Relativistic Quantum Plasma Research Articles

Surface waves on the relativistic quantum plasma half-space

We present a theoretical investigation on the propagation of surface waves on the relativistic quantum plasma half-space. The dispersion relations of surface plasmon polaritons (SPPs) and electrostatic surface waves containing relativistic quantum corrected terms are derived. Results show that the frequency of SPPs has a blue-shift, and surface Langmuir oscillations can propagate on the cold plasma half-space due to quantum effects. Numerical evaluation indicates that quantum effects to SPPs and electrostatic surface waves are significant and observable.

Linear and nonlinear wave propagation in weakly relativistic quantum plasmas

We consider a recently derived kinetic model for weakly relativistic quantum plasmas. We find that that the effects of spin-orbit interaction and Thomas precession may alter the linear dispersion relation for a magnetized plasma in case of high plasma densities and/or strong magnetic fields. Furthermore, the ponderomotive force induced by an electromagnetic pulse is studied for an unmagnetized plasma. It turns out that for this case the spin-orbit interaction always gives a significant contribution to the quantum part of the ponderomotive force.

Relativistic x-ray quantum free-electron lasers: a collective Klein–Gordon model

We present a quantum-relativistic model for the nonlinear interaction between large-amplitude electromagnetic (EM) waves and a quantum plasma. The model is based on a collective Klein–Gordon equation for the relativistic electrons, which is coupled with the Maxwell equations for the EM and electrostatic fields. The model is used to derive a nonlinear dispersion relation for the EM scattering instabilities in a relativistic quantum plasma. With application to the quantum free-electron laser (FEL), a relativistic electron beam is passing through an intense EM wave used as a wiggler to produce coherent tunable radiation. The frequency upshift of the radiation is tuned by the energy of the electron beam. The nonlinear dispersion relation reveals the importance of quantum recoil effects and oblique scattering of the radiation on the gain of the quantum FEL.

Relativistic Klein-Gordon-Maxwell multistream model for quantum plasmas

A multistream model for spinless electrons in a relativistic quantum plasma is introduced by means of a suitable fluidlike version of the Klein-Gordon-Maxwell system. The one- and two-stream cases are treated in detail. A new linear instability condition for two-stream quantum plasmas is obtained, generalizing the previously known nonrelativistic results. In both the one- and two-stream cases, steady-state solutions reduce the model to a set of coupled nonlinear ordinary differential equations, which can be numerically solved, yielding a manifold of nonlinear periodic and soliton structures. The validity conditions for the applicability of the model are addressed.

Self-focusing of Gaussian laser beam in relativistic cold quantum plasma

This paper presents an investigation of the self-focusing of Gaussian laser beam in relativistic cold quantum plasma. Employing the expression for the dielectric function of cold quantum plasma, we have setup the differential equation for beam-width parameter by using the WKB and paraxial approximation, and solved numerically. The results have been presented in the form of graphs and discussed. It is found that quantum effects plays vital role in laser–plasma interaction and significantly adds self-focusing in plasma as compared to that of classical relativistic case of reference.

Quantum ion-acoustic solitary waves in weak relativistic plasma

Small amplitude quantum ion-acoustic solitary waves are studied in an unmagnetized two- species relativistic quantum plasma system, comprised of electrons and ions. The one-dimensional quantum hydrodynamic model (QHD) is used to obtain a deformed Korteweg–de Vries (dKdV) equation by reductive perturbation method. A linear dispersion relation is also obtained taking into account the relativistic effect. The properties of quantum ion-acoustic solitary waves, obtained from the deformed KdV equation, are studied taking into account the quantum mechanical effects in the weak relativistic limit. It is found that relativistic effects significantly modify the properties of quantum ion-acoustic waves. Also the effect of the quantum parameter H on the nature of solitary wave solutions is studied in some detail.

Relativistic quantum corrections to laser wakefield acceleration

The influence of quantum effects on the interaction of intense laser fields with plasmas is investigated by using a hydrodynamic model based on the framework of the relativistic quantum theory. Starting from the covariant Wigner function and Dirac equation, the hydrodynamic equations for relativistic quantum plasmas are derived. Based on the relativistic quantum hydrodynamic equations and Poisson equation, the perturbations of electron number densities and the electric field of the laser wakefield containing quantum effects are deduced. It is found that the corrections generated by the quantum effects to the perturbations of electron number densities and the accelerating field of the laser wakefield cannot be neglected. Quantum effects will suppress laser wakefields, which is a classical manifestation of quantum decoherence effects, however, the contribution of quantum effects for the laser wakefield correction will been partially counteracted by the relativistic effects. The analysis also reveals that quantum effects enlarge the effective frequencies of plasmas, and the quantum behavior appears a screening effect for plasma electrons.

Ion acoustic shock waves in weakly relativistic multicomponent quantum plasma

Ion acoustic Shock waves (IASWs) are studied in an collisionless unmagnetized relativistic quantum electron-positron-ion(e-p-i) plasma employing the quantum hydro -dynamic(QHD) model. Korteweg-deVries- Burger equation(KdVB) is derived using small amplitude perturbation expansion method to study the nonlinear propagation of the quantum IASWs. It is found that the coefficients of the KdVB equation are significantely modified by the positron density p, relativistic factor(Ur), temperatures σ, kinematic viscosity η and quantum factor(H).

Relativistic quantum plasma dispersion functions

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 (J\"uttner) 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 calculated in this way with the existing treatments leads to the identification of errors in the literature, which we correct. We also comment on a controversy as to whether the dispersion curves in a superdense plasma pass through the region where pair creation is allowed.

Electromagnetic perturbations of the relativistic quantum plasma.

Perturbations of the relativstic quantum plasma are studied using Wigner-function techniques. In addition, a generalized fluctuation-dissipation theorem is given that relates the perturbed Wigner function to the fluctuations of the Wigner function at thermal equilibrium. As a consequence, the relativistic quantum version of the fluctuation-dissipation theorem is obtained and analyzed.

Fluctuations in the relativistic quantum plasma

The fluctuations of various parameters of the relativistic quantum plasma are studied with the use of the covariant Wigner function techniques. The fluctuations of the covariant Wigner function of the ideal Fermi gas at thermal equilibrium are calculated. The result is a function of the one particle Wigner function and the anticommutator of the Dirac fields only. As a consequence second order correlation functions of the four-current and the momentum-energy tensor are obtained and analyzed. On the basis of the fluctuation-dissipation theorem, the polarization tensors at first order in e 2 of the magnetized and the non-magnetized electron gas are derived from the four-current fluctuations of the ideal plasma. Expressions are given for the magnetized vacuum polarization in two representations, integral and discrete sums over Landau levels, for arbitrary values of the photon four-momentum. The dispersion relations of the magnetized gas are studied in the limit of low frequencies and wavenumbers. It is shown that owing to relativistic quantum effects, the characteristic frequencies of the plasma modes (plasma and Larmor frequencies) split into effective transverse and longitudinal frequencies. The existence of an acoustic mode (zero sound) for the one-component plasma is also shown.

Fluctuations in the relativistic quantum plasma: Horacio D. Sivak. Groupe d'Astrophysique Relativiste, Observatoire de Paris-Meudon, 92190 Meudon, France

Fluctuations in the relativistic quantum plasma: Horacio D. Sivak. Groupe d'Astrophysique Relativiste, Observatoire de Paris-Meudon, 92190 Meudon, France

Normal modes of a relativistic quantum plasma; The one-component plasma

The normal modes of a relativistic electron gas are studied on the basis of the Boltzmann-Vlasov kinetic equation via a projection operator formalism. A general framework is constructed in which the fully relativistic Vlasov self-consistent force term appears as a symmetric operator acting in the Hilbert space of one-particle states. The plasma-dynamical equations are obtained by projecting onto the subspace consisting of the charge, energy and momentum densities, plus the nonconserved current density. The eigenmodes of these equations include two transverse and two longitudinal plasma modes, and one damped heat mode. They are explicitly calculated up to second order in the wave vector and to first order in the collision frequency.

Transverse modes of a relativistic quantum plasma

The dispersion relation for long-wavelength transverse plasma weves propagating in a one-component relativistic quantum plasma is derived from the relativistic Boltzmann-Vlasov equation. The result is consistent with the one obtained from quantum electrodynamics by the method of dielectric response, but at variance with hydrodynamical calculations. The discrepancy is explained by making a distinction between collective and collision dominated plasmas.

Excitation spectrum of the relativistic quantum plasma

Using a covariant Wigner function approach developed elsewhere, the excitation modes of a relativistic quantum plasma are obtained. With this technique, the derivation is quite similar to the usual derivation (i.e. non-quantum) and hence can be applied to more involved cases.

Covariant Wigner function approach for relativistic quantum plasmas

In this paper a general formalism for the treatment of relativistic quantum plasmas is given. It is manifestly covariant and rests on the use of a (covariant) relativistic Wigner function. Here it is applied to the particular case where spin effects are neglected (in most astrophysical applications this is a good approximation): a relativistic quantum Bogoliubov-Born-Green-Kirkwood-Yvan (BBGKY) hierarchy is given. The Vlasov approximation (Hartree approximation) is then considered and dispersion relations are obtained. Limiting cases (relativistic nonquantum high-temperature plasma and relativistic degenerate zero-temperature plasma) obtained previously by other authors are found anew. Finally, the formalism given appears to be much simpler and physically more transparent than many-body techniques used elsewhere.

Microscopic plasmadynamical modes in a relativistic quantum plasma in absence of dissipation

The non-dissipative plasma-dynamical modes for a one-component relativistic plasma are derived in the weak-coupling approximation. The calculations are made along the same general lines as those of Balescu et al. [1, 2] in the non-quantum case : the modes are obtained by standard perturbation theory around the homogeneous collision operator. The generalization is however far from trivial, as the variables of spin and the possibility of electron-positron pair formation must now enter the theory. New hydrodynamical frequencies occur, due to the spin degrees of freedom ; furthermore, spin oscillations may be excited even in a homogeneous medium, a phenomenon linked to the well-known "Zitterbewegung" ; the behaviour of the eigenfrequencies is discussed for a totally degenerate and for a non-degenerate gas in both the ultra-relativistic and the non-relativistic limit.