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 case of an infinitesimal damping the result coincides with the known expression.
Two kinds of the quantum electrodynamic radiative corrections to electromagnetic interaction and their influence on properties of highly dense quantum plasmas are considered. Linear radiative correction to the Coulomb interaction are considered. Its contribution in the spectrum of the Langmuir waves is presented. The second kind of the radiative corrections is related to nonlinearity of the Maxwell equations for strong electromagnetic field. Its contribution in spectrum of transverse waves of magnetized plasmas is briefly discussed. At consideration of the Langmuir wave spectrum we included ef…
The incomplete plasma dispersion function is a generalization of the plasma dispersion function in which the defining integral spans a semi-infinite, rather than infinite, domain. It is useful for describing the linear dielectric response and wave dispersion in non-Maxwellian plasmas when the distribution functions can be approximated as Maxwellian over finite, or semi-infinite, intervals in velocity phase-space. A ubiquitous example is the depleted Maxwellian electron distribution found near boundary sheaths or double layers, where the passing interval can be modeled as Maxwellian with a lowe…
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.
Very simple explicit analytical expressions are discussed, which are able to describe the dispersion relations of longitudinal waves in strongly coupled plasma systems such as one-component plasma and weakly screened Yukawa fluids with a very good accuracy. Applications to other systems with soft pairwise interactions are briefly discussed.
Newton-Raphson method in complex space is used to numerically solve the transcendental dispersion relation of low frequency shear Alfven waves in fusion plasmas. The equation exhibits several physically relevant basins of attraction. The method is shown to be efficient and fast in solving this equation, with very small portion of non-converging points.
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.
High-frequency photons traveling in plasma exhibit a linear polarizability that can influence the dispersion of linear plasma waves. We present a detailed calculation of this effect for Langmuir waves as a characteristic example. Two alternative formulations are given. In the first formulation, we calculate the modified dispersion of Langmuir waves by solving the governing equations for the electron fluid, where the photon contribution enters as a ponderomotive force. In the second formulation, we provide a derivation based on the photon polarizability. Then, the calculation of ponderomotive f…
A nonlinear dispersion of a general stationary wave in collisionless plasma is obtained in a non-differential form from a single-particle oscillation-center Hamiltonian. For electrostatic oscillations in nonmagnetized plasma, considered as a paradigmatic example, the linear dielectric function is generalized, and the trapped particle contribution to the wave frequency shift $Δω$ is found analytically as a function of the wave amplitude $a$. Smooth distributions yield $Δω\sim a^{1/2}$, as usual. However, beam-like distributions of trapped electrons result in different power laws, or even a loga…
Space plasmas are known to be out of (local) thermodynamic equilibrium, as observations show direct or indirect evidences of non-thermal velocity distributions of plasma particles. Prominent are the anisotropies relative to the magnetic field, anisotropic temperatures, field-aligned beams or drifting populations, but also, the suprathermal populations enhancing the high-energy tails of the observed distributions. Drifting bi-Kappa distribution functions can provide a good representation of these features and enable for a kinetic fundamental description of the dispersion and stability of these …
Relativistic quantum plasma dispersion functions are defined and the longitudinal and transverse response functions for an electron (plus positron) gas are written in terms of them. The dispersion is separated into Landau-damping, pair-creation and dissipationless regimes. Explicit forms are given for the RQPDFs in the cases of a completely degenerate distribution and a nondegenerate thermal (Jüttner) distribution. Particular emphasis is placed on the relation between dissipation and dispersion, with the dissipation treated in terms of the imaginary parts of RQPDFs. Comparing the dissipation c…
Extreme-ultraviolet pulses can propagate through ionised solid-density targets, unlike optical pulses and, thus, have the potential to probe the interior of such plasmas on sub-femtosecond timescales. We present a synthetic diagnostic method for solid-density laser-generated plasmas based on the dispersion of an extreme-ultraviolet attosecond probe pulse, in a pump--probe scheme. We demonstrate the theoretical feasibility of this approach through calculating the dispersion of an extreme-ultraviolet probe pulse propagating through a laser-generated plasma. The plasma dynamics is calculated usin…
Binary complex plasmas consist of microparticles of two different species and can form two-dimensional square lattices under certain conditions. The dispersion relations of the square lattice waves are derived for the longitudinal and transverse in-plane modes, assuming that the out-of-plane mode is suppressed by the strong vertical confinement. The results are compared with the spectra obtained in Langevin dynamics simulations. Furthermore, we investigate the dependence of the dispersion relation on the charge ratio and mass ratio of the two particle species.
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…
A hitherto difficult and unsolved issue in plasma physics is how to give a general numerical solver for complicated plasma dispersion relation, although we have long known the general analytical forms. We transform the task to a full-matrix eigenvalue problem, which allows to numerically calculate all the dispersion relation solutions exactly free from convergence problem and give polarizations naturally for arbitrarily complicated multi-scale fluid plasma with arbitrary number of components. Attempt to kinetic plasma via $N$-point Padé approximation of plasma dispersion function also shows go…
A simple approach to describe the long-wavelength dispersion of the longitudinal (plasmon) mode of the classical one-component-plasma (OCP), with the main objective to correctly capture the onset of negative dispersion, is proposed. The approach is applicable to both three-dimensional and two-dimensional OCP. The predicted onset of negative dispersion compares well with the available results from numerical simulations and more sophisticated theoretical models.
Basic, local kinetic theory of ion temperature gradient driven (ITG) mode, with adiabatic electrons is reconsidered. Standard unstable, purely oscillating as well as damped solutions of the local dispersion relation are obtained using a bracketing technique that uses the argument principle. This method requires computing the plasma dielectric function and its derivatives, which are implemented here using modified plasma dispersion functions with curvature and their derivatives, and allows bracketing/following the zeros of the plasma dielectric function which corresponds to different roots of t…
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 dispersion properties of low frequency dust acoustic waves in the strong coupling regime are investigated experimentally in an argon plasma embedded with a mixture of kaolin and $MnO_2$ dust particles. The neutral pressure is varied over a wide range to change the collisional properties of the dusty plasma. In the low collisional regime the turnover of the dispersion curve at higher wave numbers and the resultant region of $\partialω/\partial k < 0$ are identified as signatures of dust-dust correlations. In the high collisional regime dust neutral collisions produce a similar effect and pr…
We derive dispersion relations for a system of identical particles confined in a two-dimensional annular harmonic well and which interact through a Yukawa potential, e.g., a dusty plasma ring. When the particles are in a single chain (i.e., a one-dimensional ring) we find a longitudinal acoustic mode and a transverse optical mode which show approximate agreement with the dispersion relation for a straight configuration for large radii of the ring. When the radius decreases, the dispersion relations modify: there appears an anticrossing of the modes near the crossing point resulting in a freque…
Topological Langmuir-Cyclotron Wave (TLCW) is a recently identified topological surface excitation in magnetized plasmas. We show that TLCW originates from the topological phase transition at the Langmuir wave-cyclotron wave resonance. By isofrequency surface analysis and 2D and 3D time-dependent simulations, we demonstrate that the TLCW can propagate robustly along complex phase transition interfaces in a unidirectional manner and without scattering. Because of these desirable features, the TLCW could be explored as an effective mechanism to drive current and flow in magnetized plasmas. The a…
A dispersion relation for a commonly used hybrid model of plasma physics is developed, which combines fully kinetic ions and a massless-electron fluid description. Although this model and variations of it have been used to describe plasma phenomena for about 40 years, to date there exists no general dispersion relation to describe the linear wave physics contained in the model. Previous efforts along these lines are extended here to retain arbitrary wave propagation angles, temperature anisotropy effects, as well as additional terms in the generalized Ohm's law which determines the electric fi…
Fermi Dirac free electron model is applied to very dense plasmas with medium or low temperatures. While Boltzmann statistics can lead to very high densities of ionized electrons, only at very high temperatures, Fermi Dirac statistics can support the high densities of ionized electrons at medium or low temperatures due to the high degeneracies obtained in this model. Since very dense plasmas may be obtained at low temperatures the corresponding black body radiation with the plasma luminosity will be quite small. On the other hand gravitational effects might be quite large due to the high densit…
Particle dynamics are investigated in plasma turbulence, using self-consistent kinetic simulations, in two dimensions. In steady state, the trajectories of single protons and proton-pairs are studied, at different values of plasma "beta" (ratio between kinetic and magnetic pressure). For single-particle displacements, results are consistent with fluids and magnetic field line dynamics, where particles undergo normal diffusion for very long times, with higher "beta" being more diffusive. In an intermediate time range, with separations lying in the inertial range, particles experience an explosi…
A fully relativistic treatment of Bernstein waves in an electron-positron pair plasma has remained too formidable a task owing to the very complex nature of the problem. In this article, we perform contour integration of the dielectric response function and numerically compute the dispersion curves for a uniform, magnetized, relativistic electron-positron pair plasma. The behavior of the dispersion solution for several cases with different plasma temperatures is highlighted. In particular, we find two wave modes that exist only for large wavelengths and frequencies similar to the cyclotron fre…
A new generalization of curvature modified plasma dispersion functions is introduced in order to express Dupree renormalized dispersion relations used in quasi-linear theory. For instance the Dupree renormalized dispersion relation for gyrokinetic, toroidal ion temperature gradient driven (ITG) modes, where the Dupree's diffusion coefficient is assumed to be a low order polynomial of the velocity, can be written entirely using generalized curvature modified plasma dispersion functions: Knm's. Using those, Dupree's formulation of renormalized quasi-linear theory is revisited for the toroidal IT…
In the present paper we calculate the dielectric functions of an ultra-relativistic plasma, such as an electron-positron or a quark-gluon plasma. We use classical transport theory and take into account collisions within the relaxation time approximation. From these dielectric functions we derive the dispersion relations of longitudinal and transverse plasma waves.
We propose a new and effective method to find plasma oscillatory and wave modes. It implies searching a pair of poles of two-dimensional (in coordinate $x$ and time $t$) Laplace transform of self-consistent plasma electric field $E(x,t) \to E_{p_1p_2}$, where $p_1 \equiv -i ω$, $p_2 \equiv i k$ are Laplace transform parameters, that is determining a pair of zeros of the following equation $$\frac1{E_{p_1p_2}} = 0 .$$ This kind of conditional equation for searching double poles of $E_{p_1p_2}$ we call ``general dispersion equation'', so far as it is used to find the pair values ($ω^{(n)}, k^{(n…
Spectra of phonons with out-of-plane polarization were studied experimentally in a 2D plasma crystal. The dispersion relation was directly measured for the first time using a novel method of particle imaging. The out-of-plane mode was proven to have negative optical dispersion, comparison with theory showed good agreement. The effect of the plasma wakes on the dispersion relation is briefly discussed.
Using the quantum magnetohydrodynamics (QMHD) model, linear dispersion of magnetosonic waves are studied in a quasineutral quantum electron-ion plasma in two distinct regimes of nonrelativistic and relativistic degeneracies considering also the plasma composition effect. It is shown that the paramagnetic spin effects of the degenerated electrons plays a key role in dynamics of magnetosonic waves. The linear wave-speed is found to have minimum value at some degeneracy parameter in such plasmas. This is due to delicate interplay between relativistic degeneracy and the Pauli spin-magnetization. I…
The analytical solution of the boundary problem on behaviour (oscillations) of the electronic plasmas with arbitrary degree of degeneration of electronic gas in a slab of the conducting medium is received. The kinetic Vlasov---Boltzmann equation with integral of collisions type BGK (Bhatnagar, Gross and Krook) and Maxwell equation for electric field are applied. Mirror (reflections) boundary conditions are used.
The propagation of the laser pulses in the underdense plasma is a very crucial aspect of laser-plasma interaction process. In this work, we explored the two regimes of laser propagation in plasma, one with $a_0 < 1$ and other with $a_0 \gtrsim 10$. For $a_0<1$ case, we used a cold relativistic fluid model, wherein apart from immobile ions no further approximations are made. The effect of the laser pulse amplitude, pulse duration, and plasma density is studied using the fluid model and compared with the expected scaling laws and also with the PIC simulations. The agreement between the fluid mod…
A general, fast, and effective approach is developed for numerical calculation of kinetic plasma dispersion relations. The plasma dispersion function is approximated by $J$-pole expansion. Subsequently, the dispersion relation is transformed to a standard matrix eigenvalue problem of an equivalent linear system. The result is accurate for $J=8$ except the solutions that are the little interesting heavily damped modes. In contrast to conventional approaches, such as Newton's iterative method, this approach can give either all the solutions in the system or a few solutions around the initial gue…
A general dispersion-relation solver that numerically evaluates the full propagation properties of all the waves in fluid plasmas is presented. The effects of anisotropic pressure, external magnetic fields and beams, relativistic dynamics, as well as local plasma inhomogeneity are included. [Computer Physics Communications, (2013); doi: 10.1016/j.cpc.2013.10.012; code: http://cpc.cs.qub.ac.uk/summaries/AERF\_v1\_0.html]
Many particle quantum hydrodynamics based on the Darwin Hamiltonian (the Hamiltonian corresponding to the Darwin Lagrangian) is considered. A force field appearing in corresponding Euler equation is considered in details. Contributions from different terms of the Darwin Hamiltonian in the Euler equation are traced. For example, the relativistic correction to the kinetic energy of particles leads to several terms in the Euler equation, these terms have different form. One of them has a form similar to a term appearing from the Darwin term. Hence, the two different mechanisms give analogous cont…
A generalized hydrodynamic (GHD) model depicting the behaviour of visco-elastic fluids has often been invoked to explore the behaviour of a strongly coupled dusty plasma medium below their crystallization limit. The model has been successful in describing the collective normal modes of the strongly coupled dusty plasma medium observed experimentally. The paper focuses on the study of nonlinear dynamical characteristic features of this model. Specifically, the evolution of coherent vorticity patches are being investigated here within the framework of this model. A comparison with Newtonian flui…
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…
Wave dispersion in a pulsar plasma is discussed emphasizing the relevance of different inertial frames, notably the plasma rest frame ${\cal K}$ and the pulsar frame ${\cal K}'$ in which the plasma is streaming with speed $β_{\rm s}$. The effect of a Lorentz transformation on both subluminal, $|z|<1$, and superluminal, $|z|>1$, waves is discussed. It is argued that the preferred choice for a relativistically streaming distribution should be a Lorentz-transformed Jüttner distribution; such a distribution is compared with other choices including a relativistically streaming Gaussian distribution…
The quantum electrodynamical (QED) short wavelength correction on plasma wave propagation for a non-relativistic quantum plasma is investigated. A general dispersion relation for a thermal multi-component quantum plasma is derived. It is found that the classical dispersion relation for any wave mode can be modified to include quantum and short wavelength QED effects by simple substitutions of the thermal velocity and the plasma frequency. Furthermore, the dispersion relation has been modified to include QED effects of strong magnetic fields. It is found that strong magnetic fields together wit…
The optical properties of plasmas with high densities and medium temperatures are analyzed by the use of a free electron model with Fermi-Dirac statistics. For the present collisional plasma the frequency of electron-ion collision is very large relative to the optical and infra-red frequencies. A quantum mechanical equation for the frequency of collisions is developed by the use of Fermi-Dirac statistics and Rutherford scattering theory. The validity of the Rutherford scattering theory is discussed. The influence of many weak collisions is taken into account by a Coulomb logarithmic function. …
A new cold relativistic theory is proposed to describe the Laser WakeField Accelerator (LWFA) in the presence of pulse evolutions, capable of being utilized to study the group velocity and the plasma dispersion. This new capability is mainly due to exploiting the concept of the real Lorentz-boost Pulse Co-Moving (LPCM) frame, in spite of previous studies. The theory is reduced to the well-known Quasi-Static Approximation (QSA) in the absence of the pulse evolutions, and shows excellent agreement with Particle-In-Cell (PIC) simulations in terms of its new results. The obtained results show the …
Wave dispersion in a pulsar plasma (a 1D, strongly magnetized, pair plasma streaming highly relativistically with a large spread in Lorentz factors in its rest frame) is discussed, motivated by interest in beam-driven wave turbulence and the pulsar radio emission mechanism. In the rest frame of the pulsar plasma there are three wave modes in the low-frequency, non-gyrotropic approximation. For parallel propagation these are referred to as the X, A and L modes, with the X and A modes having dispersion relation $z=z_A\approx1-1/2β_A^2$, where $z=ω/k_\parallel c$ is the phase speed and $β_Ac$ is …
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…
The derivation of the helicon dispersion relation for a uniform plasma with stationary ions subject to a constant background magnetic field is reexamined in terms of the potential formulation of electrodynamics. Under the same conditions considered by the standard derivation, the nonlinear self-coupling between the perturbed electron flow and the potential it generates is addressed. The plane wave solution for general propagation vector is determined for all frequencies and expressed in terms of a vector phasor. The behavior of the solution as described in vacuum units depends upon the ratio o…
Compressional waves propagating in the partially ionised solar lower atmospheric plasmas can easily steepen into nonlinear waves, including shocks. Here we investigate the effect of weak dispersion generated by Hall currents perpendicular to the ambient magnetic field on the characteristics of shock waves. Our study will also focus on the interplay between weak dispersion and partial ionisation of the plasma. Using a multiple scale technique we derive the governing equation in the form of a Korteweg-de Vries-Burgers equation. The effect of weak dispersion on shock waves is obtained using a per…
The problem of calculation of electromagnetic field energy outside the transparency domain is discussed. It is shown that charged particle contribution to the energy of electromagnetic perturbations in the general case can be described in terms of bilinear combination of the dielectric polarizability of the medium. The explicit form of such contribution is found. The relations obtained are used to generalize the Planck's law to the case of absorptive medium.
The effects of the non-linearity of the medium on the growth rate of filamentation instability in a magnetized plasma interacting with an intense laser pulse, is investigated. The non-linearity of the medium, modeled by Kerr non-linearity, is an important factor, which determines the rate of instability growth. Sensitivity of the rate of filamentation growth, to the Kerr non-linear coefficient could be adjusted by the external magnetic field and laser intensity.
The expansion of a dense plasma through a more rarefied ionised medium is a phenomenon of interest in various physics environments ranging from astrophysics to high energy density laser- matter laboratory experiments. Here this situation is modeled via a 1D Particle-In-Cell simulation; a jump in the plasma density of a factor of 100 is introduced in the middle of an otherwise equally dense electron-proton plasma with an uniform proton and electron temperature of 10eV and 1keV respectively. The diffusion of the dense plasma, through the rarified one, triggers the onset of different nonlinear ph…
Thermally excited waves in a Plasma crystal were numerically simulated using a Box_Tree code. The code is a Barnes_Hut tree code proven effective in modeling systems composed of large numbers of particles. Interaction between individual particles was assumed to conform to a Yukawa potential. Particle charge, mass, density, Debye length and output data intervals are all adjustable parameters in the code. Employing a Fourier transform on the output data, dispersion relations for both longitudinal and transverse wave modes were determined. These were compared with the dispersion relations obtaine…
Radiation of short-wavelength plasma waves is studied in a cold (Te=0.5eV), large (1.2m length, 70 cm diameter), uniform, Maxwellian laboratory magnetoplasma in the upper-hybrid frequency range. Although the characteristic parameter of spatial dispersion b2=VTe2/c2 is very small (b2<10-6), dispersion characteristics of the upper hybrid plasma waves is found to be strongly modified by the thermal motion of plasma electrons. Indeed, the resonance cone-like dispersion of UH plasma waves has been observed only if the parameter range satisfies simultaneously two inequalities: wc<w<2wc, wp<w<wuh. In…
The dispersion relation of kinetic Alfvén wave in inertial regime is studied in a three component non-degenerate streaming plasma. A lin- ear dispersion relation using fluid- Vlasov equation for quantum plasma is also derived. The quantum correction CQ raised due to the insertion of Bohm potential in Vlasov model causes the suppression in the Alfven wave frequency and the growth rates of instability. A number of analytical expressions are derived for various modes of propagation. It is also found that many system parameters, i.e, streaming velocity, dust charge, num- ber density and quantum co…
A fluid theory has been developed by taking account of gyro-viscosity to study wave propagation characteristics in a homogeneous pair-ion magnetized plasma with a cylindrical symmetry. The exact dispersion relations derived by the Hankel-Fourier transformation are shown comparable with those observed in the experiment by Oohara and co-workers. The gyro-viscosity is responsible for the change in propagation characteristics of the ion cyclotron wave from forward to backward by suppressing the effect of the thermal pressure which normally causes the forward nature of dispersion. Although the expe…
A numerical model for a 2D-monolayer plasma crystal was established using the Box_tree code. Box_tree is a Barnes_Hut tree code which has proven effective in modeling systems composed of large numbers of particles. Thermally excited waves in this plasma crystal were numerically simulated and dispersion relations for both the longitudinal and transverse wave modes were found. These were compared with the dispersion relations extrapolated from experiment as well as a theory based on harmonic approximation. The results were found to agree with theoretical dispersion relations under different wave…
