Relativistic Plasma Research Articles

Formation of population inversions in relativistic plasmas through nonresonant interactions with Alfvén waves

We solve the full quasilinear kinetic equation governing nonresonant interactions of Alfv\'en waves with relativistic plasmas. This work was motivated by the need to determine the energy available for the synchrotron maser in the context of fast radio bursts (FRBs). This interaction can result in plasma heating and the formation of population inversions necessary for the maser. We find that population inversions containing $\ensuremath{\sim}1%--10%$ of the distribution's energy form in the relativistic regime, providing an explanation for the formation of the inversion in the environment expected near FRBs.

Suppression of bremsstrahlung losses from relativistic plasma with energy cutoff.

We study the effects of redistributing superthermal electrons on bremsstrahlung radiation from hot relativistic plasma. We consider thermal and nonthermal distribution of electrons with an energy cutoff in the phase space and explore the impact of the energy cutoff on bremsstrahlung losses. We discover that the redistribution of the superthermal electrons into lower energies reduces radiative losses, which is in contrast to nonrelativistic plasma. Finally, we discuss the possible relevance of our results for open magnetic field line configurations and prospects of the aneutronic fusion based on proton-boron-11 (p-B11) fuel.

A Variational Approach to Resistive General Relativistic Two-Temperature Plasmas

We develop an action principle to construct the field equations for dissipative/resistive general relativistic two-temperature plasmas, including a neutrally charged component. The total action is a combination of four pieces: an action for a multifluid/plasma system with dissipation/resistivity and entrainment; the Maxwell action for the electromagnetic field; the Coulomb action with a minimal coupling of the four-potential to the charged fluxes; and the Einstein–Hilbert action for gravity (with the metric being minimally coupled to the other action pieces). We use a pull-back formalism from spacetime to abstract matter spaces to build unconstrained variations for the neutral, positively, and negatively charged fluid species and for three associated entropy flows. The full suite of field equations is recast in the so-called “3+1” form (suitable for numerical simulations), where spacetime is broken up into a foliation of spacelike hypersurfaces and a prescribed “flow-of-time”. A previously constructed phenomenological model for the resistivity is updated to include the modified heat flow and the presence of a neutrally charged species. We impose baryon number and charge conservation as well as the Second Law of Thermodynamics in order to constrain the number of free parameters in the resistivity. Finally, we take the Newtonian limit of the “3+1” form of the field equations, which can be compared to existing non-relativistic formulations. Applications include main sequence stars, neutron star interiors, accretion disks, and the early universe.

Exact and paraxial Airy propagation of relativistic electron plasma wavepackets

The different forms of propagation of relativistic electron plasma wavepackets in terms of Airy functions are studied. It is shown that exact solutions can be constructed showing accelerated propagations along coordinates transverse to the thermal speed cone coordinate. Similarly, Airy propagation is a solution for relativistic electron plasma waves in the paraxial approximation. This regime is considered in time domain, when paraxial approximation is considered for frequency, and in space domain, when paraxial approximation is considered for wavelength. In both different cases, the wavepackets remain structured in the transverse plane. Using these solutions we are able to define generalized and arbitrary Airy wavepackets for electron plasma waves, depending on arbitrary spectral functions. Examples of this construction are presented. These electron plasma Airy wavepackets are the most general solutions of this kind.

High-energy synchrotron flares powered by strongly radiative relativistic magnetic reconnection: 2D and 3D PIC simulations

ABSTRACT The time evolution of high-energy synchrotron radiation generated in a relativistic pair plasma energized by reconnection of strong magnetic fields is investigated with 2D and 3D particle-in-cell (PIC) simulations. The simulations in this 2D/3D comparison study are conducted with the radiative PIC code OSIRIS, which self-consistently accounts for the synchrotron radiation reaction on the emitting particles, and enables us to explore the effects of synchrotron cooling. Magnetic reconnection causes compression of the plasma and magnetic field deep inside magnetic islands (plasmoids), leading to an enhancement of the flaring emission, which may help explain some astrophysical gamma-ray flare observations. Although radiative cooling weakens the emission from plasmoid cores, it facilitates additional compression there, further amplifying the magnetic field B and plasma density n, and thus partially mitigating this effect. Novel simulation diagnostics utilizing 2D histograms in the n-B space are developed and used to visualize and quantify the effects of compression. The n-B histograms are observed to be bounded by relatively sharp power-law boundaries marking clear limits on compression. Theoretical explanations for some of these compression limits are developed, rooted in radiative resistivity or 3D kinking instabilities. Systematic parameter-space studies with respect to guide magnetic field, system size, and upstream magnetization are conducted and suggest that stronger compression, brighter high-energy radiation, and perhaps significant quantum electrodynamic effects such as pair production, may occur in environments with larger reconnection-region sizes and higher magnetization, particularly when magnetic field strengths approach the critical (Schwinger) field, as found in magnetar magnetospheres.

Modulation of electromagnetic waves in a relativistic degenerate plasma at finite temperature

We study the modulational instability (MI) of a linearly polarized electromagnetic (EM) wave envelope in an intermediate regime of relativistic degenerate plasmas at a finite temperature (T≠0) where the thermal energy (KBT) and the rest-mass energy (mec2) of electrons do not differ significantly, i.e., βe≡KBT/mec2≲ (or ≳) 1, but the Fermi energy (KBTF) and the chemical potential energy (μe) of electrons are still a bit higher than the thermal energy, i.e., TF>T and ξe=μe/KBT≳1. Starting from a set of relativistic fluid equations for degenerate electrons at finite temperature, coupled to the EM wave equation and using the multiple scale perturbation expansion scheme, a one-dimensional nonlinear Schödinger (NLS) equation is derived, which describes the evolution of slowly varying amplitudes of EM wave envelopes. Then, we study the MI of the latter in two different regimes, namely, βe<1 and βe>1. Like unmagnetized classical cold plasmas, the modulated EM envelope is always unstable in the region βe>4. However, for βe≲1 and 1<βe<4, the wave can be stable or unstable depending on the values of the EM wave frequency, ω, and the parameter ξe. We also obtain the instability growth rate for the modulated wave and find a significant reduction by increasing the values of either βe or ξe. Finally, we present the profiles of the traveling EM waves in the form of bright (envelope pulses) and dark (voids) solitons, as well as the profiles (other than traveling waves) of the Kuznetsov–Ma breather, the Akhmediev breather, and the Peregrine solitons as EM rogue (freak) waves, and discuss their characteristics in the regimes of βe≲1 and βe>1.

Spatial Intermittency of Particle Distribution in Relativistic Plasma Turbulence

Relativistic magnetically dominated turbulence is an efficient engine for particle acceleration in a collisionless plasma. Ultrarelativistic particles accelerated by interactions with turbulent fluctuations form nonthermal power-law distribution functions in the momentum (or energy) space, f(γ)d γ ∝ γ −α d γ, where γ is the Lorenz factor. We argue that in addition to exhibiting non-Gaussian distributions over energies, particles energized by relativistic turbulence also become highly intermittent in space. Based on particle-in-cell numerical simulations and phenomenological modeling, we propose that the bulk plasma density has lognormal statistics, while the density of the accelerated particles, n, has a power-law distribution function, . We argue that the scaling exponents are related as β ≈ α + 1, which is broadly consistent with numerical simulations. Non-space-filling, intermittent distributions of plasma density and energy fluctuations may have implications for plasma heating and for radiation produced by relativistic turbulence.

Vlasov-Klimontovich Equation in Action

This paper outlines a variety of possible applications of the Vlasov equation and its generalization, i.e., the Klimontovich equation, in various areas of many-body physics. In particular, these equations are shown to be used in relativistic plasma physics, the theory of semi-classical Bloch electrons, and the metriplectic description of dissipative processes.

High-order finite-difference entropy stable schemes for two-fluid relativistic plasma flow equations

In this article, we propose high-order finite-difference entropy stable schemes for the two-fluid relativistic plasma flow equations. This is achieved by exploiting the structure of the equations, which consists of three independent flux components. The first two components describe the ion and electron flows, which are modeled using the relativistic hydrodynamics equation and the third component is Maxwell's equations. The coupling of the ion and electron flows and electromagnetic fields is via source terms only, but the source terms do not affect the entropy evolution. To design semi-discrete entropy stable schemes, we extend the entropy stable schemes for relativistic hydrodynamics in [1] to three dimensions. This is then coupled with entropy stable discretization of the Maxwell's equations. Finally, we use SSP-RK schemes to discretize in time. We also propose ARK-IMEX schemes to treat the stiff source terms; the resulting nonlinear set of algebraic equations is local (at each discretization point) and hence can be solved cheaply using the Newton's Method. The proposed schemes are then tested using various test problems to demonstrate their stability, accuracy and efficiency.

Synchrotron Cutoff in Ultraluminous X-Ray Sources

The origin of spectral curvature at energies E ≃ 10 keV in ultraluminous X-ray sources (ULXs) is not well understood. In this paper, we propose a novel mechanism based on synchrotron radiation to explain this cutoff. We show that relativistic plasma can give rise to the observed spectral curvature for neutron star magnetic fields due to the variation in the latitude of synchrotron radiation. We analyze the NuSTAR data of two bright pulsar ULXs, NGC 5907 ULX1 and NGC 7793 P13, and provide estimates of the physical parameters of these sources. We fit the data for synchrotron emission at various latitudes and show that the spectral cutoff in these cases can be explained for a large range of acceptable physical parameters, e.g., a semirelativistic plasma with γ ≃ 20 for high latitudes or a highly relativistic plasma (γ ≃ 105) for emission close to the electron’s orbital plane in a typical magnetic field of B ≃ 1012 G. We also discuss how such an emission mechanism can be distinguished from other proposed models. A corollary to our study is that most ULXs might be neutron stars as they display such a spectral cutoff.

Confinement time and ambipolar potential in a relativistic mirror-confined plasma

Advanced aneutronic fusion fuels such as proton-Boron11 tend to require much higher temperatures than conventional fuels like deuterium–tritium. For electrons, the bulk plasma temperature can approach a substantial fraction of the rest mass. In a mirror confinement system, where the electrons are confined by an ambipolar potential of at least five electron temperatures, the tail electrons which can escape the potential are fully relativistic, which must be taken into account in calculating their confinement. In this paper, simple estimates are employed to extend the scaling of the confinement time into the relativistic regime. By asymptotically matching this scaling to known solutions in the non-relativistic limit, accurate forms for the confinement time (and thus, the ambipolar potential) are obtained. These forms are verified using finite-element-based Fokker–Planck simulations over a wide range of parameters. Comparing relativistic and nonrelativistic mirror-confined plasmas with the same ratio of confining potential |eϕ| to electron temperature Te and the same mirror ratio R, the net result is a decrease in the confinement time due to relativistic effects by a factor of S≡(1+15Te/8mec2)/(1+2|eϕ|/mec2).

On the quadruple Beltrami fields in thermally relativistic electron-positron-ion plasma

A thermally relativistic electron-positron-ion (EPI) plasma self-organizes into a quadruple Beltrami (QB) field. The QB field, which is the combination of four Beltrami fields, is described by four scale parameters. These scale parameters are often either real or both real and complex in nature. The values of the scale parameters are determined by Beltrami parameters, relativistic temperatures, and the densities of plasma species. It is demonstrated that all the scale parameters become real at higher relativistic temperatures and ion densities, which naturally lead to paramagnetic structures. It is also shown that the scale separation in the QB state provides the possibility of field and flow generation in such thermally relativistic plasmas. The present study may have implications for space, astrophysical and laboratory plasmas.

Global dynamics for a collisionless charged plasma in Bianchi spacetimes in Eddington-inspired-Born–Infeld gravity

We consider a Bianchi type I–IX physical metric g, an auxiliary metric q with a collisionless charged relativistic plasma in Eddington-inspired-Born–Infeld theory. We first derive a governing system of second order nonlinear partial differential equations. Then, by the characteristics method applied to the Vlasov equation whose solution is the distribution function f, we manage to construct an iterated sequence. This leads to the existence and uniqueness of a local solution on an interval , with . Then under certain assumptions of smallness on the mean curvatures in both directions, the Eddington parameter k and the dimensionless parameter λ, we show that this solution is global in time.

Sensitivity of synchrotron radiation to the superthermal electron population in mildly relativistic plasma

Synchrotron radiation has markedly different behavior in ∼ 10 keV and in ∼ 100 keV plasma. We show that high-energy electrons that occupy the tail of velocity distribution function have disproportionate impact on power loss of ∼ 100 keV plasma. If electrons with energy more than cutoff energy are redistributed while keeping the Maxwellian distribution function below cutoff energy intact, both emission and absorption of synchrotron radiation act to decrease the lost power. These novel radiation transport effects in non-equilibrium plasma suggest large utility in the deconfinement of high-energy electrons to reduce synchrotron radiation in applications where the radiation is deleterious.

The wave energy density and growth rate for the resonant instability in relativistic plasmas

ABSTRACT The wave instability acts in astrophysical plasmas to redistribute energy and momentum in the absence of frequent collisions. There are many different types of waves, and it is important to quantify the wave energy density and growth rate for understanding what types of wave instabilities are possible in different plasma regimes. There are many situations throughout our Universe where plasmas contain a significant fraction of relativistic particles. Theoretical estimates for the wave energy density and growth rate are constrained to either field-aligned propagation angles or non-relativistic considerations. Based on linear theory, we derive the analytic expressions for the energy density and growth rate of an arbitrary resonant wave with an arbitrary propagation angle in relativistic plasmas. For this derivation, we calculate the Hermitian and anti-Hermitian parts of the relativistic-plasma dielectric tensor. We demonstrate that our analytic expression for the wave energy density presents an explicit energy increase in resonant waves in the wavenumber range where the analytic expression for the growth rate is positive (i.e. where a wave instability is driven). For this demonstration, we numerically analyse the loss-cone driven instability, as a specific example, in which the whistler-mode waves scatter relativistic electrons into the loss cone in the radiation belt. Our analytic results further develop the basis for linear theory to better understand the wave instability, and have the potential to combine with quasi-linear theory, which allows to study the time evolution of not only the particle momentum distribution function but also resonant wave properties through an instability.

Analytical evaluation of the Dnestrovskii functions occurring in weakly relativistic, magnetized, and thermal plasmas

AbstractIn this paper, we established an effective formula for Dnestrovskii functions based on the binomial expansion theorem which frequently appears in a weakly relativistic loss cone distribution, relativistic, magnetized, and thermal plasmas. The obtained formulas are expressed in terms of binomial coefficients and incomplete Gamma functions. Therefore, the proposed approach is a fully useful method to evaluate Dnestrovskii functions and related physical properties of plasmas. Calculation results of the Dnestrovskii functions are compared with other numerical and theoretical models and indicated acceptable agreement. The results of the calculations demonstrate that the derived formula is valid for a wide range of parameters.

Ion acoustic solitons collision in spin-polarized relativistic quantum plasma

The dynamics of electrostatic ion acoustic solitons collision in relativistic magnetized spin-polarized plasma is studied using a Magnetized Relativistic Quantum Hydrodynamics model. The plasmas components are relativistic degenerate electron with spin-up (n e↑) and spin-down (n e↓) concentrations, and relativistic inertial classical ions. In two-dimensional plasma geometry, a homogeneous external magnetic field is provided along the z-direction, i.e. . The extended Poincare Lighthill Kuo (PLK) approach is used to calculate the Kortewegde Vries equations for oppositely moving ion-acoustic solitons. Before and after collision, their trajectories and associated phase shifts are computed. Only negative polarity pulses of ion acoustic solitons are observed in our stated relativistic magnetized plasma. The spin density popularization ratio κ is shown to have a significant impact on the phase shifts of colliding solitons. It is found that when κ increases, one soliton's phase shift increases while the other soliton's phase shift decreases. The relativistic effects are also analyzed numerically and found that the phase shift of colliding ions acoustic solitons grows as the relativistic component rises from weakly to ultra-relativistic. It is observed that the phase shift of both solitons is to be dependent on their phase velocity with each other. Our research is noteworthy in that it focuses on, the astrophysical systems such as white dwarf, neutron star and pulsar.

Radiation reaction effects in relativistic plasmas: The electrostatic limit.

We study the evolution of electrostatic plasma waves, using the relativistic Vlasov equationextended by the Landau-Lifshitz radiation reaction, accounting for the back-reaction due to the emission of single particle Larmor radiation. In particular, the Langmuir wave damping is calculated as a function of wave number, initial temperature, and initial electric field amplitude. Moreover, the background distribution function loses energy in the process, and we calculate the cooling rate as a function of initial temperature and initial wave amplitude. Finally, we investigate how the relative magnitude of wave damping and background cooling varies with the initial parameters. In particular, it is found that the relative contribution to the energy loss associated with background cooling decreases slowly with the initial wave amplitude.

Electron-positron pair plasmas: past, present, and future

An overview of recent progress highlights remaining challenges and future opportunities associated with producing and studying relativistic pair plasmas in the lab.

Hypermagnetic power spectra and the phases of Sakharov oscillations

If the gauge fields are amplified from the inflationary vacuum, the quantum mechanical initial data correspond to travelling waves that turn asymptotically into standing waves whose phases only depend on the evolution of the gauge coupling. We point out that these gauge analogs of the Sakharov oscillations are exchanged by the duality symmetry and ultimately constrain both the relative scaling of the hypermagnetic power spectra and their final asymptotic values. Unlike the case of the density contrasts in a relativistic plasma, the standing oscillations never develop since they are eventually overdamped by the finite value of the conductivity as soon as the corresponding modes are comparable with the expansion rates after inflation. We show that the late-time value of the magnetic field is not determined at radiation dominance (and in spite of the value of the wavenumber) but it depends on the moment when the wavelengths (comparable with the Mpc) get of the order of the Hubble radius before equality. This means that the magnetogenesis requirements are only relaxed if the post-inflationary expansion rate is slower than radiation but the opposite is true when the plasma expands faster than radiation and the corresponding power spectra are further suppressed. After combining the present findings with the evolution of the gauge coupling we show that these results are consistent with a magnetogenesis scenario where the gauge coupling is always perturbative during the inflationary stage while, in the dual case, the same requirements cannot be satisfied.