Plasmas in Charge and Thermal Equilibrium; Arc Processes

It is generally accepted that the equation of state of the Debye and HUckel theory, originally developed for strong electrolytes basing on the classical statistical mechanics, is applicable to the high temperature plasmas in thermal equilibrium. However, if we were to apply the classical statistical mechanics to the fully ionized plasmas, the partition function would diverge because of the short range attraction between a pair of positive and negative charges, and there is a doubt whether the contribution of this infinite attraction may not overcome the contribution of the Debye·HUckel term. In this paper the equation of state of high temperature plasmas is investigated in. consideration of the quantum mechanics; and it is shown that the Debye-HUckel approximation. surely applies to the plasmas of low density of the order 101~_1017 or so at high temperatures where Ae::;'ao/Z, where Z is the charge of a nucleus, A. the de Broglie wave length of an electron and ao the Bohr radius. This result is obtained by reducing the problem to that of a suitable classical gas and confirming that the contribution of the watermelon terms--which is considered as the leading correction to the Debye-HUckel approximation--is negligible compared with that of the ring terms considered in the Debye-HUckel approximation.

We calculate the energy and hydrostatic pressure densities of a hot quark-gluon plasma in thermal equilibrium through diagrammatic analyses of the statistical average, $\langle \Theta_{\mu \nu} \rangle$, of the energy-momentum-tensor operator $\Theta_{\mu \nu}$. To leading order at high temperature, the energy density of the long wave length modes is consistently extracted by applying the hard-thermal-loop resummation scheme to the operator-inserted no-leg thermal amplitudes $\langle \Theta_{\mu \nu} \rangle$. We find that, for the long wave length gluons, the energy density, being positive, is tremendously enhanced as compared to the noninteracting case, while, for the quarks, no noticeable deviation from the noninteracting case is found.

We study the basic results of quantum statistics of plasma in thermal equilibrium. First, we discuss the findings of early pioneers of quantum statistics of plasma, such as Max Planck, that the statistical thermodynamics of charged particles requires new concepts. We summarize the exact limiting results for low-density thermodynamics based on diagrammatic expansions and the concepts of Larkin–Matsubara–Kelbg and analyze hydrogen and helium plasmas. We discuss three relevant quantities that determine plasma thermodynamics: the atomic partition function, the equation of state (EOS), and the ionization potential depression. We provide improved virial expansions for the EOS that allow for an adequate description of the path integral Monte Carlo data up to intermediate densities. Taking into account existing controversies about the atomic partition function and the lowering of ionization energy, we show how the classical plasma theories of Planck and Unsöld can be integrated into modern quantum statistical methods. Typically, our partition functions disappear quickly at higher temperatures. This differs from many codes used for astrophysical and technical calculations; exceptions are the ACTEX and SAHA-S codes.

We present EUV light curves and spectra of three Seyfert galaxies. The data were obtained from EUVE observations of the galaxies Mrk 279, Mrk 478, and Ton S180. The variability in the light curves provides an upper limit to the size of the EUV-emitting region which excludes the broad-line region and diffuse intercloud regions as the source of this emission. The EUV spectra are all characterized by discrete line features; in the case of Mrk 478, we find the lines vary on timescales of less than 1 day. These results allow us to rule out various models proposed for Seyfert galaxies. Comparing these spectra in their rest frames, we find that several of these features appear at the same wavelengths. A composite EUV spectrum is produced from these redshift-corrected spectra. The most striking feature in the composite spectrum is an emission feature at ~79 A, which is also observed in the spectra of each of the individual galaxies. It is difficult to explain this feature by emission from a photoionized or collision-driven plasma in thermal equilibrium. We suggest this line feature may be the fluorescent transition of neutral Fe related to the 6.4 keV Kα emission that has frequently been observed in the X-ray spectra of Seyfert galaxies. If this interpretation is correct, this result imposes strong constraints on the distribution of warm material in these galaxies.

Doppler radars find a widespread use in the estimation of the velocity of discrete hard-targets as described elsewhere in this volume. In case of soft-targets — collections of vast numbers of weakly scattering elements filling the radar beam— the emphasis typically shifts to collecting the statistics of random motions of the scattering elements — i.e., Doppler spectral estimation — from which thermal or turbulent state of the target can be inferred, as appropriate. For instance, in case of a plasma in thermal equilibrium, e.g., the quiescent ionosphere, a Doppler radar of sufficient power-aperture-product can detect, in addition to the plasma drift velocities, the densities, temperatures, and even current densities of charged particle populations of the probed plasma — such Doppler radars used in ionospheric research are known as incoherent scatter radars (ISR). In this chapter wewill provide a simplified description of ISR spectral theories (e.g., Kudeki &Milla, 2011) and also discussmagnetoionic propagation effects pertinent to ionospheric applications of ISR’s at low latitudes. A second chapter in this volume focusing on in-beam imaging of soft-targets by Hysell & Chau (2012) is pertinent to non-equilibrium plasmas and complements the topics covered in this article.

We consider multi-component electrolyte solutions and plasmas in thermal equilibrium and define thermodynamic quantities for number densities which do not necessarily satisfy the condition of charge neutrality. It is shown that these quantities play a role in compressibility theorems for the pair correlation functions and in the generalized Debye shielding length. A fourth moment condition for the pair correlation functions is derived. We discuss to what extent non-uniform systems may be described in terms of local thermodynamics with added coulomb interactions.

In this paper, the authors have presented a formulation of the kinetics of complex plasmas, having dust of different materials (different work functions) and size distributions, which is based on the number and energy balance of constituents; this is in deference to the present emphasis on considering complex plasma as an open system. The formulation is based on a size-independent dust surface potential; this simplifies the problem to a form, similar to that for the case of uniform size dust grains, characterized by the mean <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$(a_{m})$</tex></formula> and the root mean square <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$(a_{rms})$</tex></formula> radius of the dust particles. Two cases, viz., complex plasma in thermal equilibrium and complex plasma irradiated by monochromatic radiation, have been considered in detail, and corresponding computations have been made for a mixture of two varieties of dust grains having high <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$(\varphi_{2} &gt; h\nu)$</tex></formula> and low <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$(h\nu &gt; \varphi_{1})$</tex></formula> work functions. The relevance of the first case to flames and rocket exhausts has been pointed out. The fluctuation of charge corresponding to individual dust grains has also been evaluated. A discussion based on numerical results and conclusion have been also given.

We study an ultrarelativistic QED plasma in thermal equilibrium. Plasmons---photon collective excitations---are postulated to correspond not to poles of the retarded photon propagator but to poles of the propagator multiplied by the fine-structure constant. This product is an invariant of the renormalization group that is independent of an arbitrarily chosen renormalization scale. In addition, our proposal is physically motivated since one needs to scatter a charged particle off a plasma system to probe its spectrum of collective excitations. We present a detailed calculation of the QED running coupling constant at finite temperature using the Keldysh-Schwinger representation of the real-time formalism. We discuss the issue of how to choose the renormalization scale and show that the temperature is a natural choice which prevents the breakdown of perturbation theory through the generation of potentially large logarithmic terms. Our method could be applied to anisotropic systems where the choice of the renormalization scale is less clear, and could have important consequences for the study of collective modes.

Effects of the spatiotemporal inhomogeneity of a plasma in thermal equilibrium on the local and output characteristics of a Faraday-type MHD generator were investigated using numerically modeled turbulence data of the temperature and the velocity. The conditions of Saha equilibrium in the range of the temperature level and the frequency were given. The mean conductivity formula was also given as a function of the rms fiuctuation. The average correlations between the electric field fluctuation and that of the conductivity in the mean Ohm's law were evaluated in terms of the mean electrical parameters. Rosa's G-factor was modified to include the spatiotemporal conductivity variance. It was shown that the 1D anisotropic model somewhat underestimates the effective plasma resistance of the turbulent MHD plasma with 2D anisotropy.

Incoherent scattering is determined by the spectral density of electron-density fluctuations. This quantity has previously been calculated for a plasma in thermal equilibrium. We have extended the theory to include spatially homogeneous nonequilibrium states of a hot plasma. An elementary derivation of the previous results and the new results is given in terms of dressed test particles. Numerical calculations have been carried out for a plasma with hot electrons and cold ions, and for a plasma in which the electrons have a net drift relative to the ions.

An expression is obtained for the low-velocity stopping power of an electron plasma in thermal equilibrium, which applies for all degrees of plasma degeneracy. In the limit of high densities the result agrees with the Fermi-Teller approximation for a cold plasma, and with a previous approximation of Skupsky (1977) for all degeneracies. It gives better agreement with the Lindhard-Winther result (1964) at lower (metallic) densities for cold plasmas, and it also agrees with a previous result of Arista and Brandt (1981) in the opposite limit of dilute nondegenerate plasmas.

An alternative form of the nonrelativistic permittivity tensor for a homogeneous magnetized plasma in thermal equilibrium is derived in the linear approximation. The derivation follows the lines of Trubnikov’s derivation of the relativistic permittivity tensor and is restricted to a collisionless electron plasma. In the case of a Maxwellian equilibrium distribution, the final form is equivalent to Gordeev’s integral form of the permittivity tensor. The analysis is, with minor modification, applicable to plasma comprised of multiple particle species. Unlike the standard formulas, the alternative formula presented in this article yields the components of the permittivity tensor by means of partial derivatives of a scalar kernel integral. Besides the cyclotron harmonic resonance frequencies, where the permittivities in the nonrelativistic approximation become singular, the alternative formula is manifestly valid for all wave frequencies without any restrictions on the wave vector and the thermal energy.

The low-frequency magnetic field spectrum in the primordial plasma is of particular interest as a possible origin of magnetic fields in the universe (e.g., Tajima and co-workers and Cable and Tajima). We derive the magnetic field spectrum in the primordial plasma, in particular, at the epoch of primordial nucleosynthesis. The pioneering study of Cable and Tajima of the electromagnetic fluctuations, based on the fluctuation-dissipation theorem, is extended. Our model describes both the thermal and collisional effects in a plasma. It is based on a kinetic description with the Bhatnagar, Gross, and Krook (BGK) collision term. It is shown that the zero-frequency peak found by Cable and Tajima decreases. At high frequencies, the blackbody spectrum is obtained naturally without the necessity of the link procedure used by them. At low frequencies $(\ensuremath{\omega}&lt;~4{\ensuremath{\omega}}_{\mathrm{pe}},$ where ${\ensuremath{\omega}}_{\mathrm{pe}}$ is the electron plasma frequency), it is shown that the magnetic field spectrum has more energy than the blackbody spectrum in vacuum.

The quantum equation of state of the electron‐ion‐plasmas in thermal equilibrium is derived; the pressure until the third virial coefficient is calculated. We consider only the thermal equilibrium plasma in the case of nλ3ab ≪ 1 where λ2ab = ((ħ2)/(mabKT)) is the thermal De Broglie wavelength. The formulas contain the contributions of the exchange effects. Our equation of state is compared with result of Ebeling et al. who calculated the pressure until the second virial coefficient only and in the case of χλee ≪ 1 where χ is the Debye length. Upon comparison with Ebeling et al. one observes that the considerable contribution of the third virial coefficient in the region of high temperatures (© 2011 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Stark broadening measurements in plasmas produced by laser ablation of hydrogen containing compounds