Potential (electrostatic) surface waves in plasma half-space with degenerate electrons are studied using the quasi-classical mean-field kinetic model. The wave spectrum and the collisionless damping rate are obtained numerically for a wide range of wavelengths. In the limit of long wavelengths, the wave frequency $ω$ approaches the cold-plasma limit $ω=ω_p/\sqrt{2}$ with $ω_p$ being the plasma frequency, while at short wavelengths, the wave spectrum asymptotically approaches the spectrum of zero-sound mode propagating along the boundary. It is shown that the surface waves in this system remain weakly damped at all wavelengths (in contrast to strongly damped surface waves in Maxwellian electron plasmas), and the damping rate nonmonotonically depends on the wavelength, with the maximum (yet small) damping occuring for surface waves with wavelength of $\approx5πλ_{F}$, where $λ_{F}$ is the Thomas-Fermi length.
We carry out a systematic study of the dispersion relation for linear electrostatic waves in an arbitrarily degenerate quantum electron plasma. We solve for the complex frequency spectrum for arbitrary values of wavenumber $k$ and level of degeneracy $μ$. Our finding is that for large $k$ and high $μ$ the real part of the frequency $ω_{r}$ grows linearly with $k$ and scales with $μ$ only because of the scaling of the Fermi energy. In this regime the relative Landau damping rate $γ/ω_{r}$ becomes independent of $k$ and varies inversly with $μ$. Thus, damping is weak but finite at moderate level…
A two-dimensional generalized hydrodynamics (GH) model is developed to study the full spectrum of both longitudinal and transverse dust acoustic waves (DAW) in strongly coupled complex (dusty) plasmas, with memory-function-formalism being implemented to enforce high-frequency sum rules. Results are compared with earlier theories (such as quasi-localized charge approximation and its extended version) and with a self-consistent Brownian dynamics simulation. It is found that the GH approach provides good account, not only for dispersion relations, but also for damping rates of the DAW modes in a …
Warm dense matter (WDM) is an exotic state on the border between condensed matter and dense plasmas. Important occurrences of WDM include dense astrophysical objects, matter in the core of our Earth, as well as matter produced in strong compression experiments. As of late, x-ray Thomson scattering has become an advanced tool to diagnose WDM. The interpretation of the data requires model input for the dynamic structure factor $S(q,ω)$ and the plasmon dispersion $ω(q)$. Recently the first \textit{ab initio} results for $S(q,ω)$ of the homogeneous warm dense electron gas were obtained from path i…
A unified, fast, and effective approach is developed for numerical calculation of the well-known plasma dispersion function with extensions from Maxwellian distribution to almost arbitrary distribution functions, such as the $δ$, flat top, triangular, $κ$ or Lorentzian, slowing down, and incomplete Maxwellian distributions. The singularity and analytic continuation problems are also solved generally. Given that the usual conclusion $γ\propto\partial f_0/\partial v$ is only a rough approximation when discussing the distribution function effects on Landau damping, this approach provides a useful…
Classical Molecular Dynamics (MD) simulations for a one-component plasma (OCP) are presented. Quantum effects are included in the form of the Kelbg potential. Results for the dynamical structure factor are compared with the Vlasov and RPA (random phase approximation) theories. The influence of the coupling parameter $Γ$, degeneracy parameter $ρΛ^3$ and the form of the pair interaction on the optical plasmon dispersion is investigated. An improved analytical approximation for the dispersion of Langmuir waves is presented.
The past studies treated the perturbed distribution of circulating electrons as adiabatic one when studying the dispersion relation of electrostatic geodesic acoustic mode(GAM). In this paper, the flow of electron geodesic current (FEGC) is added to modify this adiabatic distribution. Based on the drift kinetic theory, it is found that FEGC obviously increases the magnitude of the standard GAM's frequency and reduces its damping rate. The increase of frequency results from the contribution of FEGC to the radial flow. The reason for the reduction of damping rate is that when the effect of FEGC …
Relativistic effects on dispersion in a degenerate electron gas are discussed by comparing known response functions derived relativistically (by Jancovici) and nonrelativistically (by Lindhard). The main distinguishing feature is one-photon pair creation, which leads to logarithmic singularities in the response functions. Dispersion curves for longitudinal waves have a similar tongue-like appearance in the relativistic and nonrelativistic case, with the main relativistic effects being on the Fermi speed and the cutoff frequency. For transverse waves the nonrelativistic treatment has a nonphysi…
Effects of non-thermal high-energy electrons on Langmuir wave-particle interaction are investigated by an initial value approach. A Vlasov-Poisson simulation is employed which is based on the splitting scheme by Cheng and Knorr [Cheng, C.Z. and G. Knorr, 1976: J. Comput. Phys. 22, 330-351.]. The kappa distribution function is taken as an example of non-thermal electrons. The modification is manifested as an increase in the Landau damping rate and a decrease in the real frequency for a long wavelength limit. A part of the analyses by the modified plasma dispersion function [Summers, D. and R.M.…
We present a study of the standard plasma physics test, Landau damping, using the Particle-In-Cell (PIC) algorithm. The Landau damping phenomenon consists of the damping of small oscillations in plasmas without collisions. In the PIC method, a hybrid discretization is constructed with a grid of finitely supported basis functions to represent the electric, magnetic and/or gravitational fields, and a distribution of delta functions to represent the particle field. Approximations to the dispersion relation are found to be inadequate in accurately calculating values for the electric field frequenc…
Excitation of nonlinear ion acoustic wave (IAW) by an external electric field is demonstrated by Vlasov simulation. The frequency calculated by the dispersion relation with no damping is verified much closer to the resonance frequency of the small-amplitude nonlinear IAW than that calculated by the linear dispersion relation. When the wave number $ kλ_{De} $ increases, the linear Landau damping of the fast mode (its phase velocity is greater than any ion's thermal velocity) increases obviously in the region of $ T_i/T_e < 0.2 $ in which the fast mode is weakly damped mode. As a result, the dev…
Surface plasmon polaritons (SPPs) in a semi-bounded degenerate plasma (e.g., a metal) are studied using the quasiclassical mean-field kinetic model, taking into account the spatial dispersion of the plasma (due to quantum degeneracy of electrons) and electron-ion (electron-lattice, for metals) collisions. SPP dispersion and damping are obtained in both retarded ($ω/k_z\sim c$) and non-retarded ($ω/k_z\ll c$) regions, as well as in between. It is shown that the plasma spatial dispersion significantly affects the properties of SPPs, especially at short wavelengths (less than the collisionless sk…
The nonlinear theory of Landau damping of electrostatic wave envelopes (WEs) is revisited in a quantum electron-positron (EP) pair plasma. Starting from a Wigner-Moyal equation coupled to the Poisson equation and applying the multiple scale technique, we derive a nonlinear Schr{ö}dinger (NLS) equation which governs the evolution of electrostatic WEs. It is shown that the coefficients of the NLS equation, including the nonlocal nonlinear term, which appears due to the resonant particles having group velocity of the WEs, are significantly modified by the particle dispersion. The effects of the q…
We study the nonlinear wave modulation of Langmuir waves (LWs) in a fully degenerate plasma. Using the Wigner-Moyal equation coupled to the Poisson equation and the multiple scale expansion technique, a modified nonlocal nonlinear Schr{ö}dinger (NLS) equation is derived which governs the evolution of LW envelopes in degenerate plasmas. The nonlocal nonlinearity in the NLS equation appears due to the group velocity and multi-plasmon resonances, i.e., resonances induced by the simultaneous particle absorption of multiple wave quanta. We focus on the regime where the resonant velocity of electron…
Examination of equilibrium radiation in plasma media shows that the spectral energy distribution of such radiation is different from the Planck equilibrium radiation. Using the approach of quantum electrodynamics the general relation for the spectral energy density of equilibrium radiation in a system of charged particles is found. The obtained result takes into account the influence of plasma on equilibrium radiation through the explicit transverse dielectric permittivity which takes into account spatial and frequency dispersion, as well as the finite collisional damping. For the limiting cas…
The theory of plasma waves and Landau damping in Maxwellian plasmas, Landau's ``rule of pass around poles'' include doubtful statements, particularly related to an artificial ``constructing'' of the dispersion equation, what should allow the possibility of its solution otherwise not existing at all, and the possibility of analytical continuations of corresponding very specific ruptured functions in the one-dimensional Laplace transformation, used by Landau, what is the base of his theory. We represent, as an accessible variant, a more general alternative theory based on a two-dimensional Lapla…
Applying the separated spin evolution quantum hydrodynamics to two-dimensional electron gas in plane samples and nanotubes located in external magnetic fields we find new kind of wave in electron gas, which is called the spin-electron acoustic wave. Separate spin-up electrons and spin-down electrons evolution reveals in replacement of the Langmuir wave by the couple of hybrid waves. One of two hybrid waves is the modified Langmuir wave. Another hybrid wave is the spin-electron acoustic wave. We study dispersion of these waves in two dimensional structures of electrons. We also consider depende…
The existence of new electro-acoustic (EA) waves [named here `degenerate pressure driven EA' (DPDEA) waves] propagating in a degenerate quantum plasma (DQP) system [containing non-inertial, cold, non-relativistically (NR)/ultra-relativistically (UR) degenerate electron species (DES), and inertial, cold, NR degenerate positive particle species (PPS)] is predicted for the first time. The DPDEA waves, in which the inertia is mainly provided by the mass density of the inertial PPS, and the restoring force is mainly provided by the non-inertial, NR/UR DES, are new since they are completely disappea…
Oblique propagation of the spin-electron acoustic waves in degenerate magnetized plasmas is considered in terms of quantum kinetics with the separate spin evolution, where the spin-up electrons and the spin-down electrons are considered as two different species with different equilibrium distributions. It is considered in the electrostatic limit. Corresponding dispersion equation is derived. Analytical analysis of the dispersion equation is performed in the long-wavelength limit to find an approximate dispersion equation describing the spin-electron acoustic wave. The approximate dispersion eq…
Within the framework of the hypothesis offered by authors about complex-valued nature of physical quantities, the effect of the Landau damping has been explored with assumption that not only frequency can be a small imaginary component but also a wave vector. The numerical solution of the obtained dispersion equation testifies that uncollisional damping is accompanied in a certain region of space by antidumping of waves, and in particular situations antidumping may prevail over damping. It is possible that this effect may explain the experimental difficulties connected with inhibition of insta…
The decays of the Langmuir waves in dense plasmas are computed using the dielectric function theory widely used in the solid state physics. Four cases are considered: a classical plasma, a Maxwellian plasma, a degenerate quantum plasma, and a partially degenerate plasma. The result is considerably different from the conventional Landau damping theory.
We have studied the linear dispersion relation for Langmuir waves in plasmas of very high density, based on the Dirac-Heisenberg-Wigner formalism. The vacuum contribution to the physical observables leads to ultra-violet divergences, that are removed by a charge renormalization. The remaining vacuum contribution is small, and is in agreement with previously derived expressions for the time-dependent vacuum polarization. The main new feature of the theory is a damping mechanism similar to Landau damping, but where the plasmon energy give rise to creation of electron-positron pairs. The dependen…
To calculate linear oscillations and waves in dynamics of gas and plasma one uses as a rule the old classical method of dispersion equation for complex frequencies $ω$ and wave numbers $k$: $ε(ω,k)=0$. This method appears to be inapplicable, f.e., in the case of waves in Maxwellian collisionless plasma when dispersion equation has no solutions. By means of some refined sophistication L.~Landau in 1946 has suggested in this case actually to replace the dispersion equation with another one, having a specific solution (``Landau damping'') and being now widely used in plasma physics. Recently we h…
We study the nonlinear propagation of ion-acoustic waves (IAWs) in an unmagnetized collisionless plasma with the effects of electron and ion Landau damping in the weak quantum (semiclassical) regime, i.e., when the typical ion-acoustic (IA) length scale is larger than the thermal de Broglie wavelength. Starting from a set of classical and semiclassical Vlasov equations for ions and electrons, coupled to the Poisson equation, we derive a modified (by the particle dispersion) Korteweg-de Vries (KdV) equation which governs the evolution of IAWs with the effects of wave-particle resonance. It is f…
The results of a theoretical investigation on the stopping power of ions moving in a disordered two-dimensional degenerate electron gas are presented. The stopping power for an ion is calculated employing linear response theory using the dielectric function approach. The disorder, which leads to a damping of plasmons and quasiparticles in the electron gas, is taken into account through a relaxation time approximation in the linear response function. The stopping power for an ion is calculated in both the low- and high-velocity limits. In order to highlight the effects of damping we present a c…
Chromospheric and prominence plasmas contain neutral atoms, which may change the plasma dynamics through collision with ions. Most of the atoms are neutral hydrogen, but a significant amount of neutral helium may also be present in the plasma with a particular temperature. Damping of MHD waves due to ion collision with neutral hydrogen is well studied, but the effects of neutral helium are largely unknown. We aim to study the effect of neutral helium in the damping of Alfven waves in solar partially ionized plasmas. We consider three-fluid magnetohydrodynamic (MHD) approximation, where one com…
The paper, authored by J. A. S. Lima et al, was published in Phys. Rev. E in 2000 has discussed the dispersion relation and Landau damping of Langmuir wave in the context of the nonextensive statistics proposed by Tsallis. It has been cited by many authors because the dispersion relation in Tsallis formalism present a good fit to the experimental data when q<1, while the classical result based on Maxwellian distribution only provides a crude description. However, the results obtained in this paper are problematic. In this comments on the paper we shall derive the correct analytic formulas both…
In this paper we have criticized the so-called Landau damping theory. We have analyzed solutions of the standard dispersion equations for longitudinal (electric) and transversal (electromagnetic and electron) waves in half-infinite slab of the uniform collisionless plasmas with non-Maxwellian and Maxwellian-like electron energy distribution functions. One considered the most typical cases of both the delta-function type distribution function (the plasma stream with monochromatic electrons) and distribution functions, different from Maxwellian ones as with a surplus as well as with a shortage i…
After approximate replacing of Maxwellian distribution exponent with the rational polynomial fraction we have obtained precise analytical expression for and calculated the principal value of logarithmically divergent integral in the electron wave dispersion equation. At the same time our calculations have shown the presence of strong collisionless damping of the electromagnetic low-velocity (electron) wave in plasmas with Maxwellian-like electron velocity distribution function at some small, of the order of several per cents, differences from Maxwellian distribution in the main region of large…
We present a derivation of the dispersion relation for electrostatic oscillations (ESOs) in a zero temperature quantum plasma. In the latter, degenerate electrons are governed by the Wigner equation, while non-degenerate ions follow the classical fluid equations. The Poisson equation determines the electrostatic wave potential. We consider parameters ranging from semiconductor plasmas to metallic plasmas and electron densities of compressed matter such as in laser-compression schemes and dense astrophysical objects. Due to the wave diffraction caused by overlapping electron wave function due t…
We consider the relativistic ion-acoustic mode in a plasma composed by cold ions and an ultra-degenerate electron gas, described the relativistic Vlasov-Poisson system. A critical examination of popular fluid models for relativistic ion-acoustic waves is provided, comparing kinetic and hydrodynamic results. The kinetic linear dispersion relation is shown to be reproduced by the rigorous relativistic hydrodynamic equations with Chandrasekhar's equation of state.
Stability of cylindrical interface between two ideal incompressible fluids, including the magnetic field, surface tension and gravitational field is studied in linear approximation. We found that helical waves arising both in plasma comet tails and on the vertical cylindrical water jet in the air are described by the same dispersion equation where the comet tail magnetic field plays the same stabilizing role as surface tension for water jet. Hence they represent the same phenomenon of Kelvin-Helmholtz instability. Thus helical waves in comet tails and astrophysical jets may be simulated in the…
Collisionless damping of the gravitational instability in fuzzy dark matter: spectral shape and quantum-to-thermal crossover
Institute for Advanced Academic Research, Chiba University（千叶大学先进学术研究学院）；Center for Computational Sciences, University of Tsukuba（筑波大学计算科学中心）；Department of Physics, The University of Tokyo（东京大学物理学系）
