This paper covers calculation of radial distribution functions, specific energy and static electrical conductivity of CH$_2$ plasma in the two-temperature regime. The calculation is based on the quantum molecular dynamics, density functional theory and the Kubo-Greenwood formula. The properties are computed at 5 kK $\le$ $T_i$ $\le$ $T_e$ $\le$ 40 kK and ρ= 0.954 g/cm$^3$ and depend severely on the presence of chemical bonds in the system. Chemical compounds exist at the lowest temperature $T_i$ = $T_e$ = 5 kK considered; they are destroyed rapidly at the growth of $T_i$ and slower at the increase of $T_e$. A significant number of bonds are present in the system at 5 kK $\le$ $T_i$ $\le$ $T_e$ $\le$ 10 kK. The destruction of bonds correlates with the growth of specific energy and static electrical conductivity under these conditions.
The problem of the calculation of equilibrium thermodynamic properties and the establishment of statistical-thermodynamically-consistent finite bound-state partition functions in nonideal multi-component plasma systems is revised within the chemical picture. The present exploration accompanied by the introduction of a generalized accurate formulation, in terms of the solution of the inverse problem, clears ambiguities and gives a better understanding of the problem on top of pointing out weaknesses and inaccuracies/inconsistencies buried in widely used models in the literature.
An expression for the internal energy of a fluid element in a weakly coupled, magnetized, anisotropic plasma is derived from first principles. The result is a function of entropy, particle density and magnetic field, and as such plays the role of a thermodynamic potential: it determines in principle all thermodynamic properties of the fluid element. In particular it provides equations of state for the magnetized plasma. The derivation uses familiar fluid equations, a few elements of kinetic theory, the MHD version of Faraday's law, and certain familiar stability and regularity conditions.
A precise calculation that translates shifts of X-ray K-absorption edges to variations of thermodynamic properties allows quantitative characterization of interior thermodynamic properties of warm dense plasmas by X-ray absorption techniques, which provides essential information for inertial confinement fusion and other astrophysical applications. We show that this interpretation can be achieved through an improved first-principles method. Our calculation shows that the shift of K-edges exhibits selective sensitivity to thermal parameters and thus would be a suitable temperature index to warm …
To analyze nonidealities inherent to degenerate plasma, a quantum collective approach is developed. Thermodynamic functions of a system of partially degenerate electrons and strongly coupled ions are derived from first principles. The model takes into account the energy eigenvalues of i) the thermal translational particle motions, ii) the random collective electron and ion motions, and iii) the static Coulomb interaction energy of the electrons and ions in their oscillatory equilibrium positions. These statistical thermodynamic calculations lead to simple analytical expressions for internal en…
Physical properties of plasmas such as equations of state and transport coefficients are expressed in terms of correlation functions, which can be calculated using various approaches (analytical theory, numerical simulations). The method of Green's functions provides benchmark values for these properties in the low-density limit. For the equation of state and electrical conductivity, expansions with respect to density (virial expansions) are considered. Comparison of analytical results with numerical simulations is used to verify theory, to prove the accuracy of simulations, and to establish i…
Thermodynamic properties of a Yukawa system consisting of dust particles in plasma are studied in presence of an external magnetic field. It is assumed that dust particles interact with each other by modified potential in presence of magnetic field. Accordingly, a modified expression for internal energy has been obtained. A molecular dynamics code is developed to calculate this internal energy for the entire system. Based on the values of internal energy given by the code Helmholtz free energy and pressure are calculated for the system. Our study shows novel kind of behaviour for internal ener…
The problem of formulating a thermodynamically-consistent finite internal partition function (IPF) in nonideal hydrogen plasma systems is investigated and analyzed within the chemical picture revealing inaccuracies and inconsistencies buried in widely used formulations in the literature. The analysis carried out here, though performed for the simplest case of pure nonideal hydrogen plasma, it shows all specific features of the problem and is extendable to the general case of a complex multi-component plasma mixture. A criterion for the separability of the configurational component of the free …
We have explored the thermodynamics of compressed magnetized plasmas in laboratory experiments and we call these studies "magnetothermodynamics". The experiments are carried out in the Swarthmore Spheromak eXperiment device. In this device, a magnetized plasma source is located at one end and at the other end, a closed conducting can is installed. We generate parcels of magnetized plasma and observe their compression against the end wall of the conducting cylinder. The plasma parameters such as plasma density, temperature, and magnetic field are measured during compression using HeNe laser int…
The pressure and internal energy of an ultracold plasma in a state of quasi-equilibrium are evaluated using classical molecular dynamics simulations. Coulomb collapse is avoided by modeling electron-ion interactions using an attractive Coulomb potential with a repulsive core. We present a method to separate the contribution of classical bound states, which form due to recombination, from the contribution of free charges when evaluating these thermodynamic state variables. It is found that the contribution from free charges is independent of the choice of repulsive core length-scale when it is …
We study thermodynamic properties and the electrical conductivity of dense hydrogen and deuterium using three methods: classical reactive Monte Carlo (REMC), direct path integral Monte Carlo (PIMC) and a quantum dynamics method in the Wigner representation of quantum mechanics. We report the calculation of the deuterium compression quasi-isentrope in good agreement with experiments. We also solve the Wigner-Liouville equation of dense degenerate hydrogen calculating the initial equilibrium state by the PIMC method. The obtained particle trajectories determine the momentum-momentum correlation …
Thermodynamic properties of the electron-positron plasma (or gas) at high and very high temperatures are investigated. To achieve this goal we have derived a number of analytical formulas for the Fermi-Dirac distribution functions (or spectral functions) which can be applied to various Fermi gases in different cases. Almost all these formulas are represented in the form of series expansions. The coefficients in these expansions are the explicit and relatively simple functions of the $\fracμ{T}$ ratio, where $T$ is the temperature and $μ$ is the chemical potential of this Fermi system. Our new …
We briefly review analytic approximations of thermodynamic functions of fully ionized nonideal electron-ion plasmas, applicable in a wide range of plasma parameters, including the domains of nondegenerate and degenerate, nonrelativistic and relativistic electrons, weakly and strongly coupled Coulomb liquids, classical and quantum Coulomb crystals. We present improvements to previously published approximations. Our code for calculation of thermodynamic functions based on the reviewed approximations is made publicly available.
In previous work we provided the explicit form of the nonlinear PDEs, subjected to the appropriate boundary conditions, which have to be satisfied by transport coefficients for systems out of Onsager's region. Since the proposed PDEs are obtained without neglecting any term present in the balance equations (i.e., the mass, momentum, and energy balance equations), we propose them as a good candidate for describing also transport in thermodynamic systems in turbulent regimes. As a special case, we derive the nonlinear PDEs for transport coefficients when the thermodynamic system is subjected to …
Thermodynamic and spectral properties of a photon gas in $e^+e^-γ$ plasmas are studied. The effect of a finite effective mass of a photon, associated with the plasma frequency cutoff, is self-consistently included. In the ultra-relativistic plasma, the photon spectrum turns out to be universal with the temperature normalized plasma frequency cutoff being a fundamental constant independent of plasma parameters. Such a universality does not hold in the non-relativistic plasma.
Transition phenomena between thermodynamic branch and turbulent branch in submarginal turbulent plasma are analyzed with statistical theory. Time-development of turbulent fluctuation is obtained by numerical simulations of Langevin equation which contains submarginal characteristics. Probability density functions and transition rates between two states are analyzed. Transition from turbulent branch to thermodynamic branch occurs in almost entire region between subcritical bifurcation point and linear stability boundary.
Thermodynamics of weakly screened (near the one-component-plasma limit) Yukawa fluids in two and three dimensions is analyzed in detail. It is shown that the thermal component of the excess internal energy of these fluids, when expressed in terms of the properly normalized coupling strength, exhibits the scaling pertinent to the corresponding one-component-plasma limit (the scalings differ considerably between the two- and three-dimensional situations). This provides us with a simple and accurate practical tool to estimate thermodynamic properties of weakly screened Yukawa fluids. Particular a…
Zaghloul [Phys. Plasmas 17, 062701 (2010); arXiv:1010.1161v1] reconsiders the occupation probability formalism in plasma thermodynamics and claims inconsistencies in previous models. I show that the origin of this incorrect claim is an omission of the configurational factor from the partition function. This arXiv version is supplemented with two appendices, where I add remarks and comments on two more recent publications of the same author on the same subject: on his response to this Comment [Phys. Plasmas 17, 124705 (2010)] and on his criticism towards the Hummer and Mihalas's (1988) formalis…
High-density lithium plasmas are expected to be generated in the Inertial Confinement Fusion (ICF) reactor chamber due to energy deposition of the prompt X-rays and ion debris in the first wall. These dense plasmas are encountered in many other applications as well. The design and optimization of such lithium-based applications requires information about the thermodynamic properties of Li fluid over a wide range of parameters including the high-energy-density regime. A model that takes into account all essential features of strongly-coupled plasmas of metal vapors is developed and used to pred…
This work is devoted to the thermodynamics of high-temperature dense hydrogen plasmas in the pressure region between $10^{-1}$ and $10^2$ Mbar. In particular we present for this region results of extensive calculations based on a recently developed path integral Monte Carlo scheme (direct PIMC). This method allows for a correct treatment of the thermodynamic properties of hot dense Coulomb systems. Calculations were performed in a broad region of the nonideality parameter $Γ\lesssim 3$ and degeneracy parameter $n_e Λ^3 \lesssim 10$. We give a comparison with a few available results from other …
The layered crystal formation in dusty plasma medium depicted by the Yukawa interaction amidst dust has been investigated using Molecular Dynamics simulations. The multilayer structures are shown to form in the presence of a combined gravitational and external electric field force (representing the sheath field in experiments) along the ^ z direction. A detailed study of the dependence of the number of crystal layer formation, their width etc., on various system parameters (viz., the external field profile and the screening length of Yukawa interaction) have been analyzed. The structural prope…
In this work we calculate the thermodynamic properties of hydrogen-helium plasmas with different mass fractions of helium by the direct path integral Monte Carlo method. To avoid unphysical approximations we use the path integral representation of the density matrix. We pay special attention to the region of weak coupling and degeneracy and compare the results of simulation with a model based on the chemical picture. Further with the help of calculated deuterium isochors we compute the shock Hugoniot of deuterium. We analyze our results in comparison with recent experimental and calculated dat…
The structural properties of strongly coupled ions in dense plasmas with moderately to strongly degenerate electrons are investigated in the framework of the one-component plasma model of ions interacting through a screened pair interaction potential. Special focus is put on the description of the electronic screening in the Singwi-Tosi-Land-Sjoelander (STLS) approximation. Different crosschecks and analyses using ion potentials obtained from ground-state quantum Monte Carlo data, the random phase approximation (RPA), and existing analytical models are presented for the computation of the stru…
A survey on the dynamical and thermodynamical properties of plasmas with strong Coulomb interactions in the quasi-classical density-temperature region is given. First the basic theoretical concepts describing nonideality are discussed. The chemical picture is introduced. It is shown that the nonideal plasma subsystem of the free charges has a rather large quasi-classical regime, where the quantum effects yield only corrections to the merely classical dynamics. The plasma of free charges may be described by effective potentials which incorporate quantum effects in an approximative way. The simp…
Limiting structure of thermodynamic functions of gaseous plasmas is under consideration in the limit of zero temperature and density. Remarkable tendency, which was claimed previously (Iosilevskiy and Gryaznov, 1985) is carried to extreme. Both equations of state, thermal and caloric ones obtain in this limit identical stepped structure ("ionization stairs") for plasma of any single element when this limit (T -> 0, n -> 0) is carried out at fixed value of chemical potential for electrons (or atoms). The same stepped structure is valid for plasma of mixtures or compounds. This structure appears…
A new code called VAAQP (Variational Average-Atom in Quantum Plasmas) is reported. The model as well as main results of previous studies are briefly recalled. The code is based on a new fully variational model of dense plasmas at equilibrium with quantum treatment of all electrons. The code can calculate the Average Atom structure and the mean ionization from the variational equations respecting the virial theorem and without imposing the neutrality of the Wigner-Seitz sphere. The formula obtained for the electronic pressure is simple and does not require any numerical differentiation. A descr…
A general approach for deriving the expression of reference (density of) distribution functions, F^0, by statistical thermodynamics and the definition of local equilibrium conditions is illustrated. This procedure may be adopted for a system subject to an arbitrary number of thermodynamic forces. For concreteness, we analyze the case of a system submitted to three independent thermodynamic forces and the local equilibrium corresponds to the configuration of minimum entropy production condition and the maximum entropy principle. In this limit case, we show that the derived expression of distrib…
Limiting structure of thermodynamic functions of gaseous plasmas is under consideration in the limit of low temperature and density. The remarkable tendency, that was claimed previously [High Temp. 19, 799 (1981)], is carried to extreme. In the limit discussed, when temperature and density tend to zero at constant value of electron chemical potential, both equations of state (thermal and caloric) obtain almost identical stepped structure ("ionization stairs") when their special forms being exposed i.e. PV/RT for thermal EOS and (U - 3/2PV) for caloric EOS. At the same time all thermodynamic di…
The influence of a constant uniform magnetic field on the thermodynamic properties of a partially ionized hydrogen plasma is studied. Using the method of Green' s function various interaction contributions to the thermodynamic functions are calculated. The equation of state of a quantum magnetized plasma is presented within the framework of a low density expansion up to the order e^4 n^2 and, additionally, including ladder type contributions via the bound states in the case of strong magnetic fields (2.35*10^{5} T << B << 2.35*10^{9} T). We show that for high densities (n=10^{27-30} m^{-3}) an…
Magnetothermodynamics (MTD) is the study of compression and expansion of magnetized plasma with an eye towards identifying equations of state for magneto-inertial fusion experiments. We present recent results from SSX experiments on the thermodynamics of compressed magnetized plasmas. In these experiments, we generate twisted flux ropes of magnetized, relaxed plasma accelerated from one end of a $1.5~m$ long copper flux conserver, and observe their compression in a closed conducting boundary installed at the other end. Plasma parameters are measured during compression. The instances of ion hea…
The spontaneous evolution of magnetic reconnection in generalized situations (with thermodynamic asymmetry regarding the current sheet and magnetic shear) is investigated using two-dimensional magnetohydrodynamic simulation. We focus on the asymptotic state of temporal evolution, i.e., the self-similarly expanding phase (Nitta et al. 2001). 1) A long fast-mode shock is generated in front of the shorter plasmoid as in the shear-less thermodynamically asymmetric case; however, the sheared magnetic component weakens the shock. This fast shock may work as a particle acceleration site. 2) The short…
Thermodynamic characteristics of the radiation of condensed combustion products presented in the form of agglomerates of metal-oxide nanoparticles demonstrate deviations from the classical Planck's law. We propose to interpret these deviations in terms of the non-additive entropy of the photon system interacting with the heterogeneous combustion products, which makes it possible to use the non-extensive Tsallis thermodynamics for their description. It is assumed that the non-additive character of the radiation entropy in heterogeneous plasma can be explained by the influence of long-range inte…
In numerous realizations of complex plasmas, dust-dust interactions are characterized by two screening lengths and are thus better described by a combination of Yukawa potentials. The present work investigates the static correlations and the thermodynamics of repulsive dense bi-Yukawa fluids based on the fact that such strongly coupled systems exhibit isomorph invariance. The strong virial-potential energy correlations are demonstrated with the aid of molecular dynamics simulations, an accurate analytical expression for the isomorph family of curves is obtained and an empirical expression for …
We show that a Faddeev-Niemi non-linear sigma model describes in the long wavelength limit a wide class of steady-state, knotted physical systems far from thermodynamic equilibrium which are stable against perturbations of temperature and interact weakly with the external world. In these systems temperature gradients are negligible, inertial effects are negligible in comparison with diffusion effects, entropy is mainly produced through Joule and-or viscous heating, the macroscopic state is described by specifying a unit vector at each point, and the Gauss linking number of this unit vector is …
We study the thermodynamic properties of a partially ionized hydrogen plasma in strong magnetic fields, B ~ 10^{12}-10^{13} G, typical of neutron stars. The properties of the plasma depend significantly on the quantum-mechanical sizes and binding energies of the atoms, which are strongly modified by thermal motion across the field. We use new fitting formulas for the atomic binding energies and sizes, based on accurate numerical calculations and valid for any state of motion of the atom. In particular, we take into account decentered atomic states, neglected in previous studies of thermodynami…
We develop an analytical equation of state (EOS) for magnetized fully ionized plasmas, which cover a wide range of temperatures and densities, from low-density classical plasmas to relativistic, quantum plasma conditions. This EOS directly applies to calculations of structure and evolution of strongly magnetized white dwarfs and neutron stars. We review available analytical and numerical results for thermodynamic functions of the nonmagnetized and magnetized Coulomb gases, liquids, and solids. We propose a new analytical expression for the free energy of solid Coulomb mixtures. Based on recent…
Thermodynamic quantities of Coulomb plasmas consisting of point-like ions immersed in a compressible, polarizable electron background are calculated for ion charges Z=1 to 26 and for a wide domain of plasma parameters ranging from the Debye-Hueckel limit to the crystallization point and from the region of nondegenerate to fully degenerate nonrelativistic or relativistic electrons. The calculations are based on the linear-response theory for the electron-ion interaction, including the local-field corrections in the electronic dielectric function. The thermodynamic quantities are calculated in t…
This work is concerned with the development of a novel, accurate equation of state for describing partially ionised air plasma in local thermodynamic equilibrium. One key application for this new equation of state is the simulation of lightning strike on aircraft. Due to the complexities of species ionisation and interaction, although phenomenological curve fitting of thermodynamic properties is possible, these curves are intractable for practical numerical simulation. The large difference in size of the parameters (many orders of magnitude) and complexity of the equations means they are not s…
Application of the ion sphere model (ISM), well known in the context of the one-component-plasma, to estimate thermodynamic properties of model Yukawa systems is discussed. It is shown that the ISM approximation provides fairly good estimate of the internal energy of the strongly coupled Yukawa systems, in both fluid and solid phases. Simple expressions for the excess pressure and isothermal compressibility are derived, which can be particularly useful in connection to wave phenomena in strongly coupled dusty plasmas. It is also shown that in the regime of strong screening a simple considerati…
The Effect of Expansion and Instabilities in the Thermodynamic Regulation of the Young Solar Wind Plasma
Universidad de Santiago de Chile（圣地亚哥智利大学）；Center for Interdisciplinary Research in Astrophysics and Space Sciences (CIRAS)（天体物理学与空间科学跨学科研究中心）；Universidad de Concepción（康塞普西翁大学）；Universidad de Chile（智利大学）
It is shown that the thermodynamic maximum entropy principle predicts negative specific heat for a stationary magnetically self-confined current-carrying plasma torus. Implications for the magnetic self-confinement of fusion plasma are considered.
The formation of plasma crystals confined in an external one-dimensional parabolic potential well is simulated for a normal experimental environment employing a computer code called BOXITREE. Under appropriate conditions, crystals were found to form layered systems. The system's structural phase transitions, including transitions between crystals with differing numbers of layers and the same number of layers but different intralayer structures, were investigated and found to agree with previous theoretical and experimental research results. One- to two-layer transitions were examined in detail…
Analytical equation of state for pure alkali metals (lithium, sodium, potassium, rubidium and cesium) in equilibrium gas phase is proposed. This equation has a simple form, generalizes the equation of state for a perfect gas and is universal for all alkali elements. It correctly reproduces the experimental data for the equilibrium gas phase over a wide range of pressures (up to $\sim 10^5$~Pa) and temperatures (up to $\sim 3 \cdot 10^3$~K). On the basis of this equation of state, expressions for thermal and caloric coefficients as well as for \textit{other physical characteristics} are obtaine…
We develop analytic approximations of thermodynamic functions of fully ionized nonideal electron-ion plasma mixtures. In the regime of strong Coulomb coupling, we use our previously developed analytic approximations for the free energy of one-component plasmas with rigid and polarizable electron background and apply the linear mixing rule (LMR). Other thermodynamic functions are obtained through analytic derivation of this free energy. In order to obtain an analytic approximation for the intermediate coupling and transition to the Debye-Hueckel limit, we perform hypernetted-chain calculations …
A new class of exact electrostatic solutions of the Vlasov-Maxwell equations based on the Jeans's theorem is proposed for studying the evolution and properties of two-dimensional anisotropic plasmas that are far from thermodynamic equilibrium. In particular, the free expansion of a slab of electron-ion plasma into vacuum is investigated.
Different advanced bridge function closures are utilized to investigate the structural and thermodynamic properties of dense Yukawa one-component plasma liquids within the framework of integral equation theory. The isomorph-based empirically modified hypernetted-chain, the variational modified hypernetted-chain, the Rogers-Young and the Ballone-Pastore-Galli-Gazzillo approaches are compared at the level of thermodynamic properties, radial distribution functions and bridge functions. The comparison, based on accuracy and computational speed, concludes that the two modified hypernetted-chain app…
The polytropic process characterizes the thermodynamics of space plasma particle populations. The polytropic index, $γ$, is particularly important as it describes the thermodynamic behavior of the system by quantifying the changes in temperature as the system is compressed or expanded. Using Wind spacecraft plasma and magnetic field data during $01/1995 - 12/2018$, we investigate the thermodynamic evolution in 336 Interplanetary Coronal Mass Ejection (ICME) events. For each event, we derive the index $γ$ in the sheath and magnetic ejecta structures, along with the pre- and post- event regions.…
