the column-anode plasma of a glow discharge, acted upon by a space-independent electric field and initiated by a constant influx at the cathode side of the plasma, is investigated in inert gas plasmas. The investigations are based on a new method for numerically solving the one-dimensional inhomogeneous Boltzmann equation of the electrons including electron–electron interaction in weakly ionized, collision-dominated plasmas. A detailed analysis of the spatial behaviour of the velocity distribution function and relevant macroscopic properties of the electrons is given for various degrees of ionization and electric field strengths. A significant impact of the electron–electron collisions on the relaxation structure and the resultant relaxation length already at relatively low ionization degrees has been found for low to medium electric fields.

Detection of Nitrogen and Neon in the X-Ray Spectrum of GP Comae Berenices with XMM/Newton

We report on X-ray spectroscopic observations with XMM/Newton of the ultracompact, double white dwarf binary GP Com. With the Reflection Grating Spectrometers (RGSs), we detect the Lyα and Lyβ lines of hydrogen-like nitrogen (N VII) and neon (Ne X), as well as the helium-like triplets (N VI and Ne IX) of these same elements. All the emission lines are unresolved. These are the first detections of X-ray emission lines from a double-degenerate, AM CVn system. We detect the resonance (r) and intercombination (i) lines of the N VI triplet, but not the forbidden (f) line. The implied line ratios for N VI, R = f/i < 0.3 and G = (f + i)/r ≈ 1, combined with the strong resonance line are consistent with formation in a dense, collision-dominated plasma. Both the RGS and EPIC/MOS spectra are well fitted by emission from an optically thin thermal plasma with an emission measure proportional to (kT/6.5 keV)0.8 (model cevmkl in XSPEC). Helium, nitrogen, oxygen, and neon are required to adequately model the spectrum; however, the inclusion of sulphur and iron further improves the fit, suggesting that these elements may also be present at low abundance. We confirm in the X-rays the underabundance of both carbon and oxygen relative to nitrogen, first deduced from optical spectroscopy by Marsh et al. The average X-ray luminosity of ≈3 × 1030 ergs s-1 implies a mass accretion rate ≈ 9 × 10-13 M☉ yr-1. The implied temperature and density of the emitting plasma, combined with the presence of narrow emission lines and the low- value, are consistent with production of the X-ray emission in an optically thin boundary layer just above the surface of the white dwarf.

Improved Transport Equations for Fully Ionized Gases

We have developed fluid transport equations for fully ionized gases that improve the description of Coulomb collisions. The aim has been to develop simple and versatile equations that can easily be implemented in numerical models and thus be applied to a large variety of space plasmas, while they still accurately describe thermal forces and energy flows in collision-dominated plasmas. Based on exact solutions to the Boltzmann equation in the collision-dominated limit, the correction term to the velocity distribution function that account for particle flows is assumed to be proportional to the third power of the velocity, leading to a near isotropic core distribution. Applying the fluid equations derived from this new velocity distribution to a collision-dominated electron-proton plasma with a small temperature gradient, the resulting electron heat flux, as well as the thermal force between electrons and protons, deviate less than 25% from the exact results of classical transport theory. The new equations predict a factor of 4 reduction in the thermal force acting on heavy, minor ions caused by an imposed heat flux, compared with fluid equations that are in common use today. The improved description of thermal forces is expected to be important for modeling the composition of stellar atmospheres.

Radiation dynamics of post-breakdown laser induced plasma

A radiation dynamic model is developed for a post-breakdown stage of a laser induced plasma expanding into vacuum. The model describes the plasma formed on a small solid particle, which is completely vaporized by a laser. The symmetry of the expanding plasma is spherical. The time frame for the applicability of the model is somewhat between a hundreds of nanoseconds, after the laser pulse is terminated, and a few microseconds, when the plasma ceases to emit. The model is based on a system of gas dynamic equations coupled with the equation of radiative transfer. Local thermodynamic equilibrium is assumed, allowing the application of the collision-dominated plasma model as well as standard statistical distributions. Calculations are performed for a dual SiC system, although calculations for any arbitrary number of system's components are permitted. The model has two implications. First, an analytical expression for the plasma radiation dynamics is obtained by artificially setting the initial conditions. Second, from experimentally measured plasma parameters, information is deduced about the initial state of the plasma. The main model input parameters are the total number and distribution of plasma species and the initial distribution of temperature. Some of the other model inputs, such as the speed of the plasma front and the temperature profile across the plasma can be directly measured, thus providing valuable experimental feedback to the model. The model outputs are the evolution of plasma temperature, the spatial and temporal distributions of atoms, ions and electron number densities and the evolution of the plasma spectrum in a desirable spectral window (e.g. 280–290 nm for the chosen in this work SiC system).

Effects of poloidal variation of neutral density on Pfirsch–Schlüter transport near the tokamak edge

Effects of neutral particles on plasma flows and radial transport in a collision-dominated plasma are discussed, with a particular attention given to the modifications due to a poloidal variation of the neutral density. It is found that neutrals are of no importance if the radial particle transport is on a Pfirsch–Schlüter level. If, on the other hand, anomalous effects increase this transport to the Pfirsch–Schlüter radial heat transport level or higher, neutral effects become important in determining the radial heat transport, radial electric field, and the ion parallel flow velocity.

Application of Plane Probe to Weakly Ionized Plasmas.

Probe characteristics are numerically obtained in a wide range of electron temperatures and densities for the collision-dominated plasma sheath in which the fundamental Langmuir theory of the electrostatic probe fails. The asymptotic theory of Cohen for continuum conservation equations is applied to the ellipsoidal probe, and to the plane probe as the limiting case. It is found that, for the collision-dominated plasma sheath, significant errors in measured electron temperature are expected if the fundamental Langmuir theory is used to evaluate the temperature from the measured probe current and voltage. For quick evaluation of the electron temperature in such plasmas, the bound triple-probe method is proposed, and numerical results are summarized in a graphical form for practical use.

Weakly ionized plasma in a supersonic plasma flow

The structure of the ion acoustic precursor of a shock wave in a weakly ionized collision-dominated plasma is studied numerically. It is shown that the simultaneous action of the nonlinearity, dispersion, and dissipation leads to the formation of an oscillating profile of the ion density in the precursor. There exist regimes in which the charged-particle density decreases abruptly and simultaneously the number of maxima in its profile within the precursor becomes smaller as the shock wave velocity increases in a jumplike manner. This effect is analogous to the corresponding hydrodynamic effect in narrow shallow channels (the “Houston's horse” effect). In the stage preceding this jumplike process, local regions may appear in which the degree of plasma ionization is elevated. Such plasma “bunches” give rise to the strong reverse action of the charged particles on the neutral component, resulting in the “stretching” of the precursor. This phenomenon is resonant in character and occurs in a narrow range of shock wave velocities.

Line ratios for helium-like ions: Applications to collision-dominated plasmas

The line ratios R and G of the three main lines of He-like ions (triplet: resonance, intercombination, forbidden lines) are calculated for CV, NVI, OVII, NeIX, MgXI, and SiXIII. These ratios can be used to derive electron density n_e and temperature T_e of hot late-type stellar coronae and O, B stars from high-resolution spectra obtained with Chandra (LETGS, HETGS) and XMM-Newton (RGS). All excitation and radiative processes between the levels and the effect of upper-level cascades from collisional electronic excitation and from dielectronic and radiative recombination have been considered. When possible the best experimental values for radiative transition probabilities are used. For the higher-Z ions (i.e. NeIX, MgXI, SiXIII) possible contributions from blended dielectronic satellite lines to each line of the triplets were included in the calculations of the line ratios R and G for four specific spectral resolutions: RGS, LETGS, HETGS-MEG, HETGS-HEG. The influence of an external stellar radiation field on the coupling of the 2^3S (upper level of the forbidden line) and 2^3P levels (upper levels of the intercombination lines) is taken into account. This process is mainly important for the lower-Z ions (i.e. CV, NVI, OVII) at moderate radiation temperature (T_rad). These improved calculations were done for plasmas in collisional ionization equilibrium, but will be later extended to photo-ionized plasmas and to transient ionization plasmas. The values for R and G are given in extensive tables, for a large range of parameters, which could be used directly to compare to the observations.