Relativistic Fluid Model Research Articles

Nonrelativistic limit of first-order relativistic viscous fluids

Out-of-equilibrium effects may play an important role in the dynamics of neutron star mergers and in heavy-ion collisions. Bemfica, Disconzi, Noronha and Kovtun (BDNK) recently derived a causal, locally well posed, and modally stable relativistic fluid model that incorporates the effects of viscosity and heat diffusion. We study the nonrelativistic limit of this fluid model and show that causality for relativistic motion restricts the transport coefficients in the nonrelativistic limit. This restriction provides an upper bound on the ratio of the shear viscosity to the entropy density for fluids that can be described as relativistic within the BDNK model and can be exactly modeled using the Navier-Stokes equation in the nonrelativistic limit. Furthermore, we show that the Fourier law of heat conduction must be modified by higher gradient corrections for such fluids. We also show that the nonrelativistic limit of the BDNK equations of motion are never hyperbolic, in contrast to the nonrelativistic limit of extended variable models, whose nonrelativistic equations of motion can be hyperbolic or not depending on the scaling of the transport coefficients present in the auxiliary equations for viscous degrees of freedom.

Conservative finite volume scheme for first-order viscous relativistic hydrodynamics

We present the first conservative finite volume numerical scheme for the causal, stable relativistic Navier-Stokes equations developed by Bemfica, Disconzi, Noronha, and Kovtun (BDNK). BDNK theory has arisen very recently as a promising means of incorporating entropy-generating effects (viscosity, heat conduction) into relativistic fluid models, appearing as a possible alternative to the so-called M\"uller-Israel-Stewart (MIS) theory successfully used to model quark-gluon plasma. The major difference between the two lies in the structure of the system of partial differential equations (PDEs): BDNK theory only has a set of conservation laws, whereas MIS also includes a set of evolution equations for its dissipative degrees of freedom. The simpler structure of the BDNK PDEs in this respect allows for rigorous proofs of stability, causality, and hyperbolicity in full generality which have as yet been impossible for MIS. To capitalize on these advantages, we present the first fully conservative multidimensional fluid solver for the BDNK equations suitable for physical applications. The scheme includes a flux-conservative discretization, nonoscillatory reconstruction, and a central-upwind numerical flux and is designed to smoothly transition to a high-resolution shock-capturing perfect fluid solver in the inviscid limit. We assess the robustness of our new method in a series of flat-spacetime tests for a conformal fluid and provide a detailed comparison with previous approaches of Pandya and Pretorius [Phys. Rev. D 104, 023015 (2021)].

Space charge effects on radiative ultrashort laser‐plasma interactions: Relativistic fluid model

AbstractUltrashort laser‐gas interaction is a promising candidate for the intense broad band far‐infrared radiation in which the gas ionization and the resultant plasma formation occur consequently. The electron current produced in the process is the most important influential parameter which affects the far‐infrared radiation generation. Although the interacting forces of the process are the space charge electric and the laser electromagnetic forces, the effect of the former one, has not been investigated on the gas‐plasma THz generation. It is noteworthy that the space charge electric force, due to its effect on the electron distribution, has potential influence on the produced electron current and its consequent emission. Here, a 2D relativistic fluid model is presented in which the ions and the resultant space charge field are incorporated. The model investigates the air ionization, electron‐ion plasma formation, and the system's evolution, spatiotemporally. Moreover, as the model is based on the transient electron current, as the source for the electromagnetic pulse radiation, it gives the temporal profile of the radiated field in which the space charge effects are observable. Our results show that the space charge field affects the electron velocity and its resultant current. Therefore, the temporal profiles and amplitudes of the radiated field components are affected and their resemblance to the experimental data is enhanced. The results indicate that the amplitude of the radiated field increases in the presence of the space charge field. In addition, it is shown that the space charge effects become more pronounced with the laser intensity.

Relativistic air-plasma far-infrared radiation effects by ultrashort laser pulses in air

Interactions of ultrashort laser pulses with gases have a wide variety of applications including lighting control, electromagnetic radiation and remote sensing. Considering the radiation effects, the ionization process, plasma formation and the current produced due to the formed plasmas, are the important fundamental processes. Here, a 2D relativistic fluid model is presented in which the interaction of an ultrashort laser pulse with air, leading to the electromagnetic pulse generation, is investigated. As the model is relativistic, it is appropriate for the investigation of the air-plasma radiation effects at high intensities. The results show that the intense laser-air interaction is suitable for the intense broadband far-infrared pulse generation due to the fact that the wave amplitude increases with the laser intensity. Moreover, for the laser intensities above 1020 W/m2, the laser pulse magnetic field gives rise to a strong axial electron current and a consequent axial wave component, which has to be accounted for in the proposed physical models. In addition, the Fourier transform analysis reveals that the radiated pulse is broadband and its frequency spectrum is not affected by the laser intensity.

Laser pulse dispersion in underdense plasma and associated ion acceleration by relativistic self-induced transparency

The propagation of laser pulses in the underdense plasma is a very crucial aspect of the laser-plasma interaction process. In this work, we explored the two regimes of laser propagation in the plasma, one with a0 < 1 and the other with a0≳10. For the a0 < 1 case, we used a cold relativistic fluid model, wherein apart from immobile ions no further approximations are made. The effects of laser pulse amplitude, pulse duration, and plasma density are studied using the fluid model and compared with the expected scaling laws and also with the particle-in-cell (PIC) simulations. The agreement between the fluid model and the PIC simulations are found to be excellent. Furthermore, for the a0≳10 case, we used the PIC simulations alone. The delicate interplay between the conversion from the electromagnetic field energy to the longitudinal electrostatic fields results in dispersion, and so the redshift of the pump laser pulse. The dispersed pulse is then allowed to be incident on the subwavelength two-layer composite target. The underdense plasma before the target regulates the dispersion of the pulse. We observed an optimum pretarget plasma density which results in the acceleration of the ions from the secondary layer to ∼170 MeV by a ∼8 fs linearly polarized Gaussian laser pulse with ∼8.5 × 1020 W/cm2.

Perturbative approach to the self-focusing of intense X-ray laser beam propagating in thermal quantum plasma

In this theoretical study, the problem of self-focusing of an X-ray intense laser beam in the thermal quantum plasma is studied. Using a relativistic fluid model and taking into account the hydrodynamic pressure of degenerate electrons in the zero temperature limit, the nonlinear momentum equation of electrons is solved by means of a perturbative method and the nonlinear current density of the relativistic degenerate electrons is obtained. Saving only the third-order nonlinearity of the laser beam amplitude, a nonlinear equation describing the interaction of a laser beam with the quantum plasma is derived. It is shown that considering the nonlinearity of the system through solving the nonlinear equation of the degenerate electron leads to the originally different wave equation in comparison to outcomes of the approach in which the permittivity of longitudinal waves of quantum plasma is problematically extended to the relativistic case. The evolution of the laser beam spot size with the Gaussian profile is considered, and the effect of quantum terms on the self-focusing quality is studied. It is shown that considering quantum effects leads to the decrease in the self-focusing property and the effect of Bohm tunneling potential is more dominant than the degenerate electron pressure term.

Surface plasmons in a semi-bounded massless Dirac plasma

The collective excitation of surface plasmons in a massless Dirac plasma (e.g., graphene) half-space (bounded by air) is investigated using a relativistic quantum fluid model. The unique features of such surface waves are discussed and compared with those in a Fermi plasma. It is found that in contrast to Fermi plasmas, the long-wavelength surface plasmon frequency (ω) in massless Dirac plasmas is explicitly nonclassical, i.e., ω∝1/ħ, where h=2πħ is the Planck's constant. Besides some apparent similarities between the surface plasmon frequencies in massless Dirac plasmas and Fermi plasmas, several notable differences are also found and discussed. Our findings elucidate the properties of surface plasmons that may propagate in degenerate plasmas where the relativistic and quantum effects play a vital role.

Transition from wakefield generation to soliton formation.

It is well known that when a short laser pulse propagates in an underdense plasma, it induces longitudinal plasma oscillations at the plasma frequency after the pulse, typically referred to as the wakefield. However, for plasma densities approaching the critical density, wakefield generation is suppressed, and instead the EM-pulse (electromagnetic pulse) undergoes nonlinear self-modulation. In this article we have studied the transition from the wakefield generation to formation of quasi-solitons as the plasma density is increased. For this purpose we have applied a one-dimensional relativistic cold fluid model, which has also been compared with particle-in-cell simulations. A key result is that the energy loss of the EM-pulse due to wakefield generation has its maximum for a plasma density of the order 10% of the critical density, but that wakefield generation is sharply suppressed when the density is increased further.

The effects of helical magnetostatic wiggler on the modulation instability of a laser pulse propagating through a hot magnetoplasma

In this paper, the effects of helical magnetostatic wiggler on the modulation instability of a laser pulse propagating through a hot magnetoplasma have been investigated. Using the relativistic fluid model, the propagation of intense circularly polarized laser pulse along the wiggler field has been considered. A non-linear equation which describes the interaction of laser pulse with hot magnetoplasma in the quasi-neutral approximation for both of the right- and left-hand polarizations has been derived. The effect of the wiggler magnetic strength on the growth rate of the laser pulse has been discussed. The results indicate that for the right-hand polarization, the increase of wiggler frequency leads to increasing of growth rate. Inversely, in left-hand polarization with increasing of wiggler frequency, growth rate decreases. Moreover, it is found that in hot magnetoplasma employing the wiggler field improves declines the growth of modulation instability in right-and left-hand polarization. In addition, it was found that growth rate in the high plasma temperatures saturates and reaches to a constant norm.

The effect of the wiggler magnetic field strength on the self-focusing of an intense laser pulse propagating through a magnetized non-Maxwellian plasma

In this paper, the effect of the wiggler magnetic field strength on the self-focusing of an intense laser pulse propagating through a magnetized non-Maxwellian plasma is studied. By using a relativistic fluid model, a non-linear equation describing the spot-size of the laser pulse for right- and left-hand polarizations has been derived. The evaluation of the spot-size in the self-focusing of laser pulse with the respect to the kind of polarization is investigated. Besides, the effects of wiggler magnetic field and a non-Maxwellian distribution of charge density on the evolution of the laser spot-size have been discussed. The results show that in the right-hand polarization, the existence of superthermal particles and wiggler magnetized field simultaneously cause improvement in the self-focusing quality. In addition, for the left-hand polarization, the self-focusing in the presence of wiggler field increases with an increase in the ki. Furthermore, the self-focusing decreases with an increase in the wiggler amplitudes for the left-hand polarization. Moreover, it is observed that an increase in the normalized laser frequency leads to an increase in the variation in the laser spot-size, and then the laser pulse becomes more focused.

Ion-acoustic rogue waves and breathers in relativistically degenerate electron-positron plasmas

In this paper, we employ a weakly relativistic fluid model to study the nonlinear amplitude modulation of electrostatic waves in an unmagnetized electron-positron-ion plasma. It is assumed that the degeneracy pressure law for electrons and positrons follows the Chandrasekhar limit of state whereas ions are warm and classical. The hydrodynamic approach along with the perturbation method have been applied to obtain the corresponding nonlinear Schrodinger equation (NLSE) in which nonlinearity is in balance with the dispersive terms. Using the NLSE, we could evaluate the modulational instability to show that various types of localized ion acoustic excitations exist in the form of either bright-type envelope solitons or dark-type envelope solitons. The regions of the stable and unstable envelope wave have been confined punctually for various regimes. Furthermore, it is proposed that the exact solutions of the NLSE for breather waves are the rogue waves (RWs), Akhmediev breather (AB), and Kuznetsov-Ma breather (KM) soliton. In order to show that the characteristics of breather structures is influenced by the plasma parameters (namely, relativistic parameter, positron concentration, and ionic temperature), the relevant numerical analysis of the NLSE is examined. In particular, it is observed that by increasing the values of the mentioned plasma parameters, the amplitude of the RWs will be decreased. Our results help researchers to explain the formation and dynamics of nonlinear electrostatic excitations in super dense astrophysical regimes.

Modulation and nonlinear evolution of multi-dimensional Langmuir wave envelopes in a relativistic plasma

The modulational instability (MI) and the evolution of weakly nonlinear two-dimensional (2D) Langmuir wave (LW) packets are studied in an unmagnetized collisionless plasma with weakly relativistic electron flow. By using a 2D self-consistent relativistic fluid model and employing the standard multiple-scale technique, a coupled set of Davey-Stewartson (DS)-like equations is derived which governs the slow modulation and the evolution of LW packets in relativistic plasmas. It is found that the relativistic effects favor the instability of LW envelopes in the k{\theta} plane, where k is the wave number and {\theta} the angle of modulation. It is also found that as the electron thermal velocity or {\theta} increases, the growth rate of MI increases with cutoffs at higher wave numbers of modulation. Furthermore, in the nonlinear evolution of the DS-like equations, it is seen that with an effect of the relativistic flow, a Gaussian wave beam collapses in a finite time, and the collapse can be arrested when the effect of the thermal pressure or the relativistic flow is slightly relaxed. The present results may be useful to the MI and the formation of localized LW envelopes in cosmic plasmas with a relativistic flow of electrons.

运动流体界面Rayleigh-Taylor不稳定性研究

Starting from the nonrelativistic fluid and relativistic fluid models, we study the linear growth of the Rayleigh-Taylor instability (RTI) at the interface of two ideal fluids moving with certain speed under a gravitational field, where the fluid velocity is along the gravitational field and is perpendicular to interface. Calculation shows that, the RTI growth rate for nonrelativistic fluids is independent of its reference frame or the fluid velocity. A general formula of the RTI growth rate is obtained for relativistic fluids. It shows that both the relativistic thermal pressure and macroscopic fluid velocity tend to suppress the RTI growth. Physically, when the thermal velocities of microparticles of the relativistic fluids are considerable as compared to the light speed in vacuum, the contribution of the thermal pressure to the fluid inertia cannot be ignored. Also when the fluid velocities are not negligible as compared to the light speed, the effect of relativistic-mass-increase leads to the decreased RTI growth rate. The latter is basically consistent with the time transformation effect in different reference frames.

Effect of super-thermal ions and electrons on the modulation instability of a circularly polarized laser pulse in magnetized plasma

AbstractThe modulation instability of a circularly polarized laser pulse in a magnetized non-Maxwellian plasma is investigated. Based on a relativistic fluid model, the nonlinear interaction of an intense circularly polarized laser beam with a non-Maxwellian magnetized plasma is described. Nonlinear dispersion relation and growth rate of the instability for left- and right-hand polarizations are derived. The effect of temperature, external magnetic field, value of Kappa and state of polarization on the growth rate are analyzed. It is shown that the growth rate increases with increase in the magnetic field for the right-hand polarization and inversely it decreases for the left-hand one. Also it is observed that existence of super-thermal particles causes the decrease in the growth.

Nonlinear dispersion and transverse profile of intense electromagnetic waves, propagating through electron-positron-ion hot magnetoplasma

Self-guided nonlinear propagation of intense circularly-polarized electromagnetic waves in a hot electron-positron-ion magnetoplasma is studied. Using a relativistic fluid model, a nonlinear equation is derived, which describes the interaction of the electromagnetic wave with the plasma in the quasi-neutral approximation. Transverse Eigen modes, the nonlinear dispersion relation and the group velocity are obtained. Results show that the transverse profile in the case of magnetized plasma with cylindrical symmetry has a radially damping oscillatory form. Effect of applying external magnetic fields, existence of the electron-positron pairs, changing the amplitude of the electromagnetic wave, and its polarization on the nonlinear dispersion relation and Eigen modes are studied.

Scale-lengths and instabilities in magnetized classical and relativistic plasma fluid models

The validity of the traditional plasma continuum is predicated on a hierarchy of scale-lengths, with the Debye length being considered to be effectively unresolvable in the continuum limit. In this article, we revisit the strong magnetic field case in which the Larmor radius is comparable or smaller than the Debye length in the classical plasma, and also for a relativistic plasma. Fresh insight into the validity of the continuum assumption in each case is offered, including a fluid limit on the Alfvén speed that may impose restrictions on the validity of magnetohydrodynamics (MHD) in some solar and fusion contexts. Additional implications concerning the role of the firehose instability are also explored.

Thermal behavior change in the self-focusing of an intense laser beam in magnetized electron-ion-positron plasma

AbstractSelf-focusing of an intense circularly-polarized laser beam in a hot electron-positron-ion magneto-plasma is studied. Using a relativistic fluid model, nonlinear equation describing laser-plasma interaction in the quasi-neutral approximation is derived. Expanding nonlinear current density in terms of normalized vector potential and saving only the parabolic terms, we investigated the self-focusing phenomenon for right- and left-hand circularly polarized laser beams. The evolution of laser beam spot size with Gaussian profile is considered. Effects of the external magnetic field, fraction of electron-positron pairs, and also the kind of polarization on the self-focusing property are studied. It is shown that a mixture of electron-positron pairs to the ion-electron plasma modifies the behavior of plasma with respect to the external magnetic field.

Polarization effect on the relativistic nonlinear dynamics of an intense laser beam propagating in a hot magnetoactive plasma

Nonlinear dynamics of an intense circularly polarized laser beam interacting with a hot magnetized plasma is investigated. Using a relativistic fluid model, a modified nonlinear Schrödinger equation is derived based on a quasineutral approximation, which is valid for hot plasma. Using a three-dimensional model, spatial-temporal development of the laser pulse is investigated. The occurrence of some nonlinear phenomena such as self-focusing, self-modulation, light trapping, and filamentation of the laser pulse is discussed. Also the effect of polarization and external magnetic field on the nonlinear evolution of these phenomena is studied.

Competition of circularly polarized laser modes in the modulation instability of hot magnetoplasma

The present study is aimed to investigate the problem of modulation instability of an intense laser beam in the hot magnetized plasma. The propagation of intense circularly polarized laser beam along the external magnetic field is considered using a relativistic fluid model. The nonlinear equation describing the interaction of laser pulse with magnetized hot plasma is derived in the quasi-neutral approximation, which is valid for hot plasma. Nonlinear dispersion equation for hot plasma is obtained. For left- and right-hand polarizations, the growth rate of instability is achieved and the effect of temperature, external magnetic field, and kind of polarization on the growth rate is considered. It is observed that for the right-hand polarization, increase of magnetic field leads to the increasing of growth rate. Also for the left-hand polarization, increase of magnetic field inversely causes decrease of the growth rate.

Interaction of spatially overlapping standing electromagnetic solitons in plasmas

Numerical investigations on mutual interactions between two spatially overlapping standing electromagnetic solitons in a cold unmagnetized plasma are reported. It is found that an initial state comprising of two overlapping standing solitons evolves into different end states, depending on the amplitudes of the two solitons and the phase difference between them. For small amplitude solitons with zero phase difference, we observe the formation of an oscillating bound state whose period depends on their initial separation. These results suggest the existence of a bound state made of two solitons in the relativistic cold plasma fluid model.