Nonideal Plasmas

Matter appears on our planet, in the solar system and in the rest of Universe in rather different forms.

A phase transition of gas-liquid type with an upper critical point is examined which arises in a model for charges of one sign against a compensating background. The transition parameters are dependent on the detailed assumptions about the compressibility of the background, but the occurrence of the transition is independent of approximate calculations on the equation of state. In the electron-gas (gel) model, this transition appears to rule out a Wigner crystallization. A variational principle in statistical mechanics is used to derive what is called a duplicated model for a one-component plasma, whose free energy sets an upper bound to that of a real plasma.

The applicability limit of the well-known phase diagram of complex plasmas in the κ–Γ plane (κ is the structural parameter, Γ is the coupling parameter) is under discussion. The present work is devoted to the analysis of the range of applicability of a basic assumption in the initial phase diagram, that is, linearized (Debye) screening of macro-ions by micro-ions, which leads to the Yukawa form of effective interactions between macro-ions. Parameters of non-linear screening for macro-ions were calculated within the direct Poisson–Boltzmann approximation in an averaged Wigner–Seitz cell. Two effects were revealed as a result of such calculations: (a) decomposition of all micro-ions into two subclasses, free and bound ones, and (b) significant reduction of the effective charge Z* of initial bare macro-ion Z under non-linear screening by the small high-density envelope of bound micro-ions. This effect leads to a re-normalization of initial Γ and κ into Γ* and κ* (Γ* < Γ, κ* < κ). It is assumed that the phase states of a complex plasma under non-linear screening are still the same as in the initial phase diagram, but in κ*–Γ* plane instead of the κ–Γ one. The corresponding calculated shifts of the phase states are discussed and illustrated.

Applicability limit of the well-known phase diagram of dusty plasmas in κ -Γ plane (κ is structural parameter and Γ is parameter of Coulomb nonideality) is under discussion. Existence of extensive domains with violation of plasma thermodynamic stability conditions (i.e., with negative isothermal compressibility) was also claimed if one uses well-known nonideal equations of state by (Hamaguchi S. et al., Phys. Rev. E, 1997) and (Khrapak S. et al., Phys. Rev. E, 2014). This paper is devoted to analysis of a range of applicability for basic assumption in Hamaguchi's phase diagram, i.e., linearized (Debye) screening of macroions by microions, which leads to the Yukawa form for effective interactions between macroions. Parameters of nonlinear screening for macroions were calculated within differential Poisson-Boltzmann equation. Two effects were revealed as a result of such calculations: 1) decomposition of all microions onto two subclasses, free and bound ones, and 2) significant reduction of effective charge Z* of initial bare macroion Z under nonlinear screening by small high-density envelope of bound ions. This effect leads to a renormalization of initial Γ and κ into Γ* and κ * (Γ* < Γ, κ* < κ). The main physical assumption is phase states of complex plasma under nonlinear screening, which are still the same as on the initial phase diagram, but in κ* -Γ* plane instead of κ-Γ one. Corresponding calculated shifts of phase states are discussed and illustrated.

Remarkable feature of new first-order phase transitions of gas-liquid gas-crystal types in combination with traditional solid-liquid transition are under consideration in a modified one-component plasma model (OCP) with uniform, but compressible background. Structure and parameters of this phase transition strongly depend on the value of charge number Z. Under high values of Z the model shows remarkable and completely unusual topology of phase diagram.

"Conventional" scenario of metastable melting in ordinary substances in the limit of zero temperature assumes that the melting curve reaches the matter zero isotherm ("cold curve"). The same is true for standard variant of one-component plasma model on rigid compensating background in both limits: classical and "cold" quantum melting. The modified OCP on uniform, but compressible background shows the completely different scenario of the metastable melting closure. The remarkable feature of this scenario is that the liquid freezing curve terminates at liquid spinodal curve of 1st-order liquid gas phase transition, which takes place in this type of OCP models ("spinodal decomposition").

Relativistic and correlation contributions to the polarizational energy losses of heavy projectiles moving in dense two-component plasmas are analyzed within the method of moments that allows one to reconstruct the Lindhard loss function from its three independently known power frequency moments. The techniques employed result in a thorough separation of the relativistic and correlation corrections to the classical asymptotic form for the polarizational losses obtained by Bethe and Larkin. The above corrections are studied numerically at different values of plasma parameters to show that the relativistic contribution enhances only slightly the corresponding value of the stopping power.

Simulation data on hydrogen-like plasmas, modelled with the Kelbg pseudopotential, are treated within the classical theory of moments. The possibility is analyzed for the model inverse dielectric function to satisfy five convergent sum rules and other exact relations. The sum rules are the power frequency moments of the loss function and the latter are calculated using the hypernetted chain approximation with the Kelbg interaction potential. An approach to the reconstruction of the Nevanlinna parameter function is proposed and successfully tested against the simulation data. Conclusions on the applicability of the Kelbg potential are drawn and a model is put forward to define the Coulomb dielectric function with the space dispersion taken into account. (© 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

We report on a development of an alternative method of HED plasma diagnostics using the ideas of the method of moments [I.M. Tkachenko, J. Ortner, and J. Alcober, J. de Physique IV 10, 195 (2000)]. (© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this work the previously developed method of calculation of HF electro-conductivity of non-ideal plasma is applied to the area of higher electron densities, up to 1024 cm-3 and in the temperature range 30 000 K ≤ T ≤ 200 000 K. The computations are carried out in the frequency range (0, 1·ωp), ωp being the plasma frequency. A good agreement with the previously published data is obtained.

We study the high-velocity-projectile limit of the polarizational contribution to the in-plane stopping power in a strongly coupled two-dimensional electron liquid. The dielectric formalism based on the method of moments is employed. The frequency moments of the loss function are calculated using the model Hamiltonian including the two-dimensional Coulomb interaction potential proportional to the inverse power of k. We prove that the leading term of the high-velocity asymptote, as in the random-phase approximation, is not affected by correlations.

The in-plane polarizational stopping power of heavy-ion diclusters in a two-dimensional strongly coupled electron liquid is studied. Analytical expressions for the stopping power of both fast and slow projectiles are derived. To go beyond the random-phase approximation we make use of the inverse dielectric function obtained by means of the method of moments and some recent analytical expressions for the static local-field correction factor.

The fusion of light nuclei is the main source of valuable energy. Recent experiments with intense, ultrafast laser pulses acting on deuterium clusters have shown that these clusters can explode with sufficient kinetic energy to produce DD nuclear fusion. In earlier work (2004) we discussed already the effect of microfields on fusion processes in ion clusters. In view of the relevance of the problem we take up the problem again and discuss enhancement effects due to nonequilibrium velocity distributions with long tails and their influence on the relative motions on the ions. In particlular we discuss fractional kinetic equations including the influence of plasma microfields and finite size effects. We study the influence of nonequilibrium effects in the velocity distribution due to the Coulomb explosion of the clusters. The role of Cauchy-Lorentz nonequilibrium distributions of the velocity including long tails is discussed and their influence on the fusion rates is estimated (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

We presnt the result of MD simulations of the electric microfield in symmetrical plasmas

The laser induced double ionization of helium is considered. We propose a heuristic nonsequential picture which explains the enhancement of double ionization rate in comparison with a sequential ionisation process. According to this picture the rst electron reaches the continuum by eld induced tunnel ionization. A rescattering mechanism, which is strongly regulated by electric plasma microelds, leads to the impact ionization or excitation of the single ionized helium. It is shown that the complex process of impact excitation combined with the tunnel ionization of the excited single ionized helium is the most probable process for not to high laser intensities. Simple analytic formulas for the ionization rate within these processes are given. The theoretical results are in good agreement with experimental data. PACS numbers: 32.80.Fb, 34.80.Kw, 52.25.Tx Typeset using REVT E X 1 I. INTRODUCTION A theory of tunneling ionization of complex atoms by an intense laser eld w...

The quantum statistical treatment of the Rutherford model, considering matter as a system of point charges (electrons and nuclei) is analyzed. First, in the historical context, the solutions of different fundamental problems, such as the divergence of the partition function, elaborated by Herzfeld, Planck, Brillouin and Rompe - most of the relevant papers published in the Annalen der Physik, are discussed. Beyond this, the modern state of art is presented and new results are given which explain, why bound states according to a discrete part of the spectra occur only in a valley in the temperature-density plane. Based on the actual state of the quantum statistics of Coulomb systems, virial expansions within the canonical ensemble and the grand ensemble and combinations are derived. The following transitions along isotherms are studied: (i) the formation of bound states occurring by increasing the density from low to moderate values, (ii) the disappearance of bound state effects at higher densities due to medium effects. Within the physical picture we calculate isotherms of pressure for Hydrogen in a broad density region and show that in the region between $20\, 000$ K and $100\, 000$ K and particle densities below $10^{22}$ cm$^{-3}$ the cross-over from full to partial ionization may be well described by the contributions of extended ring diagrams and ladder diagrams.

The influence of a constant uniform magnetic field on the ionization equilibrium and the thermodynamic properties of a nondegenerate partially ionized hydrogen plasma is studied for weak magnetic fields. Using the methods developed in a previous work, various interaction contributions to the thermodynamic functions are given. The equation of state of a quantum magnetized plasma is presented within the framework of a virial expansion up to the second order in the fugacities, including ladder type contributions corresponding to bound states. A simple interpolation formula for an effective partition function is proposed, connecting the low- and high-field results. Furthermore, a closed analytical approximation for the thermodynamic functions in the chemical picture and a Saha equation for weakly magnetized plasmas are presented.

In the first part we calculate the pair correlation functions for the free plasma component of electron-ion plasmas and the correspondig thermodynamic functions by solving HNC-integral equations using the free Slater functions. Then we check for linearity of the thermodynamic functions for large Gamma-parameters. Finally the result of calculations within the chemical picture (PACH) are discussed.

We study plasma transport coupled to soliton-like excitations in layers of atoms interacting by Morse forces. We investigate the bound states between charges and solitonic excitations, called solectrons. The atomic dynamics is given by nonlinear classical Langevin equations including nonlinear couplings and sources of noise. It is shown that solitonic excitations are of particular high stability against perturbations move with sound velocity. The dynamics of free imbedded charges (electrons) is modelled in the framework of tight-binding approximations and stochastic master equations. Assuming that the charges are attracted by local compressions it is shown that rather stable bound states between charges and soliton-like excitations are formed, which can carry electricity with sound velocity.

We investigate the effects of Pauli blocking on the properties of hydrogen at high pressures. In this region recent experiments have shown a transition from insulating behavior to metal-like conductivity. To describe this transition, several effects have to be taken into account, an important one is the quantum character of the electrons. As electron states can only be occupied once (Pauli blocking), atomic states need more phase space than available at high densities, and bound states disintegrate subsequently (Mott effect). We calculate the energy shifts due to Pauli blocking and discuss the Mott effect solving an effective Schrödinger equation for strongly correlated systems. Additionally, we include corrections due to polarization effects. The ionization equilibrium is treated on the basis of an advanced chemical approach based on the assumption that the system is a gas-like mixture of chemical species. We calculate the Pauli shifts by variational methods and discuss corrections due to polarization. Results for the ionization equilibrium in the region 5,000 < T[K] < 15,000, 0. 1 < ρ[g cm−3] < 1 are presented, where the transition from a neutral hydrogen gas to a highly ionized plasma occurs. We show that the transition to a highly conducting state is softer than predicted in earlier work.

We analyze the quantum statistical treatment of bound states in Hydrogen considered as a system of electrons and protons. Within this physical picture we calculate analytically isotherms of pressure for Hydrogen in a broad density region and compare to some results from the chemical picture. Our study is restricted to the range of intermediate temperatures 104K < T < 105K and not too high densities n < 1024 protons per cm3, the formation of molecules is neglected. First we resume in detail the two transitions along isotherms: (i) formation of bound states occurring by increasing the density from low to moderate values, (ii) the destruction of bound states in the high density region, modelled here by Pauli-Fock effects. Avoiding chemical models we will show, why bound states according to a discrete part of the spectra occur only in a valley in the T-p plane. First we study virial expansions in the canonical ensemble and then in the grand canonical ensemble. We show that in fugacity representations the population of bound states saturates at higher density and that a combination of both representations provides quickly converging equations of state. In the case of degenerate systems we calculated first the density-dependent energy levels, and find the pressure in Hartree-Fock-Wigner approximation showing the prominent role of Pauli blocking and Fock effects in the selfenergy (© 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

We study the thermodynamic instabilities dur to nonideality effects qnd possible phase transitions in H-, Xe,- Cs-, Li-, Na-,K-,Rb-plasmas and gives estimates for the critical data. Further we investigate the effects of nonideality on the ionization coefficients and show, that nonideality may lead to drastic enhancement of ionization.

We analyze the strong density dependence of ionization kinetics. First the shifts of the energy levels is studied and the possibility of phase transitions due to nonideality effects and cahnging the time behaviour of the rlaxation processes in hydrogen - like plasmas.

The phase diagram of Helium plamsa is analyzed. It is shown, taht there may be several plasma phase transitions due to nonideality connected with first and second ionization of He. The so far hypothetical crtital and triple points of the He - plasma are calculated and discussed.

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