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 approach are compared with extensive available simulation results revealing a truly unprecedented level of accuracy in the entire dense liquid region of the Yukawa phase diagram.
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.
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.
Different advanced bridge function closures are utilized to investigate the structural and thermodynamic properties of dense Yukawa one-component plasma liquids within the framework of integral equation theory. The isomorph-based empirically modified hypernetted-chain, the variational modified hypernetted-chain, the Rogers-Young and the Ballone-Pastore-Galli-Gazzillo approaches are compared at the level of thermodynamic properties, radial distribution functions and bridge functions. The comparison, based on accuracy and computational speed, concludes that the two modified hypernetted-chain app…
The 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…
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-…
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 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…
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. …
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 …
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 …
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…
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…
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…
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…
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 …
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…
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…
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…
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…
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…
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…
Quantum Calculation of Classical Kinetic Equations: A Novel Approach for Numerical Analysis of 6D Boltzmann-Maxwell Equations in Collisionless Plasmas Using Quantum Computing
The electron-electron pair distribution functions (PDF) of the 2-D electron fluid (2DEF) in the quantum regime (at T=0) are calculated using a classical-map-hyper-netted-chain (CHNC) scheme and compared with currently available Quantum Monte-Carlo (QMC) simulations in the coupling range r_s=1 to 50. We iteratively extract the bridge function of the "equivalent" classical 2-D liquid in the quantum regime. These bridge functions B(r) are relatively insensitive to spin-polarization effects. The structure of the bridge functions changes significantly for r_s>6, suggesting the onset of strongly cor…
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.
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 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 …
The formula for dielectric function of non-degenerate and maxwellian collisional plasmas is transformed to the form, convenient for research. Graphic comparison of longitudinal dielectric functions of quantum and classical non-degenerate collisional plasmas is made.
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.
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.
Brown, Preston, and Singleton (BPS) produced an analytic calculation for energy exchange processes for a weakly to moderately coupled plasma: the electron-ion temperature equilibration rate and the charged particle stopping power. These precise calculations are accurate to leading and next-to-leading order in the plasma coupling parameter, and to all orders for two-body quantum scattering within the plasma. Classical molecular dynamics can provide another approach that can be rigorously implemented. It is therefore useful to compare the predictions from these two methods, particularly since th…
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…
