In the long-wavelength limit k=0, the response function has been investigated with respect to the external and internal fields which is expressed by the external and internal conductivity, respectively. Molecular dynamics (MD) simulations are performed to obtain the current-current correlation function and the dynamical collision frequency which are compared with analytical expressions. Special attention is given to the dynamical collision frequency and the description of plasma oscillations in the case of k=0. The relation between the external and internal conductivity and to the current-current correlation function is analyzed.
On the basis of a quantum-statistical approach to the electrical conductivity of nonideal plasmas we derive analytical results in the classical low-density regime, in the degenerate Born limit, and for the contribution of the Debye-Onsager relaxation effect. These explicit results are used to construct an improved interpolation formula of the electrical conductivity valid in a wide range of temperature and density which allows to compare with available experimental data of nonideal plasmas.
Within generalized linear response theory, an expression for the dielectric function is derived which is consistent with standard approaches to the electrical dc conductivity. Explicit results are given for the first moment Born approximation. Some exact relations as well as the limiting behaviour at small values of the wave number and frequency are investigated.
The Coulomb log (log Λ) approximation is widely used to approximate electron transport coefficients in dense plasmas. It is a classical approximation to the momentum transport cross section. The accuracy of this approximation for electrical conductivity in dense plasmas is assessed by comparing to fully quantum mechanical calculations for realistic scattering potentials. It is found that the classical approximation is accurate to +/-10% when log Λ > 3, irrespective of the plasma species. The thermodynamic regime (density and temperature) for which log Λ > 3 corresponds to does, however, strong…
A new model for the electrical conductivity of dense plasmas with a mixture of ion species, containing no adjustable parameters, is presented. The model takes the temperature, mass density and relative abundances of the species as input. It takes into account partial ionization, ionic structure, and core-valence orthogonality, and uses quantum mechanical calculations of cross sections. Comparison to an existing high fidelity but computationally expensive method reveals good agreement. The new model is computationally efficient and can reach high temperatures. A new mixing rule is also presente…
A self-consistent 1-D model was developed to study the effects of non-local electron conductivity on power absorption and plasma density profiles in a planar inductively coupled argon discharge at low pressures (< 10 mTorr). The model consisted of three modules: (1) an electron energy distribution function (EEDF) module to compute the non-Maxwellian EEDF, (2) a non-local electron kinetics module to predict the non-local electron conductivity, RF current, electric field and power deposition profiles in the non-uniform plasma, and (3) a heavy species transport module to solve for the ion density…
The problems of high linear conductivity in an electric field, as well as nonlinear conductivity, are considered for plasma-like systems. First, we recall several observations of nonlinear fast charge transport in dusty plasma, molecular chains, lattices, conducting polymers and semiconductor layers. Exploring the role of noise we introduce the generalized Fokker-Planck equation. Second, one-dimensional models are considered on the basis of the Fokker-Planck equation with active and passive velocity-dependent friction including an external electrical field. On this basis it is possible to find…
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 …
We present an approach which allows the consistent treatment of bound states in the context of the dc conductivity in dense partially ionized noble gas plasmas. Besides electron-ion and electron-electron collisions, further collision mechanisms owing to neutral constituents are taken into account. Especially at low temperatures $T\approx 1 {\rm eV}$, electron-atom collisions give a substantial contribution to the relevant correlation functions. We suggest an optical potential for the description of the electron-atom scattering which is applicable for all noble gases. The electron-atom momentum…
A new formulation of the Kubo-Greenwood conductivity for average atom models is given. The new formulation improves upon previous by explicitly including the ionic-structure factor. Calculations based on this new expression lead to much improved agreement with ab initio results for DC conductivity of warm dense hydrogen and beryllium, and for thermal conductivity of hydrogen. We also give and test a slightly modified Ziman-Evans formula for the resistivity that includes a non-free electron density of states, thus removing an ambiguity in the original Ziman-Evans formula. Again results based on…
Formulas for transverse conductance and dielectric permeability in quantum degenerate collisional plasma with arbitrary variable collision frequency in Mermin's approach are deduced. Frequency of collisions of particles depends arbitrarily on a wave vector. For this purpose the kinetic Shrödinger - Boltzmann equation with collision integral of relaxation type in momentum space is applied. The case of degenerate Fermi plasma is allocated and investigated. The special case of frequency of collisions proportional to the module of a wave vector is considered. The graphic analysis of the real and i…
A rigorous and most general covariant kinetic formalism is developed to study the nonlinear waves interaction in relativistic Vlasov plasmas. The typical nonlinear plasma reaction is a nonlinear current measured by the nonlinear plasma conductivity, and these quantities are derived here on the basis of relativistic Vlasov-Maxwell equations. Knowing the nonlinear plasma conductivity allows us to determine all plasma modes nonlinearly excited in plasma. The general covariant form of nonlinear conductivity is provided first for any value of plasma temperature and for the whole complex frequency p…
The electrical conductivity in dense plasmas can be calculated with the relaxation-time approximation provided that the interaction potential between the scattering electron and the ion is known. To date there has been considerable uncertainty as to the best way to define this interaction potential so that it correctly includes the effects of ionic structure, screening by electrons and partial ionization. Current approximations lead to significantly different results with varying levels of agreement when compared to bench-mark calculations and experiments. We present a new way to define this p…
Formulas for transverse conductance and dielectric permeability in quantum non-degenerate and Maxwellian collisional plasma with arbitrary variable collision frequency in Mermin's approach are deduced. Frequency of collisions of particles depends arbitrarily on a wave vector. The special case of frequency of collisions proportional to the module of a wave vector is considered. The graphic analysis of the real and imaginary parts of dielectric function is made.
By using the generalized Boltzmann equation of transport and the first-order approximation of Chapman-Enskog expansion on the kappa-distribution function, we study the thermal conductivity and Dufour effects in the weakly ionized and magnetized plasma. We show that in the kappa-distributed plasma, the thermal conductivity and Dufour coefficient are significantly different from those in the Maxell-distributed plasma, and the transverse thermal conductivity and Dufour coefficient in the kappa-distributed plasma are generally greater than those in the Maxwell-distributed plasma, and the Righi-Led…
Methods for modelling the electrical conductivity of dense plasmas and liquid metals, based upon the well-known Ziman formula, are reviewed from a general perspective, and some earlier inconsistencies relating to its application to finite temperature systems are resolved. A general formula for the conductivity of a Lorentzian two-component plasma in thermal equilibrium is derived from the Lenard-Balescu collision integral in which both energy and momentum exchange between ions and electrons are accounted for. This formula is used as a basis for some generalizations of the Ziman formula, which …
The low-density limit of the electrical conductivity $σ(n,T)$ of hydrogen as the simplest ionic plasma is presented as function of temperature T and mass density n in form of a virial expansion of the resistivity. Quantum statistical methods yield exact values for the lowest virial coefficients which serve as benchmark for analytical approaches to the electrical conductivity as well as for numerical results obtained from density functional theory based molecular dynamics simulations (DFT-MD) or path-integral Monte Carlo (PIMC) simulations. While these simulations are well suited to calculate $…
Formulas for transversal conductance and dielectric permeability (dielectric function) in quantum Maxwell collisional plasma are deduced. The kinetic equation with collision integral in the form relaxation type is used.
The problem of determining the effective conductivity tensor of a magnetoactive turbulent plasma is considered in the approximation of isolated particles. Additional gyrotropicterms are shown to appear in the conductivity tensor in the presence of mean, nonzero magnetic helicity. The dispersion of propagating electro- magnetic waves changes, additional modes and additional rotation of the polarization plane appear, and the waves can be amplified. The properties acquired by plasma with helicity are similar those observed in chiral and bianisotropic electrodynamic media.
We point out that confusion sometimes arises when using a chemical potential in plasma with Coulomb interactions. The results of our consideration are applied to the discussion of nuclear reactions screening. Finally, we present a transparent derivation of the thermal conductivity coefficient of a degenerate electron gas.
The collision operator for a relativistic plasma is reformulated in terms of an expansion in spherical harmonics. In this formulation the collision operator is expressed in terms of five scalar potentials which are given by one-dimensional integrals over the distribution function. This formulation is used to calculate the electrical conductivity of a uniform electron-ion plasma with infinitely massive ions.
Equilibrium molecular dynamics simulations are used to calculate the thermal conductivity of the one component plasma (OCP) via the Green-Kubo formalism over a broad range of Coulomb coupling strength, $0.1\leΓ\le180$. These simulations address previous discrepancies between computations using equilibrium versus nonequilibrium methods. Analysis of heat flux autocorrelation functions show that very long ($6\times10^5ω_p^{-1}$) time series are needed to reduce the noise level to allow $\lesssim2\%$ accuracy. The new simulations provide the first accurate data for $Γ\lesssim 1$. This enables a te…
We study the influence of equation-of-state (EOS) model on the interpretation of electrical conductivity measurements in strongly coupled plasma of tungsten by Korobenko et al. (2002 Plasma Physics Reports 28(12) 1008--1016). Three different semiempirical EOS models for tungsten are used. Discrepancies in obtained thermodynamic parameters and specific resistivity values as compared with calculation results of Korobenko et al. are analysed.
We study the diffusion and thermal conductivity of charged particles in the weakly ionized plasma with the power-law q-distributions in nonextensive statistics and without the magnetic field. Electrons and ions have different q-parameters and temperature. We derive new expressions of the diffusion, thermal diffusion, thermal conductivity and thermoelectric coefficients of electrons and ions respectively in the plasma. It is shown that these transport coefficients depend significantly on the q-parameters in the power-law q-distributed plasma and thus they have different properties from those de…
The method of moments is used to calculate the dynamic conductivity of strongly coupled fully ionized hydrogen plasmas. The electron density $n_{e}$ and temperature $T$ vary in the domains $ 10^{21} < n_{e} < 10^{24} {\rm cm}^{-3}$, $10^{4} {\rm K} < T < 10^{6} {\rm K}$. The results are compared to some theoretical data.
Formulas for transverse conductance in quantum collisional plasma are deduced. The kinetic equation in momentum space in the relaxation approach is used. It is shown, that at Planck's constant tends to zero the derived formula transfers to the classical one. It is shown also, that when electron collision frequency tends to null (i.e. plasma becomes collisionless), the conductance formula transfers in the known formula inferred earlier by Lindhard.
Formulas for transverse conductance in quantum non-degenerate collisional plasma are deduced. The kinetic equation in momentum space in the relaxation approach is used. It is shown, that at $\hbar\to 0$ the derived formula transfers to the classical one. It is shown also, that when values of dimensionless wave numbers are small, the conductance formula transfers in the known formula for classical non-degenerate plasmas.
Formulas for transversal electric conductivity and dielectric permeability of quantum collisional plasma are deduced. The kinetic equation for a density matrix in relaxation approaching in momentum space is used. It is shown, that when Planck's constant tends to zero, these deduced formulas pass in classical expressions and when frequency of electron collision tends to zero (i.e. plasma passes in collisionless plasma), the deduced formulas pass in deduced earlier by Lindhard. It is shown also, that when the wave number tends to zero, quantum conductivity passes in the classical one. Graphic co…
Formulas for transverse conductance in quantum Maxwellian collisional plasma are deduced. The kinetic Von Neumann equation in momentum space with collision integral in the relaxation form is used. It is shown, that at Planck's constant tends to zero the derived formula transfers to the classical one. It is shown also, that when values of dimensionless wave numbers are small, the conductance formula transfers in the known formula for classical Maxwellian plasmas.
Formulas for calculation of transverse dielectric function and transverse electric conductivity in quantum collisional Maxwellian plasma are obtained. The Wigner -- Vlasov -- Boltzmann kinetic equation with collision integral in BGK (Bhatnagar, Gross and Krook) form in coordinate space is used. Various special cases are in\-ves\-ti\-gated. Comparison with Lindhard's formula has been carried out.
The kinetic description of magnetic susceptibility and Landau diamagnetism of quantum collisional plasmas with any degeration of electronic gas is given. The correct expression of electric conductivity of quantum collisional plasmas with any degeration of electronic gas (see A. V. Latyshev and A. A. Yushkanov, Transverse electrical conductivity of a quantum collisional plasma in the Mermin approach. - Theor. and Math. Phys., V. 175(1):559-569 (2013)) is used.
Formulas for longitudinal electric conductivity and dielectric permeability in the quantum non-degenerate collisional plasma with the frequency of collisions depending on momentum in Mermin' approach are received. The kinetic equation in momentum space in relaxation approximation is used. It is shown that when Planck's constant tends to zero, the deduced formula passes to the corresponding formula for classical plasma. It is shown also that when frequency of collisions of particles of plasma tends to zero (plasma passes to collisionless one), the deduced formula passes to the known Lindhard' f…
Formulas for calculation of transversal dielectric function and transversal electric conductivity in quantum non-degenerate collisional plasmas under arbitrary degree of degeneracy of the electron gas are received. The Wigner-Vlasov-Boltzmann kinetic equation with collision integral in BGK (Bhatnagar, Gross and Krook) form in coordinate space is used. Various special cases are investigated
A generalized Ohm's law is derived to treat strongly magnetized plasmas in which the electron gyrofrequency significantly exceeds the electron plasma frequency. The frictional drag due to Coulomb collisions between electrons and ions is found to shift, producing an additional transverse resistivity term in the generalized Ohm's law that is perpendicular to both the current ($\vc{J}$) and the Hall ($\vc{J} \times \vc{B}$) direction. In the limit of very strong magnetization, the parallel resistivity is found to increase by a factor of 3/2, and the perpendicular resistivity to scale as $\ln (ω_{…
Detailed deducing of formulas for longitudinal electric conductivity and dielectric permeability in the quantum degenerate collisional plasma with constant collision frequency in Mermin' approach is given. The kinetic Schrödinger-Boltzmann equation in momentum space in relaxation approximation is used. It is shown that when collision frequency of plasma particles tends to zero (plasma passes to collisionless one), the deduced formula for dielectric function passes to the known Lindhard' formula for collisionless plasmas. It is shown that the deduced formula for dielectric permeability coincide…
The controversy with respect to the role of electron-electron collisions in the dynamic conductivity of dense plasmas is resolved. In particular, the dc conductivity is analyzed in the low-density, non-degenerate limit where the Spitzer theory is valid and electron-electron collisions lead to the well-known reduction of the result for a Lorentz plasma. With increasing degeneracy, the contribution of electron-electron collisions to the dc conductivity is decreasing and can be neglected for the liquid metal domain where the Ziman-Faber theory is applicable. We show how electron-electron collisio…
The conditions for the excitation of current and voltage oscillations in the plasma of a three-electrode current and voltage stabilizer are experimentally investigated. It was found that in the regimes under consideration, the plasma has negative conductivity, which causes oscillations. A highly efficient method for suppressing plasma instabilities is proposed, based on controlling the sign of differential plasma conductivity by adjusting the concentration of slow electrons using an external electrode. The proposed method makes it possible to achieve a high level of stability of the energy cha…
We study the linear Vlasov equation with a given electric field $E \in \mathcal{S}$, where $\mathcal{S}$ is the space of Schwartz functions. The associated damped partial differential equation has a unique tempered solution, which fixes the needed Cauchy datum. This tempered solution then converges to the causal solution of the linear Vlasov equation when the damping parameter goes to zero. This result allows us to define the plasma conductivity operator $σ$, which gives the current density $j = σ(E)$ induced by the electric field $E$. We prove that $σ$ is continuous from $\mathcal{S}$ to its …
Two-dimensional fully kinetic particle-in-cell simulations of an electrodeless plasma thruster, which uses a magnetic nozzle, were conducted to investigate the thrust generation induced by the internal plasma current. The results clearly show that the $\bf{E} \times \bf{B}$ and diamagnetic current densities are the major components of the internal plasma current. The simulated pressure structures reproduced the experimentally observed structures well. The results for various magnetic field strengths reveal that the $\bf{E} \times \bf{B}$ effect decreases and the diamagnetic effect becomes domi…
In a new toroidal laboratory plasma device including a poloidal magnetic field created by an internal circular conductor, the confinement efficiency of the magnetized plasma and the turbulence level are studied in different situations. The plasma density is greatly enhanced when a sufficient poloidal magnetic field is established. Moreover, the instabilities and the turbulence usually found in toroidal devices without shear of the magnetic field lines are suppressed when the rotational transform is present. The measurement of the plasma decay time allows to determine the confinement time of th…
The results of MHD plane shock waves with infinite electrical conductivity are generalized for a plasma with a finite conductivity. We derive the adiabatic curves that describe the evolution of the shocked gas as well as the change in the entropy density. For a parallel shock (i.e., in which the magnetic field is parallel to the normal to the shock front) we find an expression for the shock thickness which is a function of the ambient magnetic field and of the finite electrical conductivity of the plasma. We give numerical estimates of the physical parameters for which the shock thickness is o…
Low-frequency properties of a plasma are examined within the average-atom approximation, which presumes that scattering of a conducting electron on each atom takes place independently of other atoms. The relaxation time tau distinguishes a high-frequency region omega tau > 1, where the single-atom approximation is applicable explicitly, from extreme low frequencies omega tau < 1, where, naively, the single-atom approximation is invalid. A proposed generalization of the formalism, which takes into account many-atom collisions, is found to be accurate in all frequency regions, from omega =0 to o…
Relative transverse drift (with respect to the ambient magnetic field) between the weakly magnetized electrons and the unmagnetized ions at the lower altitude (80 km) and between the weakly magnetized ions and unmagnetized dust at the higher altitude (90 km) gives rise to the finite Hall conductivity in the Earth's mesosphere. If, on the other hand, the number of free electrons is sparse in the mesosphere and most of the negative charge resides on the weakly magnetized, fine, nanometre sized dust powder and positive charge on the more massive, micron sized, unmagnetized dust, the sign of the H…
We summarize several semi-phenomenological approaches to estimate the internal energy of one-component-plasma (OCP) in two (2D) and three (3D) dimensions. Particular attention is given to a hybrid approach, which reproduces the Debye-H$\ddot{\text{u}}$ckel asymptote in the limit of weak coupling, the ion sphere (3D) and ion disc (2D) asymptotes in the limit of strong coupling, and provides reasonable interpolation between these two limits. More accurate ways to estimate the internal energy of 2D and 3D OCP are also discussed. The accuracy of these analytic results is quantified by comparison w…
The analysis of nonlinear interaction of transversal electromagnetic field with quantum collisionless plasma is carried out. Formulas for calculation electric current in quantum collisionless plasma at any temperature are deduced. It has appeared, that the nonlinearity account leads to occurrence of the longitudinal electric current directed along a wave vector. This second current is orthogonal to the known transversal classical current, received at the classical linear analysis. The case of degenerate electronic plasma is considered. The concept of longitudinal-transversal conductivity is en…
In this paper we study the influence of the magnetised thermal conductivity on the propagation of a nanosecond $10^{14} \mathrm{Wcm}^{-2}$ laser in an underdense plasma by performing simulations of a paraxial model laser in a plasma with the full Braginskii magnetised transport coefficients. Analytic theory and simulations show the shortening of the self-focal length of a laser beam in a plasma as a result of the reduction of the plasma thermal conductivity in a magnetic field. Furthermore the filamentation of a laser via the thermal mechanism is found to have an increased spatial growth rate …
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…
LHD inward-shifted configurations are unstable to resistive MHD pressure-gradient-driven modes. Sawtooth like activity was observed during LHD operation. The main drivers are the unstable modes $1/2$ and $1/3$ in the middle and inner plasma region which limit the plasma confinement efficiency of LHD advanced operation scenarios. The aim of the present research is to study the hard MHD limit of $1/2$ sawtooth like activity, not observed yet in LHD operation, and to predict its effects on the device performance. Previous investigations pointed out this system relaxation can be an internal disrup…
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 …
With the use of correct expression of the electric conductivity of quantum collisional degenerate plasmas (A. V. Latyshev and A. A. Yushkanov, Transverse electrical conductivity of a quantum collisional plasma in the Mermin approach, - Theor. and Math. Phys., {\bf 175}(1): 559-569 (2013)) the kinetic description of a magnetic susceptibility is obtained and the formula for calculation of Landau diamagnetism is deduced.
A simple model for the dielectric function of a completely ionized plasma with an arbitrary ionic charge, that is valid for long-wavelength high-frequency perturbations is derived using an approximate solution of a linearized Fokker-Planck kinetic equation for electrons with a Landau collision integral. The model accounts for both the electron-ion collisions and the collisions of the subthermal (cold) electrons with thermal ones. The relative contribution of the latter collisions to the dielectric function is treated phenomenologically, introducing some parameter $\varkappa$ that is chosen in …
With the use of correct expression of the electric conductivity of quantum collisional plasmas (A. V. Latyshev and A. A. Yushkanov, {\it Transverse electrical conductivity of a quantum collisional plasma in the Mermin approach}. - Theor. and Math. Phys., {\bf 175}(1): 559-569 (2013)) the kinetic description of a magnetic susceptibility is obtained and the formula for calculation of Landau diamagnetism is deduced.
Our analysis of the model [J. Phys.: Conf. Ser. 941 (2017) 012008] elaborated for interpreting the initial stage of the fast nonlocal transport events, which exhibit immediate response, in the heat diffusion time scale, of the spatial profile of electron temperature to its local perturbation, shows that the nonlocal transport by electromagnetic (EM) waves needs too high reflectivity of vacuum vessel walls to describe the experimental data. Here we try another model, which assumes high internal reflections and is compatible with the "wild cable" transport of TEM waves along magnetically-bound s…
We numerically study the effects of varying electric conductivity and magnetic permeability of the bounding wall on a kinematic dynamo in a sphere for parameters relevant to Madison plasma dynamo experiment (MPDX). The dynamo is excited by a laminar, axisymmetric flow of von Karman type. The flow is obtained as a solution to the Navier-Stokes equation for an isothermal fluid with a velocity profile specified at the sphere's boundary. The properties of the wall are taken into account as thin-wall boundary conditions imposed on the magnetic field. It is found that an increase in the permeability…
The effect of radiative heat-loss function and finite ion Larmor radius (FLR) corrections on the thermal instability of infinite homogeneous viscous plasma has been investigated incorporating the effects of thermal conductivity and finite electrical resistivity for the formation of a molecular cloud. The general dispersion relation is derived using the normal mode analysis method with the help of relevant linearized perturbation equations of the problem. Furthermore the wave propagation along and perpendicular to the direction of external magnetic field has been discussed. Stability of the med…
