A closed expression for the momentum evolution of a test particle in weakly-coupled plasma is derived, starting from quantum many particle theory. The particle scatters from charge fluctuations in the plasma rather than in a sequence of independent binary collisions. Contrary to general belief, Bohr's (rather than Bethe's) Coulomb logarithm is the relevant one in most plasma applications. A power-law tail in the distribution function is confirmed by molecular dynamics simulation.
An expression for the effective Coulomb logarithm in one-component-plasma is proposed, which allows to extend the applicability of the classical formula for the self-diffusion coefficient to the strongly coupled regime. The proposed analytical approximation demonstrates reasonable agreement with previous numerical simulation results. Relevance to weakly screened Yukawa systems (and, in particular, complex plasmas) is discussed.
Particle-in-cell (PIC) simulations were performed to study the impact of Coulomb scattering on the performance of argon plasma based thermionic converters. Using a simplified model, studies from the 1970's have concluded that plasma resistance, brought on by Coulomb collisions, causes a shift in the IV-curves of thermionic converters that use an argon plasma to mitigate space charge, thereby strongly limiting their electricity generation capability. In this work the impact of Coulomb collisions in such devices were studied as a function of the relative electrical potential between the electrod…
Transport coefficients for Coulomb collision processes, e.g., friction, energy exchange, and resistivity, are calculated for Debye-screened (Yukawa) plasmas including correlation effects within the binary collision approximation. A generalized Coulomb logarithm, $Ξ(Λ)$, is required, which asymptotes to $\ln Λ$ in the weakly coupled limit, but is significantly modified when $Λ\lesssim 10^2$ due to large angle collisions. In the regime $10^{-2} \lesssim Λ\lesssim 10^2$, $Ξ$ can be substantially larger for attractive collisions than repulsive.
The behaviour of a collisional plasma which is optically thin to cyclotron radiation is considered, and the distribution functions accessible to it on the various timescales in the system are calculated. Particular attention is paid to the limit in which the collision time exceeds the radiation emission time, making the electron distribution function strongly anisotropic. Unusually for plasma physics, the collision operator can nevertheless be calculated analytically although the plasma is far from Maxwellian. The rate of radiation emission is calculated and found to be governed by the collisi…
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…
Based on the results of exact consideration of electron-ion Coulomb interaction, by numerical simulations for ultimate absorption coefficient, we study the practically more interesting case of absorption of hard x-ray quanta of frequency when photon energy is of the order of plasma temperature, in high temperature plasma, within the high nuclear charges as well (at which the Born approximation is not applicable), constituting the temperature dependence of one-photon absorption coefficient. It is shown that one can achieve the efficient absorption coefficient in these cases.
In this letter we derive an action principle for Coulomb collisions in plasmas. Although no natural Lagrangian exists for the Landau-Fokker-Planck equation, an Eulerian variational formulation is found considering the system of partial differential equations that couple the distribution function and the Rosenbluth potentials. Exact conservation laws are derived after generalizing the energy-momentum stress tensor for second order Lagrangians and, in the case of a test-particle population in a given plasma background, the action principle is shown to correspond to the Langevin equation for indi…
An orbit following code is developed to calculate ion beam trajectories in magnetized plasmas. The equation of motion (the Newton's equation) is solved including the Lorentz force term and Coulomb collisional relaxation term. Furthermore, a new algorithm is introduced by applying perturbation method regarding the collision term as a small term. The reduction of computation time is suggested.
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.
Two kinds of the quantum electrodynamic radiative corrections to electromagnetic interaction and their influence on properties of highly dense quantum plasmas are considered. Linear radiative correction to the Coulomb interaction are considered. Its contribution in the spectrum of the Langmuir waves is presented. The second kind of the radiative corrections is related to nonlinearity of the Maxwell equations for strong electromagnetic field. Its contribution in spectrum of transverse waves of magnetized plasmas is briefly discussed. At consideration of the Langmuir wave spectrum we included ef…
The creation of a spatially extended stable DC complex plasma crystal is a big experimental challenge and a topical area of research in the field of dusty plasmas. In this paper we describe a newly built and commissioned dusty plasma experimental device, DPEx-II, at the Institute for Plasma Research. The device can support the formation of large sized Coulomb crystals in a DC glow discharge plasma. The plasma in this L-shaped table-top glass chamber is produced between a circular anode and a long tray shaped cathode. It is characterized with the help of various electrostatic probes over a rang…
We study the expansion of a cold, non-neutral ion plasma into the vacuum. The plasma is made from cold rubidium atoms in a magneto-optical trap (MOT) and is formed via ultraviolet photoionization. We employ time-delayed plasma extraction and imaging onto a position- and time-sensitive micro-channel plate detector to analyze the plasma. We report on the formation and persistence of plasma shock shells, pair correlations in the plasma, and external-field-induced plasma focusing effects. We also develop trajectory and fluid descriptions to model the data and to gain further insight. The simulatio…
Strong correlation effects in classical and quantum plasmas are discussed. In particular, Coulomb (Wigner) crystallization phenomena are reviewed focusing on one-component non-neutral plasmas in traps and on macroscopic two-component neutral plasmas. The conditions for crystal formation in terms of critical values of the coupling parameters and the distance fluctuations and the phase diagram of Coulomb crystals are discussed.
We describe quantum hydrodynamic equations with the Coulomb exchange interaction for three and two dimensional plasmas. Explicit form of the force densities are derived. We present non-linear Schrodinger equations (NLSEs) for the Coulomb quantum plasmas with the exchange interaction. We show contribution of the exchange interaction in the dispersion of the Langmuir, and ion-acoustic waves. We consider influence of the spin polarization ratio on strength of the Coulomb exchange interaction. This is important since exchange interaction between particles with same spin direction and particles wit…
We present long-time simulations of expanding ultracold neutral plasmas, including a full treatment of the strongly coupled ion dynamics. Thereby, the relaxation dynamics of the expanding laser-cooled plasma is studied, taking into account elastic as well as inelastic collisions. It is demonstrated that, depending on the initial conditions, the ionic component of the plasma may exhibit short-range order or even a superimposed long-range order resulting in concentric ion shells. In contrast to ionic plasmas confined in traps, the shell structures are built up from the center of the plasma cloud…
Coulomb implosion mechanism of the negatively charged ion acceleration in laser plasmas is proposed. When a cluster target is irradiated by an intense laser pulse and the Coulomb explosion of positively charged ions occurs, the negative ions are accelerated inward. The maximum energy of negative ions is several times lower than that of positive ions. The theoretical description and Particle-in-Cell simulation of the Coulomb implosion mechanism and the evidence of the negative ion acceleration in the experiments on the high intensity laser pulse interaction with the cluster targets are presente…
The friction force on a test particle traveling through a plasma that is both strongly coupled and strongly magnetized is studied using molecular dynamics simulations. In addition to the usual stopping power component aligned antiparallel to the velocity, a transverse component that is perpendicular to both the velocity and Lorentz force is observed. This component, which was recently discovered in weakly coupled plasmas, is found to increase in both absolute and relative magnitude in the strongly coupled regime. Strong coupling is also observed to induce a third component of the friction forc…
Outer envelopes of neutron stars consist mostly of fully ionized, strongly coupled Coulomb plasmas characterized by typical densities about 10^4-10^{11} g/cc and temperatures about 10^4-10^9 K. Many neutron stars possess magnetic fields about 10^{11}-10^{14} G. Here we briefly review recent theoretical advances which allow one to calculate thermodynamic functions and electron transport coefficients for such plasmas with an accuracy required for theoretical interpretation of observations.
Spacecraft observations have shown that the proton temperature in the solar wind falls off with radial distance more slowly than expected for an adiabatic prediction. Usually, previous studies have been focused on the evolution of the solar-wind plasma by using the bulk speed as an order parameter to discriminate different regimes. In contrast, here, we study the radial evolution of pure and homogeneous fast streams (i.e. well-defined streams of coronal-hole plasma that maintain their identity during several solar rotations) by means of re-processed particle data, from the HELIOS satellites be…
The behaviour of a strongly-magnetized collisional electron-positron plasma which is optically thin to cyclotron radiation is considered, and the distribution functions accessible to it on the various timescales in the system are calculated. Particular attention is paid to the limit in which the collision time exceeds the radiation emission time, making the electron distribution function strongly anisotropic. Indeed, these are the exact conditions likely to be attained in the first laboratory electron-positron plasma experiments currently being developed, which will typically have very low den…
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 …
The electrostatic potential of a moving dust grain in a complex plasma with magnetized ions is computed using linear response theory, thereby extending our previous work for unmagnetized plasmas [P. Ludwig et al., New J. Phys. 14, 053016 (2012)]. In addition to the magnetic field, our approach accounts for a finite ion temperature as well as ion-neutral collisions. Our recently introduced code \texttt{Kielstream} is used for an efficient calculation of the dust potential. Increasing the magnetization of the ions, we find that the shape of the potential crucially depends on the Mach number $M$.…
Molecular dynamics simulations are used to model ion and neutral temperature evolution in partially-ionized atmospheric pressure plasma at different ionization fractions. Results show that ion-ion interactions are strongly coupled at ionization fractions as low as 10^-5 and that the temperature evolution is influenced by effects associated with the strong coupling. Specifically, disorder-induced heating is found to rapidly heat ions on a timescale of the ion plasma period (~10s ps) after an ionization pulse. This is followed by the collisional relaxation of ions and neutrals, which cools ions …
We apply the many-particle quantum hydrodynamics including the Coulomb exchange interaction to magnetized quantum plasmas. We consider a number of wave phenomenon under influence of the Coulomb exchange interaction. Since the Coulomb exchange interaction affects longitudinal and transverse-longitudinal waves we focus our attention to the Langmuir waves, Trivelpiece-Gould waves, ion-acoustic waves in non-isothermal magnetized plasmas, the dispersion of the longitudinal low-frequency ion-acoustic waves and low-frequencies electromagnetic waves at $T_{e}\gg T_{i}$ . We obtained the numerical simu…
While ion heating by elastic electron-ion collisions may be neglected for a description of the evolution of freely expanding ultracold neutral plasmas, the situation is different in scenarios where the ions are laser-cooled during the system evolution. We show that electron-ion collisions in laser-cooled plasmas influence the ionic temperature, decreasing the degree of correlation obtainable in such systems. However, taking into account the collisions increases the ion temperature much less than what would be estimated based on static plasma clouds neglecting the plasma expansion. The latter l…
The potential of the Dense Plasma Focus (DPF) for industrial applications in many fields is well recognized, although yet to be realized in practice. Particularly attractive is the possibility of its use as inexpensive industrial source of nuclear reactions for diverse high value applications such as fast pulsed neutron radiography of hydrogenous materials, non-intrusive neutron interrogation of concealed organic contraband and rapid production of short lived radioisotopes for medical diagnostics and therapy. Recently, it has been suggested that it may be possible to operate the DPF efficientl…
We develop a projection imaging technique to study ultracold plasma dynamics. We image the charged particle spatial distributions by extraction with a high-voltage pulse onto a position-sensitive detector. Measuring the 2D width of the ion image at later times (the ion image size in the first 20 $μ$s is dominated by the Coulomb explosion of the dense ion cloud), we extract the plasma expansion velocity. These velocities at different initial electron temperatures match earlier results obtained by measuring the plasma oscillation frequency. The electron image size slowly decreases during the pla…
The study presented in this paper has shown that the generation of hard x rays and high-energy ions, which are detected in pinch implosion experiments, may be associated with the Coulomb explosion of the hot spot that is formed due to the outflow of the material from the pinch cross point. During the process of material outflow, the temperature of the hot spot plasma increases, and conditions arise for the plasma electrons to become continuously accelerated. The runaway of electrons from the hot spot region results in the buildup of positive space charge in this region followed by a Coulomb ex…
Recently developed analytic approximation for the equation of state of fully ionized nonideal electron-ion plasma mixtures [Potekhin et al., Phys. Rev. E, 79, 016411 (2009); arXiv:0812.4344], which covers the transition between the weak and strong Coulomb coupling regimes and reproduces numerical results obtained in the hypernetted chain (HNC) approximation, is modified in order to fit the small deviations from the linear mixing in the strong coupling regime, revealed by recent Monte Carlo simulations. In addition, a mixing rule is proposed for the regime of weak coupling, which generalizes po…
The melting of 2D dust clusters caused by one additional particle in the lower layer has experimentally been observed to undergo a two-step transition, which divides the phase of the cluster into three stages. The first transition is a jump of the dust kinetic energy due to the onset of an instability of the lower-layer particle, shifting the cluster from an ordinary to a hot crystalline state. The second transition is the actual phase transition into a liquid state, which occurs at a decisively lower gas pressure. The detailed dynamical properties of the system during the transition were dete…
The standard picture of the Coulomb logarithm in the ideal plasma is controversial, the arguments for the lower cut off need revision. The two cases of far subthermal and of far superthermal electron drift motions are accessible to a rigorous analytical treatment. We show that the lower cut off $b_{\min}$ is a function of symmetry and shape of the shielding cloud, it is not universal. In the subthermal case shielding is spherical and $b_{\min}$ is to be identified with the de Broglie wavelength; at superthermal drift the shielding cloud exhibits cylindrical (axial) symmetry and $b_{\min}$ is t…
The viscosity tensor of the magnetized one-component plasma, consisting of five independent shear viscosity coefficients, a bulk viscosity coefficient, and a cross coefficient, is computed using equilibrium molecular dynamics simulations and the Green-Kubo relations. A broad range of Coulomb coupling and magnetization strength conditions are studied. Magnetization is found to strongly influence the shear viscosity coefficients when the gyrofrequency exceeds the Coulomb collision frequency. Three regimes are identified as the Coulomb coupling strength and magnetization strength are varied. The …
Two-Stream Instability and Bernstein-Greene-Kruskal Mode Formation in Coulomb One Component Plasma
University of Kashmir（克什米尔大学）；Indian Institute of Technology Jammu（贾姆穆印度理工学院）；Institute for Plasma Research（等离子体研究所）；Homi Bhabha National Institute（霍米·巴巴国民学院）
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…
The recently proposed effective potential theory [Phys. Rev. Lett. 110, 235001 (2013)] allows evaluating transport in coupled plasmas with the well-developed formalisms for systems with binary collisions. To facilitate practical implementation of this concept in fluid models of multi-component plasmas, compact expressions for the transport coefficients in terms the generalized Coulomb logarithms are summarized from existing prescriptions. For weakly coupled plasmas, characterized by Debye-shielded Coulomb interaction potential, expressions become fully analytical. In coupled plasmas the genera…
The dynamical structure factor of a Coulomb crystal of ions is calculated at arbitrary temperature below the melting point taking into account multi-phonon processes in the harmonic approximation. In a strongly coupled Coulomb ion liquid, the static structure factor is split into two parts, a Bragg-diffraction-like one, describing incipient long-range order structures, and an inelastic part corresponding to thermal ion density fluctuations. It is assumed that the diffractionlike scattering does not lead to the electron relaxation in the liquid phase. This assumption, together with the inclusio…
Electron beams in two-dimensional systems can provide a useful tool to study energy-momentum relaxation of electrons and to generate microwave radiation stemming from plasma-beam instabilities. Naturally, these two applications cannot coexist: if beam electrons do relax, the beam is stabilized; if instability exists, it strongly distorts the distribution function of beam electrons. In this paper, we study the competition of beam relaxation due to electron-electron (e-e) collisions and development of plasma beam instability in graphene. We find that unstable plasma mode associated with a beam i…
Molecular dynamics simulations are used to assess the influence of Coulomb coupling on the energy evolution of charged projectiles in the classical one-component plasma. The average projectile kinetic energy is found to decrease linearly with time when $ν_α/ω_{p} \lesssim 10^{-2}$, where $ν_{α}$ is the Coulomb collision frequency between the projectile and the medium, and $ω_{p}$ is the plasma frequency. Stopping power is obtained from the slope of this curve. In comparison to the weakly coupled limit, strong Coulomb coupling causes the magnitude of the stopping power to increase, the Bragg pe…
An unprecedented increase of kinetic energy of laser accelerated heavy ions is demonstrated. Ultra thin gold foils have been irradiated by an ultra short laser pulse at an intensity of $6\times 10^{19}$ W/cm$^{2}$. Highly charged gold ions with kinetic energies up to $> 200$ MeV and a bandwidth limited energy distribution have been reached by using $1.3$ Joule laser energy on target. $1$D and $2$D Particle in Cell simulations show how a spatial dependence on the ions ionization leads to an enhancement of the accelerating electrical field. Our theoretical model considers a varying charge densit…
Matter of subnuclear density in the inner crusts of neutron stars consists of neutron-rich atomic nuclei immersed in strongly degenerate relativistic gas of electrons and strongly nonideal liquid of neutrons. We give a brief account of thermodynamic and kinetic properties of this matter which are greatly affected by Coulomb and nuclear interactions (a companion paper on the outer envelopes is astro-ph/0012316) and show how they can be studied from observations of thermal radiation of young (age < 100 yr) neutron stars (for a discussion of the latter possibility, see astro-ph/0012306).
Transport properties of high-energy-density plasmas are influenced by the ion collision rate. Traditionally, this rate involves the Coulomb logarithm, $\lnΛ$. Typical values of $\lnΛ$ are $\approx 10~\mbox{to}~20$ in kinetic theories where transport properties are dominated by weak-scattering events caused by long-range forces. The validity of these theories breaks down for strongly-coupled plasmas, when $\lnΛ$ is of order one. We present measurements and simulations of collision data in strongly-coupled plasmas when $\lnΛ$ is small. Experiments are carried out in the first dual-species ultrac…
In a non-ideal classical Coulomb one-component plasma (OCP) all thermodynamic properties are known to depend only on a single parameter -- the coupling parameter $Γ$. In contrast, if the pair interaction is screened by background charges (Yukawa OCP) the thermodynamic state depends, in addition, on the range of the interaction via the screening parameter $κ$. How to determine in this case an effective coupling parameter has been a matter of intensive debate. Here we propose a consistent approach for defining and measuring the coupling strength in Coulomb and Yukawa OCPs based on a fundamental …
The low-frequency electric microfield distribution in a Coulomb plasma is calculated for various plasma parameters, from weak to strong Coulomb coupling and from zero to strong electron screening. Two methods of numerical calculations are employed: the adjustable-parameter exponential approximation and the Monte Carlo simulation. The results are represented by analytic fitting formulas suitable for applications.
Dusty plasma crystals have traditionally been observed and studied in radio frequency (RF) discharge plasmas and their formation in a DC glow discharge plasma remains experimentally challenging. We report the first ever observation of a stable dusty plasma Coulomb crystal in the cathode sheath region of a DC glow discharge plasma. The observations are made in the DPEx device where crystals of mono-disperse Melamine Formaldehyde grains are produced in the background of an Argon plasma. The crystalline nature of the structure is confirmed through a host of measurements that includes the radial p…
We present a Monte Carlo implementation of the Bremsstrahlung, Bethe-Heitler and Coulomb Trident processes into the particle-in-cell (PIC) simulation framework. In order to address photon and electron-positron pair production in a wide range of physical conditions, we derive Bremsstrahlung and Bethe-Heitler cross sections taking account of screening effects in arbitrarily ionized plasmas. Our calculations are based on a simple model for the atomic Coulomb potential that describes shielding due to both bound electrons, free electrons and ions. We then describe a pairwise particle interaction al…
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.
This report addresses the moments, ${\mathfrak{G}_n}\left( {\mathbf{q}} \right) = \int_{ - \infty }^{ + \infty } {{ω^n}S\left( {\mathbf{q},ω} \right)\mathrm{d}ω},\,n \in \mathbb{N},\,n \geq - 1$, of the quantum mechanical dynamic structure factor $S\left( {\mathbf{q},ω} \right)$ for a one-component Coulomb plasma in thermodynamic equilibrium. The Fluctuation Dissipation Theorem relates these moments to integrals involving the imaginary part of the inverse longitudinal dielectric function, with the odd moments in particular being equivalent to the odd moments of the imaginary part of the invers…
The charged particle stopping power in a highly ionized and weakly to moderately coupled plasma has been calculated to leading and next-to-leading order by Brown, Preston, and Singleton (BPS). After reviewing the main ideas behind this calculation, we use a Fokker-Planck equation derived by BPS to compute the electron-ion energy partitioning of a charged particle traversing a plasma. The motivation for this application is ignition for inertial confinement fusion -- more energy delivered to the ions means a better chance of ignition, and conversely. It is therefore important to calculate the fr…
Molecular dynamics simulations reveal that a fundamental symmetry of plasma kinetic theory is broken at moderate to strong Coulomb coupling: the collision rate depends on the signs of the colliding charges. This symmetry breaking is analogous to the Barkas effect observed in charged-particle stopping experiments and gives rise to significantly enhanced electron-ion collision rates. It is expected to affect any neutral plasma with moderate to strong Coulomb coupling such as ultracold neutral plasmas (UNP) and the dense plasmas of ICF and laser-matter interaction experiments. The physical mechan…
The structure of Langmuir plasma waves carrying a finite angular orbital momentum is revised in the paraxial optics approximation. It is shown that the kinetic effects related to higher-order momenta of the electron distribution function lead to coupling of Laguerre-Gaussian modes and result in modification of the wave dispersion and damping. The theoretical analysis is compared to the three-dimensional particle-in-cell numerical simulations for a mode with orbital momentum l = 2. It is demonstrated that propagation of such a plasma wave is accompanied with generation of quasi-static axial and…
Isomorph theory is employed in order to establish a mapping between the bridge function of Coulomb and Yukawa one-component plasmas. Within an exact invariance ansatz for the bridge functions and by capitalizing on the availability of simulation-extracted Coulomb bridge functions, an analytical Yukawa bridge function is derived which is inserted into the integral theory framework. In spite of its simplicity and computational speed, the proposed integral approach exhibits an excellent agreement with computer simulations of dense Yukawa liquids without invoking adjustable parameters.
A tutorial overview on the angular scattering models of Electron-Neutral, Ion-Neutral, Neutral-Neutral, and Coulomb Collisions in Monte Carlo collision modeling on low temperature plasma
The analytic equation of state of nonideal Coulomb plasmas consisting of pointlike ions immersed in a polarizable electron background (physics/9807042) is improved, and its applicability range is considerably extended. First, the fit of the electron screening contribution in the free energy of the Coulomb liquid is refined at high densities where the electrons are relativistic. Second, we calculate the screening contribution for the Coulomb solid (bcc and fcc) and derive an analytic fitting expression. Third, we propose a simple approximation to the internal and free energy of the liquid one-c…
