Using techniques of effective field theory, we consider the thermodynamical properties of a dilute two-dimensional plasma interacting via a $1/r$ potential. The first one-loop correction to the partition function is already logarithmically divergent in the effective theory. The finite part of the one-loop induced couplings is then explicitly evaluated by matching the density-density correlator in the effective theory and in the full quantum theory. This task is performed from the formulation of the Coulomb problem in momentum space by projecting the two-dimensional momentum space onto the surface of a three-dimensional sphere. We also report some higher order results that, in the case of the one-component plasma immersed in a uniform neutralizing background, are resummed to obtain the complete leading-log partition function.
Bridge functions, the missing link in the exact description of strong correlations, are indirectly extracted from specially designed molecular dynamics simulations of classical one-component plasma liquids and accurately parameterized. Their incorporation into an advanced integral equation theory description of Yukawa one-component plasma liquids and a novel dielectric formalism scheme for quantum one-component plasma liquids leads to an unprecedented agreement with available molecular dynamics simulations and new ab initio path integral Monte Carlo simulations, respectively.
The analysis of nonlinear interaction of transversal electromagnetic field with degenerate collisionless classical and quantum plasmas is carried out. Formulas for calculation electric current in degenerate collisionless classical and quantum plasmas are deduced. It has appeared, that the nonlinearity account leads to occurrence of longitudinal electric current directed along a wave vector. This second current is orthogonal to the known transversal current, received at the classical linear analysis. Graphic comparison of density of electric current for classical degenerate Fermi plasmas and Fe…
The complementarity of the liquid and plasma descriptions of the classical one-component plasma (OCP) is explored by studying wavevector and frequency dependent dynamical quantities: the dynamical structure factor (DSF), and the dynamic local field correction (LFC). Accurate Molecular Dynamics (MD) simulations are used to validate/test models of the DSF and LFC. Our simulations, which span the entire fluid regime ($Γ= 0.1 - 175$), show that the DSF is very well represented by a simple and well known memory function model of generalized hydrodynamics. On the other hand, the LFC, which we have c…
The Bohr-van Leeuwen theorem is often summarized as saying that there is no classical magnetic susceptibility, in particular no diamagnetism. This is seriously misleading. The theorem assumes position dependent interactions but this is not required by classical physics. Since the work of Darwin in 1920 it has been known that the magnetism due to classical charged point particles can only be described by allowing velocity dependent interactions in the Lagrangian. Legendre transformation to an approximate Hamiltonian can give an estimate of the Darwin diamagnetism for a system of charged point p…
From Vlasov kinetic equation for collisionless plasmas distribution function in square-law approximation on size of electromagnetic field is received. Formulas for calculation electric current at any temperature (any degree of degeneration of electronic gas) are deduced. The case of small values of the wave numbers is considered. It is shown, that the nonlinearity account leads to occurrence the longitudinal electric current directed along a wave vector. This longitudinal current orthogonal to known transversal classical current, received at the linear analysis. From the kinetic equation with …
The analysis of nonlinear interaction of transversal electromagnetic field with Maxwellian collisionless classical and quntum plasmas is carried out. Formulas for calculation electric current in Maxwellian collisionless classical and quntum plasmas 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 current, received at the classical linear analysis. Graphic comparison of density of electric current for classical Maxwellian plasmas and Fermi-…
It is demonstrated that in high temperature collisionless plasmas the propagation of high-frequency electromagnetic waves is naturally subject to a classical Higgs mechanism which in some cases generates a very small though finite mass on the otherwise massless photons. Though this has no further obvious consequence for any plasma processes, it is very satisfactory because it explains the retardation and cut-off of electromagnetic waves when encountering plasmas. Interestingly, low frequency electromagnetic plasma waves (Alfvén waves and whistlers) remain carried by confined massless photons. …
When λ_{T} << d_{T}, where λ_{T} is the de Broglie wavelength and d_{T}, the distance of closest approach of thermal electrons, a classical analysis of the energy of a plasma can be made. In all the classical analysis made until now, it was assumed that the frequency of the fluctuations ω<< T (k_{B}=\hbar=1). Using the fluctuation-dissipation theorem, we evaluate the energy of a plasma, allowing the frequency of the fluctuations to be arbitrary. We find that the energy density is appreciably larger than previously thought for many interesting plasmas, such as the plasma of the Universe before …
We have derived tractable cubic (p=3) and quartic (p=4) fluctuation-dissipation theorems (FDTs) for the classical one-component plasma in a form that links a single (p+1)-point dynamical structure function to a linear combination of pth-order density response functions amenable to calculation from model plasma kinetic equations. For p greater than or equal to 3, we note the emergence of "remainder" contributions comprised of clusters of lower-order dynamical structure functions which can be ultimately traded for response functions vis-a-vis the linear and quadratic FDTs. Our analysis paves the…
Classical plasma with arbitrary degree of degeneration of electronic gas is considered. In plasma N (N>2) collinear electromagnatic waves are propagated. It is required to find the response of plasma to these waves. Distribution function in square-law approximation on quantities of two small parameters from Vlasov equation is received. The formula for electric current calculation is deduced. It is demonstrated that the nonlinearity account leads to occurrence of the longitudinal electric current directed along a wave vector. This longitudinal current is orthogonal to the known transversal curr…
Kinetic Vlasov equation for collisional Maxwellian plasmas is used. Collision integral of BGK (Bhatnagar, Gross and Krook) type is applied. From Vlasov equation we find distribution function of electrons in square-law approximation on size of transversal electric field. The formula for electric current calculation is deduced. This formula contains an one-dimensional quadrature. It is shown, that nonlinearity leads to revealing of the longitudinal electric current directed along a wave vector. This longitudinal current is perpendicular to known so-called transversal classical current. The class…
The results of a theoretical investigation on the stopping power of ion pair in a magnetized electron plasma are presented, with particular emphasis on the two-ion correlation effects. The analysis is based on the assumptions that the magnetic field is classically strong ($λ_B\ll a_c\ll λ_D$, where $λ_B$, $a_c$ and $λ_D$ are respectively the electron de Broglie wavelength, Larmor radius and Debye length) and that the velocity of the two ions is identical and fixed. The stopping power and % vicinage function in a plasma are computed by retaining two-ion correlation effects and is compared with …
The process of dynamical reduction of the Vlasov-Maxwell equations leads to the introduction of classical {\it zitterbewegung} effects in reduced plasma dynamics. These effects manifest themselves in the form of an asymmetric canonical energy-momentum tensor involving the decoupling of the reduced kinetic momentum ${\bf p}$ from the reduced velocity ${\bf u}$ (i.e., ${\bf u}\btimes{\bf p} \neq 0$) as well as reduced polarization and magnetization effects. The reduced intrinsic torque generated by the antisymmetric part of the canonical energy-momentum tensor, which is calculated from the reduc…
An effective theory of laser--plasma based particle acceleration is presented. Here we treated the plasma as a continuous medium with an index of refraction $n_{m}$ in which a single electron propagates. Because of the simplicity of this model, we did not need to perform PIC simulations in order to study the properties of the electron acceleration. We studied the properties of the electron motion due to the Lorentz force and the relativistic equations of motion were numerically solved and analysed. We compared our results to PIC simulations and experimental data. Keywords: Underdense plasma; E…
Certain recent semi-classical theories of spin-half quantum plasmas are examined with regard to their internal consistency, physical applicability and relevance to fusion, astrophysical and condensed matter plasmas. It is shown that the derivations and some of the results obtained in these theories are internally inconsistent and contradict well-established principles of quantum and statistical mechanics, especially in their treatment of fermions and spin. Claims of large semi-classical effects of spin magnetic moments that could dominate the plasma dynamics are found to be invalid both for si…
An ellipsoidal volume of Rydberg molecules, entrained in a supersonic molecular beam, evolves on a nanosecond timescale to form a strongly coupled ultracold plasma. We present coupled rate-equation simulations that model the underlying kinetic processes and molecular dissociation channels in both a uniformly distributed plasma and under the conditions dictated by our experimental geometry. Simulations predict a fast electron-driven collisional avalanche to plasma followed by slow electron-ion recombination. Within 20 $μ$s, release of Rydberg binding energy raises the electron temperature of a …
In a recent paper, Lucco Castello et al. [arXiv:2107.03537] performed systematic extractions of classical one-component plasma bridge functions from molecular dynamics simulations and provided an accurate parametrization that was incorporated in the novel isomorph-based empirically modified hypernetted chain approach for Yukawa one-component plasmas. Here, the extraction technique and parametrization strategy are described in detail, while the deficiencies of earlier efforts are discussed. The structural and thermodynamic predictions of the updated version of the integral equation theory appro…
It is shown that a vorticity, constructed from spin field of a quantum spinning plasma, combines with the classical generalized vorticity (representing the magnetic and the velocity fields) to yield a new grand generalized vorticity that obeys the standard vortex dynamics. Expressions for the quantum or spin vorticity, and for the resulting generalized helicity invariant are derived. Reduction of the rather complex spinning quantum system to a well known and highly investigated classical form opens familiar channels for the delineation of physics peculiar to dense plasmas spanning solid state …
Quantum Calculation of Classical Kinetic Equations: A Novel Approach for Numerical Analysis of 6D Boltzmann-Maxwell Equations in Collisionless Plasmas Using Quantum Computing
An effective approach for construction of simple approximation for description of non-ideality effects in classical one- and two-component plasma model is under discussion. General constraints i.e. positiveness and exponential type for radial distribution functions F2(r) combined with normalizing (local electroneutrality) conditions, which validity is independent on degree of non-ideality, are used for effective correction of several well-known approximated forms of F(r). Resulting corrected forms F*(r) leads to non-ideality corrections, which are asymptotically exact in the weak non-ideality …
We investigate the crystallization rate of a one-component plasma (OCP) in the context of classical nucleation theory. From our derivation of the free energy of an arbitrary distribution of solid clusters embedded in a liquid phase, we derive the steady-state nucleation rate of an OCP as a function of the Coulomb coupling parameter. Our result for the rate is in accord with recent molecular dynamics simulations, but it is greater than that of previous analytical estimates by many orders of magnitude. Further molecular dynamics simulations of the nucleation rate of a supercooled liquid OCP for …
The quantum mechanical effect on the plasma two-stream instability is studied based on the dielectric function approach. The analysis suggests that the degenerate plasma relevant to the inertial confinement fusion behaves differently from classical plasmas when the electron drift velocity is comparable to the Fermi velocity. For high wave vector comparable to the Fermi wave vector, the degenerate quantum plasma has larger regime of the two-stream instabilities than the classical plasma. A regime, where the plasma waves with the frequency larger than 1.5 times of the Langmuir wave frequency bec…
The analytical and numerical investigations of the energy loss rate of the test particle in a magnetized electron plasma are developed on the basis of the Vlasov-Poisson equations, and the main results are presented. The Larmor rotation of a test particle in a magnetic field is taken into account. The analysis is based on the assumption that the energy variation of the test particle is much less than its kinetic energy. The obtained general expression for stopping power is analyzed for three cases: (i) the particle moves through a collisionless plasma in a strong homogeneous magnetic field; (i…
One-dimensional steady-state plasma-field structures in overdense plasma are studied assuming that the electron temperature is uniform over plasma bulk and the ions are stationary. It is shown that there may exist solutions for electron distributions with cavitation regions in plasma under the action of ponderomotive force
The frequency-dependent linear response of a plasma is studied in the finite-temperature Thomas-Fermi approximation, with electron dynamics described using Bloch hydrodynamics. The variational framework of average-atoms in a plasma is used. Extinction cross-sections are calculated for several plasma conditions. Comparisons with a previously studied Thomas-Fermi Impurity in Jellium model are presented. An Ehrenfest-type sum rule, originally proposed in a full quantum approach is derived in the present formalism and checked numerically. This sum rule is used to define Bremsstrahlung and collecti…
A kinetic theory for spin plasmas is put forward, generalizing those of previous authors. In the model, the ordinary phase space is extended to include the spin degrees of freedom. Together with Maxwell's equations, the system is shown to be energy conserving. Analysing the linear properties, it is found that new types of wave-particle resonances are possible, that depend directly on the anomalous magnetic moment of the electron. As a result new wave modes, not present in the absence of spin, appear. The implications of our results are discussed.
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 wide use of a speed-independent distance as a cut-off impact parameter together with Rutherford's scattering formula, within the cut-off theory, to account for charge screening in plasma environment embodies a clear inconsistency. A new physically justified choice of the cut-off distance is introduced and used to derive a closed form expression for the effective momentum transport cross section. A simple approximation for the present Coulomb logarithm, free of special functions, is also presented and assessed. A comparison with experimentally recovered data for the reduced Coulomb conducti…
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.
A relativistic quantum field theory with nontrivial background fields is developed and applied to study waves in plasmas. The effective action of the electromagnetic 4-potential is calculated ab initio from the standard action of scalar QED using path integrals. The resultant effective action is gauge invariant and contains nonlocal interactions, from which gauge bosons acquire masses without breaking the local gauge symmetry. To demonstrate how the general theory can be applied, we study a cold unmagnetized plasma and a cold uniformly magnetized plasma. Using these two examples, we show that …
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…
The results of a theoretical investigation on the low-velocity stopping power of the ions moving in a magnetized collisional plasma are presented. The stopping power for an ion is calculated employing linear response theory using the dielectric function approach. The collisions, which leads to a damping of the excitations in the plasma, is taken into account through a number-conserving relaxation time approximation in the linear response function. In order to highlight the effects of collisions and magnetic field we present a comparison of our analytical and numerical results obtained for a no…
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. It is shown, that for degenerate plasmas the electric curr…
The response of dense quantum plasmas in the backward Raman scattering is studied. The coefficients in the backward Raman scattering is found to be underestimated (overestimated) in the classical theory if the excited Langmuir wave has low-wave vector (high-wave vector). The second order quantum perturbation theory shows that the second harmonic of the pondermotive potential arises naturally even in a single particle motion contrary to the classical plasmas.
A general field theory for classical particle-field systems is developed. Compared with the standard classical field theory, the distinguish feature of a classical particle-field system is that the particles and fields reside on different manifolds. The fields are defined on the 4D space-time, whereas each particle's trajectory is defined on the 1D time-axis. As a consequence, the standard Noether's procedure for deriving local conservation laws in space-time from symmetries is not applicable without modification. To overcome this difficulty, a weak Euler-Lagrange equation for particles is dev…
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 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.
Studies of charge-charge (ion-ion, ion-electron, and electron-electron) coupling properties for ion impurities in an electron gas and for a two component plasma are carried out on the basis of a regularized electron-ion potential without short-range Coulomb divergence. This work is motivated in part by questions arising from recent spectroscopic measurements revealing discrepancies with present theoretical descriptions. Many of the current radiative property models for plasmas include only single electron-emitter collisions and neglect some or all charge-charge interactions. A molecular dynami…
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…
Comment on: "Interacting quantum and classical waves: Resonant and non-resonant energy transfer to electrons immersed in an intense electromagnetic wave'' [Phys. Plasmas 29, 022107 (2022)]
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 …
We develop a method for calculating the equilibrium properties of the liquid-solid phase transition in a classical, ideal, multi-component plasma. Our method is a semi-analytic calculation that relies on extending the accurate fitting formulae available for the one-, two-, and three-component plasmas to the case of a plasma with an arbitrary number of components. We compare our results to those of Horowitz, Berry, & Brown (Phys. Rev. E, 75, 066101, 2007), who use a molecular dynamics simulation to study the chemical properties of a 17-species mixture relevant to the ocean-crust boundary of an …
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.
Experiments with two-dimensional (2D) plasma crystals are usually carried out in rf plasma sheaths, where the interparticle interactions are modified due to the presence of plasma wakes. The wake-mediated interactions result in the coupling between wave modes in 2D crystals, which can trigger the mode-coupling instability and cause melting. The theory predicts a number of distinct fingerprints to be observed upon the instability onset, such as the emergence of a new hybrid mode, a critical angular dependence, a mixed polarization, and distinct thresholds. In this paper we summarize these key f…
We examine the properties of linear electrostatic waves in unmagnetized quantum and classical plasmas consisting of one or two populations of electrons with analytically tractable distribution functions in the presence of a stationary neutralising ion background. Beginning with the kinetic quantum plasma longitudinal susceptibility, we assess the effects due to increasing complexity of the background distribution function. Firstly, we analyse dispersion and Landau damping in one-component plasmas and consider distribution functions with a variety of analytical properties: the Dirac delta funct…
Nonlinear interaction of a low density electron beam with a uniform plasma is studied using two-dimensional particle-in-cell (PIC) simulations. We focus on formation of coherent phase space structures in the case, when a wide two-dimensional wave spectrum is driven unstable, and we also study how nonlinear evolution of these structures is affected by the external magnetic field. In the case of isotropic plasma, nonlinear buildup of filamentation modes due to the combined effects of two-stream and oblique instabilities is found to exist and growth mechanisms of secondary instabilities destroyin…
It is shown that an undesirable curvature of the wave front of two-dimensional nonlinear wake wave excited in uniform plasma by a relativistic charged bunch or laser pulse may be compensated by radial change of the equilibrium plasma density.
The dielectric function for electron gas with parabolic energy bands is derived in a fractional dimensional space. The static response function shows a good dimensional dependance. The plasma frequencies are obtained from the roots of the dielectric functions. The plasma dispersion shows strong dimensional dependence. It is found that the plasma frequencies in the low dimensional systems are strongly dependent on the wave vector. It is weakly dependent in the three dimensional system and has a finite value at zero wave vector.
The three-dimensional evolution of a pure electron plasma is studied by means of a particle-in-cell code which solves the drift-Poisson system where kinetic effects in the motion parallel to the magnetic field are taken into account. Different results relevant to the nonlinear dynamics of trapped plasmas and low-energy electron beams are presented.
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…
Trines and Norreys state that a principle aim of their work on warm wave-breaking was ``to create some order in the diverse landscape of warm fluid models and establish which model is most suitable for the study of wave breaking in thermal plasma.'' Unfortunately, we must conclude that they have obfuscated more than they have clarified, and have advanced the waterbag model only by exaggerating or misstating its benefits while mischaracterizing features of alternative warm fluid theories.
