Using previously developed method of two-dimensional Laplace transform we obtain the characteristic equations k(ω) for electromagnetic waves in low-collision fully ionized plasma of a plane geometry. We apply here a new, different from the one used in our previous paper, iteration procedure of taking into account the Coulomb collisions. The waves are collisionally damping in the same extent as electromagnetic waves. Despite the different from previous paper form of the dispersion (poles) equation, the obtained decrements for fast and slow wave modes coincide with results obtained in our earlier paper, if one neglects the terms of higher orders in v^2/c^2, (v and c are electron and light velocities). We point out how one can determine mutually dependent boundary conditions allowing to eliminate simultaneously both the backward and kinematical waves for transversal as well as for longitudinal oscillations.
A theory for the ion acoustic wave damping in dense plasmas and warm dense matter, accounting for the Umklapp process, is presented. A higher decay rate compared to the prediction from the Landau damping theory is predicted for high-Z dense plasmas where the electron density ranges from $10^{21}$ to $ 10^{24} \mathrm{cm^{-3}}$ and the electron temperature is moderately higher than the Fermi energy.
Models of covariant linear electromagnetic constitutive relations are formulated that have wide applicability to the computation of susceptibility tensors for dispersive and inhomogeneous media. A perturbative framework is used to derive a linear constitutive relation for a globally neutral plasma enabling one to describe in this context a generalized Landau damping mechanism for non-stationary inhomogeneous plasma states.
Wave-Energy Partition Governs Weak Collisional Damping in Cold Plasmas
School of Nuclear Science and Technology, University of Science and Technology of China（中国科学技术大学核科学技术学院）；Theoretical Division, Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室理论部）
We consider contribution of the radiation damping in the quantum hydrodynamic equations for spinless particles. We discuss possibility of obtaining of corresponding non-linear Schrodinger equation (NLSE) for the macroscopic wave function. We compare contribution of the radiation damping with weakly (or semi-) relativistic effects appearing in the second order by v/c. The radiation damping appears in the third order by v/c. So it might be smaller than weakly relativistic effects, but it gives damping of the Langmuir waves which can be considerable.
Three-dimensional numerical simulations of decaying turbulence in a magnetized plasma are performed using a so-called FLR-Landau fluid model which incorporates linear Landau damping and finite Larmor radius (FLR) corrections. It is shown that compared to simulations of compressible Hall-MHD, linear Landau damping is responsible for significant damping of magnetosonic waves, which is consistent with the linear kinetic theory. Compressibility of the fluid and parallel energy cascade along the ambient magnetic field are also significantly inhibited when the beta parameter is not too small. In con…
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…
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…
Previously developed method for finding asymptotic solutions of Vlasov equations using two-dimensional (in coordinate x and time t) Laplace transform is here applied to consider transversal oscillations and waves in low-collision quasi-neutral (n_i \simeq n_e) Maxwellian electron-ion plasmas. We obtain two branches of electron waves: the ubiquitous one of high-frequency and high-velocity oscillations and the unusual low-velocity one. Taking into account Coulomb collisions in the limit m_e << m_i, \bar{v_i} << \bar{v_e}, and T_e m_e << T_i m_i results in expressions for transversal plasma-elect…
Low-frequency mangnetosonic pulses in a two-ion-species plasma are studied theoretically and by simulation with a one-dimensional electromagnetic simulation code based on a three-fluid model, with particular attention to the dynamics of minority heavy ions. It is found that heavy ions can gain some energy from the pulses. Because of this energy transfer, the pulses are damped even if the plasma is collisionless and pulse propagation is perpendicular to the magnetic field.
This paper addresses the linear and nonlinear three-dimensional propagation of an electron wave in a collisionless plasma that may be inhomogeneous, nonstationary, anisotropic and even weakly magnetized. The wave amplitude, together with any hydrodynamic quantity characterizing the plasma (density, temperature,...) are supposed to vary very little within one wavelength or one wave period. Hence, the geometrical optics limit is assumed, and the wave propagation is described by a first order differential equation. This equation explicitly accounts for three-dimensional effects, plasma inhomogene…
Asymptotic state of nonlinear Landau damping in one-dimensional plasma
Huazhong University of Science and Technology（华中科技大学）；State Key Laboratory of Advanced Electromagnetic Technology, International Joint Research Laboratory of Magnetic Confinement Fusion and Plasma Physics, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology（华中科技大学电气与电子工程学院，先进电磁技术国家重点实验室，磁约束聚变与等离子体物理国际联合研究中心）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；University of Alaska Fairbanks（阿拉斯加大学费尔班克斯分校）
The kinetic damping mechanism of low frequency transverse perturbations propagating parallel to the magnetic field in a magnetized warm electron plasma is simulated by means of electromagnetic (EM) Vlasov simulations. The short-time-scale damping of the electron magnetohydrodynamic whistler perturbations and underlying physics of finite electron temperature effect on its real frequency are recovered rather deterministically, and analyzed. The damping arises from an interplay between a global (prevailing over entire phase-space) and the more familiar resonant-electron-specific kinetic damping m…
For plasma velocity space instabilities driven by particle distributions significantly deviated from a Maxwellian, weak collisions can damp the instabilities by an amount that is significantly beyond the collisional rate itself. This is attributed to the dual role of collisions that tend to relax the plasma distribution toward a Maxwellian and to suppress the linearly perturbed distribution function. The former effect can dominate in cases where the unstable non-Maxwellian distribution is driven by collisionless transport on a time scale much shorter than that of collisions, and the growth rat…
The nonlinear theory of dust-acoustic waves (DAWs) with Landau damping is studied in an unmagnetized dusty negative-ion plasma in the extreme conditions when the free electrons are absent. The cold massive charged dusts are described by fluid equations, whereas the two-species of ions (positive and negative) are described by the kinetic Vlasov equations. A Korteweg de-Vries (KdV) equation with Landau damping, governing the dynamics of weakly nonlinear and weakly dispersive DAWs, is derived following Ott and Sudan [Phys. Fluids {\bf 12}, 2388 (1969)]. It is shown that for some typical laborator…
Experimental studies of electron-ion collision rates in an ultracold neutral plasma (UNP) can be conducted through measuring the rate of electron plasma oscillation damping. For sufficiently cold and dense conditions where strong coupling influences are important, the measured damping rate was faster by 37\% than theoretical expectations [W. Chen, C. Witte, and J. Roberts, Phys. Rev. E \textbf{96}, 013203 (2017)]. We have conducted a series of numerical simulations to isolate the primary source of this difference. By analyzing the distribution of electron velocity changes due to collisions in …
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…
Bandyopadhyay and Das [Phys. Plasmas, 9, 465-473, 2002] have derived a nonlinear macroscopic evolution equation for ion acoustic wave in a magnetized plasma consisting of warm adiabatic ions and non-thermal electrons including the effect of Landau damping. In that paper they have also derived the corresponding nonlinear evolution equation when coefficient of the nonlinear term of the above mentioned macroscopic evolution equation vanishes, the nonlinear behaviour of the ion acoustic wave is described by a modified macroscopic evolution equation. But they have not considered the case when the c…
Previously developed method for finding asymptotic solutions of Vlasov equations using two-dimensional (in coordinate x and time t) Laplace transform is applied to low-collision electron-ion plasmas. Taking into account Coulomb collisions in the limit m_e << m_i, \bar{v_i} << \bar{v_e}, and T_e m_e << T_i m_i, results in the expression for longitudinal high-frequency plasma-electron oscillation/wave decrement essentially depending on oscillation frequency ω. This expression is quite different from the used one for low-frequency plasma sound, which can be derived using expansion in asymptotical…
Collisional effects can play an essential role in the dynamics of plasma waves by setting a minimum damping rate and by interfering with wave-particle resonances. Kinetic simulations of the effects of electron-ion pitch angle scattering on Electron Plasma Waves (EPWs) are presented here. In particular, the effects of such collisions on the frequency and damping of small-amplitude EPWs for a range of collision rates and wave phase velocities are computed and compared with theory. Both the Vlasov simulations and linear kinetic theory find the direct contribution of electron-ion collisions to wav…
The distinction between the plasma dynamics dominated by collisional transport versus collective processes has never been rigorously addressed until recently. A recent paper [Yoon et al., Phys. Rev. E 93, 033203 (2016)] formulates for the first time, a unified kinetic theory in which collective processes and collisional dynamics are systematically incorporated from first principles. One of the outcomes of such a formalism is the rigorous derivation of collisional damping rates for Langmuir and ion-acoustic waves, which can be contrasted to the heuristic customary approach. However, the results…
The before described general principles and methodology of calculating electron wave propagation in homogeneous isotropic half-infinity slab of Maxwellian plasma with indefinite but in principal value sense taken integrals in characteristic equations, and the use of 2D Laplace transform method are applied to an evaluation of collision damping decrements of plane electron longitudinal and transverse waves. Damping decrement tends to infinity when the wave frequency tends to electron Langmuir frequency from above values. We considered recurrent relations for amplitudes of the overtones which for…
The Landau damping of geodesic acoustic mode (GAM) in a torodial rotating tokamak plasma is analytically investigated by taking into account the finite-orbit-width (FOW) resonance effect to the 3rd order. The analytical result is shown to agree well with the numerical solution. The dependence of the damping rate on the toroidal Mach number $M$ relies on $k_r ρ_i$. For sufficiently small $k_r ρ_i$, the damping rate monotonically decreases with $M$. For relatively large $k_r ρ_i$, the damping rate increases with $M$ until approaching the maximum and then decreases with $M$.
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…
This paper addresses the linear propagation of an electron wave in a collisionless, inhomogeneous, nonstationary and anisotropic plasma. The plasma is characterized by its distribution function, $f_H$, at zero order in the wave amplitude. This distribution function, from which are derived all the hydrodynamical quantities, may be chosen arbitrarily, provided that it solves Vlasov equation. Then, from the linearized version of the electrons equation of motion, and from Gauss law, is derived an envelope equation for the wave amplitude, assumed to evolve over time and space scales much larger tha…
The presence of multiple ion species can add additional branches to the IAW dispersion relation and change the Landau damping significantly. Different IAW modes excited by stimulated Brillouin scattering (SBS) and different SBS behaviors in several typical ignition hohlraum plasmas in the high-temperature and high-density region have been researched by Vlasov-Maxwell simulation. The slow mode in HeH or CH plasmas is the least damped mode and will be excited in SBS, while the fast mode in AuB plasmas is the least damped mode and will be excited in SBS. Due to strong Landau damping, the SBS in H…
Our last three papers provide an occasion to make some brief notes on ideology of waves in plasmas and to rehabilitate Vlasov prescription to calculate relevant logarithmically divergent integrals in the principal value sense. In this approach asymptotical solutions of plasma oscillations are selected according to self-consistent boundary physical conditions. Landau damping is absent in this case by definition. Boundary electrical field together with conditions of absence of unphysical backward and kinematical waves define single-valued dependence of boundary distribution function on electron …
We perform fully kinetic simulations of flows known to produce dynamo in magnetohydrodynamics (MHD), considering scenarios with low Reynolds number and high magnetic Prandtl number, relevant for galaxy cluster scale fluctuation dynamos. We find that Landau damping on the electrons leads to a rapid decay of magnetic perturbations, impeding the dynamo. This collisionless damping process operates on spatial scales where electrons are nonmagnetized, reducing the range of scales where the magnetic field grows in high magnetic Prandtl number fluctuation dynamos. When electrons are not magnetized dow…
The effect of spin of particles in the propagation of plasma waves is studied using a semi-classical kinetic theory for a magnetized plasma. We focus in the simple damping effects for the electrostatic wave modes besides Landau damping. Without taking into account more quantum effects than spin contribution to Vlasov's equation, we show that spin produces a new damping or instability which is proportional to the zeroth order magnetization of the system. This correction depends on the electromagnetic part of the wave which is coupled with the spin vector.
A general solution to linearized Vlasov equation for an electron electrostatic wave in a homogeneous unmagnetized plasma is derived. The quasi-linear diffusion coefficient resulting from this solution is a continuous function of omega in contrast to that derived from the traditional Vlasov treatment. The general solution is also equivalent to the Landau treatment of the plasma normal oscillations, and hence leads to the well-known Landau damping.
We demonstrate analytically that, in toroidal plasmas, scattering by drift wave turbulence could lead to appreciable damping of toroidal Alfven eigenmodes via generation of short-wavelength electron Landau damped kinetic Alfven waves. A corresponding analytic expression of the damping rate is derived, and found to be, typically, comparable to the linear drive by energetic particles. The implications of this novel mechanism on the transport and heating processes in burning plasmas are also discussed.
In this paper, we provide a theoretical description, and calculate, the nonlinear frequency shift, group velocity and collionless damping rate, $ν$, of a driven electron plasma wave (EPW). All these quantities, whose physical content will be discussed, are identified as terms of an envelope equation allowing one to predict how efficiently an EPW may be externally driven. This envelope equation is derived directly from Gauss law and from the investigation of the nonlinear electron motion, provided that the time and space rates of variation of the EPW amplitude, $E_p$, are small compared to the …
Transverse and longitudinal dielectric permittivity elements are derived for radio frequency waves in a laboratory dipole magnetic field plasma (LDMFP) accounting for the finite ring current radius. The main feature of LDMFP is the fact that, in contrast to planetary magnetospheric plasmas, the untrapped (circulating) particles can exist/circulate (together with the trapped particles) along the equilibrium magnetic field lines. To estimate the wave power absorbed in LDMFP the perturbed electric field and current density components are decomposed in a Fourier series over the poloidal angle. The…
The impedance probe is a measurement device to measure plasma parameter like electron density. It consists of one electrode connected to a network analyzer via a coaxial cable and is immersed into a plasma. A bias potential superposed with an alternating potential is applied to the electrode and the response of the plasma is measured. Its dynamical interaction with the plasma in electrostatic, kinetic description can be modeled in an abstract notation based on functional analytic methods. These methods provide the opportunity to derive a general solution, which is given as the response functio…
This article addresses the importance of accurate characterization of plasma parameters for electromagnetic compatibility (EMC) purposes. Most of EMC issues involving plasma materials are obviously multi-physics problems (linking chemical, mechanical, thermal and electromagnetic wondering) with deep interactions. One of the main objectives of this paper is to establish the theoretical effect of thermal non-equilibrium on electromagnetic wave propagation. This will be characterized throughout plasma key parameters (including complex permittivity). Numerical simulations based upon Finite Integra…
In this paper, we consider the spectral dependences of transverse electromagnetic waves generated in solar plasma at coalescence of Langmuir waves. It is shown that different spectra of Langmuir waves lead to characteristic types of transversal electromagnetic wave spectra, what makes it possible to diagnose the features of the spectra of Langmuir waves generated in solar plasma.
The effects of linear Landau damping on the nonlinear propagation of dust-acoustic solitary waves (DASWs) are studied in a collisionless unmagnetized dusty plasma with two species of positive ions. The extremely massive, micron-seized, cold and negatively charged dust particles are described by fluid equations, whereas the two species of positive ions, namely the cold (heavy) and hot (light) ions are described by the kinetic Vlasov equations. Following Ott and Sudan [Phys. Fluids {\bf 12}, 2388 (1969)], and by considering lower and higher-order perturbations, the evolution of DASWs with Landau…
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…
The multipole resonance probe is one of the recently developed measurement devices to measure plasma parameter like electron density and temperature based on the concept of active plasma resonance spectroscopy. The dynamical interaction between the probe and the plasma in electrostatic, kinetic description can be modeled in an abstract notation based on functional analytic methods. These methods provide the opportunity to derive a general solution, which is given as the response function of the probe-plasma system. It is defined by the matrix elements of the resolvent of an appropriate dynamic…
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…
The existence of standing high frequency electromagnetic (EM) solitons in a fully degenerate overdense electron plasma is studied applying relativistic hydrodynamics and Maxwell equations. The stable soliton solutions are found in both relativistic and nonrelativistic degenerate plasmas.
The dynamics of electron-plasma waves are described at arbitrary collisionality by considering the full Coulomb collision operator. The description is based on a Hermite-Laguerre decomposition of the velocity dependence of the electron distribution function. The damping rate, frequency, and eigenmode spectrum of electron-plasma waves are found as functions of the collision frequency and wavelength. A comparison is made between the collisionless Landau damping limit, the Lenard-Bernstein and Dougherty collision operators, and the electron-ion collision operator, finding large deviations in the …
The structure of the density singularity formed in a relativistically large amplitude plasma wave close to the wavebreaking limit leads to a refraction coefficient which has a coordinate dependence with discontinuous derivatives. This results in a non-exponentially small above-barrier reflection of an electromagnetic wave interacting with the nonlinear plasma wave.
A new nonlinear electromagnetic wave mode in a plasma is reported. Its existence depends on the interaction of an intense circularly polarized electromagnetic wave with a plasma, where quantum electrodynamical photon--photon scattering is taken into account. As an illustration, we consider a pair plasma and show that the new mode can be significant in astrophysical settings and in the next generation laser-plasma systems.
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 dispersion relation of an electromagnetic wave in an unmagnetized neutral plasma is well known to be w^2=wp^2+(ck)^2. A modified dispersion relation is presented taking into account the ion restoring force in the transverse direction.
The spectrum of electromagnetic waves propagating in a strongly coupled magnetized fully ionized hydrogen plasma is found. The ion motion and damping being neglected, the influence of the Coulomb coupling on the electromagnetic spectrum is analyzed.
Electromagnetic (EM) waves/disturbances are typically the best means to understand and analyze an ionized medium like plasma. However, the propagation of electromagnetic waves with frequency lower than the plasma frequency is prohibited by the freely moving charges of the plasma. In dense plasmas though the plasma frequency can be typically quite high, EM sources at such higher frequency are not easily available. It is, therefore, of interest to seek possibilities wherein a low frequency (lower than the plasma frequency) EM disturbance propagates inside a plasma. This is possible in the contex…
Ultracold plasmas (UCP) provide a well-controlled system for studying multiple aspects in plasma physics that include collisions and strong coupling effects. By applying a short electric field pulse to a UCP, a plasma electron center-of-mass (CM) oscillation can be initiated. In accessible parameter ranges, the damping rate of this oscillation is determined by the electron-ion collision rate. We performed measurements of the oscillation damping rate with such parameters and compared the measured rates to both a molecular dynamic (MD) simulation that includes strong coupling effects and to Mont…
Radiative damping in plasma-based electron accelerators is analyzed. The electron dynamics under combined influence of the constant accelerating force and the classical radiation reaction force is studied. It is shown that electron acceleration cannot be limited by radiation reaction. If initially the accelerating force was stronger than the radiation reaction force then the electron acceleration is unlimited. Otherwise the electron is decelerated by radiative damping up to a certain instant of time and then accelerated without limits. Regardless of the initial conditions the infinite-time asy…
We study the damping from neutral-ion collisions of both incompressible and compressible magnetohydrodynamic (MHD) turbulence in partially ionized medium. We start from the linear analysis of MHD waves applying both single-fluid and two-fluid treatments. The damping rates derived from the linear analysis are then used in determining the damping scales of MHD turbulence. The physical connection between the damping scale of MHD turbulence and cutoff boundary of linear MHD waves is investigated. Our analytical results are shown to be applicable in a variety of partially ionized interstellar mediu…
The existence of soliton-like electromagnetic (EM) distributions in a fully degenerate electron-positron plasma is studied applying relativistic hydrodynamic and Maxwell equations. For circularly polarized wave it is found that the soliton solutions exist both in relativistic as well as nonrelativistic degenerate plasmas. Plasma density in the region of soliton pulse localization is reduced considerably. The possibility of plasma cavitation is also shown.
Plasma waves with frequencies close to the particular gyrofrequencies of the charged particles in the plasma lose energy due to cyclotron damping. We briefly discuss the gyro-resonance of low frequency plasma waves and ions particularly with regard to particle-in-cell (PiC) simulations. A setup is outlined which uses artificially excited waves in the damped regime of the wave mode's dispersion relation to track the damping of the wave's electromagnetic fields. Extracting the damping rate directly from the field data in real or Fourier space is an intricate and non-trivial task. We therefore pr…
The dielectric properties of complex plasma containing either metal or dielectric spherical inclusions (macroparticles, dust) are investigated. We focus on surface plasmon resonances on the macroparticle surfaces and their effect on electromagnetic wave propagation. It is demonstrated that the presence of surface plasmon oscillations significantly modifies plasma electromagnetic properties by resonances and cutoffs in the effective permittivity. This leads to related branches of electromagnetic waves and to the wave band gaps. The results are discussed in the context of dusty plasma experiment…
This comment clarifies the relation of the research in a recently published article [Phys. Plasmas 14, 042503 (2007)] to other prior publications addressing the inclusion of electromagnetic and drift-kinetic electron physics in gyrokinetic simulation, raises a concern related to the inclusion of kinetic electrons in a system with magnetic shear, and discusses alternatives in the face of an important limitation on the general applicability of the algorithm described therein.
