Nonlinear set of equations for inertial or slow shear Alfven wave (SSAW) in ideal electron-positron-ion (e-p-i) plasmas are presented. The analytical solution for arbitrary amplitude SSAW in such multi-component plasmas is obtained using Sagdeev potential approach. The numerical solutions for several different cases have also been presented for illustrative purpose. It is found that the electron density dips of SSAW are formed in the super Alfvenic region. The amplitude and the width of the nonlinear shear Alfven wave reduces with the increase in the concentration of positrons in electron-ion (e-i) plasmas. The width of the soliton also depends upon the direction of propagation of the perturbation in both e-i and e-p-i plasmas.
The linear dispersion relation of a finite amplitude, parallel, circularly polarized Alfvén wave in a relativistic electron-positron plasma is derived. In the nonrelativistic regime, the dispersion relation has two branches, one electromagnetic wave, with a low frequency cutoff at $\sqrt{1+2ω_p^2/Ω_p^2}$ (where $ω_p=(4πn e^2/m)^{1/2}$ is the electron/positron plasma frequency), and an Alfvén wave, with high frequency cutoff at the positron gyrofrequency $Ω_p$. There is only one forward propagating mode for a given frequency. However, due to relativistic effects, there is no low frequency cutof…
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…
In this paper, we obtain the dispersion relation for the lower-hybrid oscillations/waves in a cold magnetized electron-positron-ion (e-p-i) plasma. It is found that the frequency of the lower-hybrid oscillations in an e-p-i plasma is approximate $1/\sqrt{3}$ times the frequency of lower-hybrid oscillations in an electron-ion (e-i) plasma, provided the plasma density is high, and the equilibrium densities of the positron and the ion are balanced. The present work may have some relevance for laboratory/astrophysical e-p-i plasmas.
The nonlinear dynamics of coupled electrostatic upper-hybrid (UH) and Alfven waves (AWs) is revisited in a magnetized electron-ion plasma with charged dust impurities. A pair of nonlinear equations that describe the interaction of UH wave envelopes (including the relativistic electron mass increase) and the density as well as the compressional magnetic field perturbations associated with the AWs is solved numerically to show that many coherent solitary patterns can be excited and saturated due to modulational instability of unstable UH waves. The evolution of these solitary patterns is also sh…
The gyrokinetic stability of electron-positron plasmas contaminated by ion (proton) admixture is studied in slab geometry. The appropriate dispersion relation is derived and solved. The ion-temperature-gradient driven instability, the electron-temperature-gradient driven instability, the universal mode, and the shear Alfven wave are considered. The contaminated plasma remains stable if the contamination degree is below some threshold, and it is found that the shear Alfven wave can be present in a contaminated plasma in cases where it is absent without ion contamination.
Nonlinear propagation of purely stationary large amplitude electromagnetic (EM) solitary waves in a magnetized electron-positron (EP) plasma is studied using a fully relativistic two-fluid hydrodynamic model which accounts for physical regimes of both weakly relativistic $(P\ll nmc^2)$ and ultrarelativistic $(P\gg nmc^2)$ random thermal energies. Here, $P$ is the thermal pressure, $n$ the number density and $m$ the mass of a particle, and $c$ is the speed of light in vacuum. Previous theory in the literature [Phys. Plasmas \textbf{11}, 3078 (2004)] is advanced and generalized by the relativist…
The dispersion properties of elliptically polarized electromagnetic (EM) waves in a magnetized electron-positron-pair (EP-pair) plasma are studied with the effects of particle dispersion associated with the Bohm potential, the Fermi degenerate pressure, and the exchange-correlation force. Two possible modes of the extraordinary or X wave, modified by these quantum effects, are identified and their propagation characteristics are investigated numerically. It is shown that the upper-hybrid frequency, and the cutoff and resonance frequencies are no longer constants but are dispersive due to these…
A long standing puzzle in fusion research comes from experiments where a sudden peripheral electron temperature perturbation is accompanied by an almost simultaneous opposite change in central temperature, in a way incompatible with local transport models. This paper shows these experiments and similar ones are fairly well quantitatively reproduced, when induction effects are incorporated in the total plasma response, alongside standard local diffusive transport, as suggested in earlier work [V.D. Pustovitov, Plasma Phys. Control. Fusion {\bf 54}, 124036 (2012)].
Resonant three-wave coupling is an important mechanism via which waves interact in a nonlinear medium. When the medium is a magnetized warm-fluid plasma, a previously-unknown formula for the coupling coefficients is derived by solving the fluid-Maxwell's equations to second order using multiscale perturbative expansions. The formula is not only general but also evaluable, whereby numerical values of the coupling coefficient can be determined for any three resonantly interacting waves propagating at arbitrary angles. As one example, coupling coefficient governing laser scattering is evaluated. …
A conservative scheme has been formulated and verified for gyrokinetic particle simulations of electromagnetic waves and instabilities in magnetized plasmas. An electron continuity equation derived from drift kinetic equation is used to time advance electron density perturbation by using the perturbed mechanical flow calculated from the parallel vector potential, and the parallel vector potential is solved by using the perturbed canonical flow from the perturbed distribution function. In gyrokinetic particle simulations using this new scheme, shear Alfvén wave dispersion relation in shearless …
Magnetohydrodynamical evolution of the Richtmyer-Meshkov instability (RMI) is investigated by two-dimensional MHD simulations. The RMI is suppressed by a strong magnetic field, whereas the RMI amplifies an ambient magnetic field by many orders of magnitude if the seed field is weak. We have found that the suppression and amplification processes can be evaluated continuously along with the amplitude of the Alfvén number $R_A$, which is defined as the ratio of the linear growth velocity of the RMI to the Alfvén speed at the interface. When the Alfvén number is less than unity, the Lorentz force …
The low frequency, long wavelength electromagnetic waves, viz, shear Alfven wave in quantum electron-positron-ion magneto plasmas, have been examined using quantum magneto hydrodynamic model. In this model, we have considered electrons and positrons are to be magnetized as well as degenerate whereas ions are magnetized but classical. We have also included the effects of exchange correlation terms which appear entirely the dynamic equations of electrons and positrons. The whole treatment is done using multi-fluid model. Our object is to study the shear Alfvén waves propagating in above said sys…
The nonlinear propagation of a circularly polarized electromagnetic (CPEM) wave in a strongly magnetized electron-positron-ion plasma is investigated. Two coupled equations describing the interaction between a high-frequency CPEM wave and the low-frequency electrostatic wake field are derived. It is found that the generation of the wake fields depends on the presence of the ion species. The wake field generation in turn leads to de-acceleration and frequency down conversion of the electromagnetic pulse.
Collisionless coupling between super Alfvénic ions and an ambient plasma parallel to a background magnetic field is mediated by a set of electromagnetic ion/ion-beam instabilities including the resonant right hand instability (RHI). To study this coupling and its role in parallel shock formation, a new experimental configuration at the University of California, Los Angeles utilizes high-energy and high-repetition-rate lasers to create a super-Alfvénic field-aligned debris plasma within an ambient plasma in the Large Plasma Device (LAPD). We used a time-resolved fluorescence monochromator and a…
We study the spatio-temporal evolution of the nonlinear electrostatic oscillations in a cold magnetized electron-positron (e-p) plasma using both analytics and simulations. Using a perturbative method we demonstrate that the nonlinear solutions change significantly when a pure electrostatic mode is excited at the linear level instead of a mixed upper-hybrid and zero-frequency mode that is considered in a recent study. The pure electrostatic oscillations undergo phase mixing nonlinearly. However, the presence of the magnetic field significantly delays the phase-mixing compared to that observed …
Using direct numerical simulations of three-dimensional magnetohydrodynamic (MHD) turbulence the spatio-temporal behavior of magnetic field fluctuations is analyzed. Cases with relatively small, medium and large values of a mean background magnetic field are considered. The (wavenumber) scale dependent time correlation function is directly computed for different simulations, varying the mean magnetic field value. From this correlation function the time decorrelation is computed and compared with different theoretical times, namely, the local non-linear time, the random sweeping time, and the A…
In this work we investigate the characteristics of the group velocity of obliquely propagating Alfvén waves in a dusty plasma typical of a stellar wind. The dispersion relation is derived with the aid of the kinetic theory for a magnetized dusty plasma consisting of electrons and ions, with distribution of momenta described by a Maxwellian function. The dust particles are considered to be immobile and have all the same size; they are electrically charged by absorption of plasma particles via inelastic collisions and by photoionization. We numerically solve the dispersion relation and calculate…
A theoretical investigation is carried out to understand the basic features of nonlinear propagation of heavy ion-acoustic (HIA) waves subjected to an external magnetic field in an electron-positron-ion (EPI) plasma which consists of cold magnetized positively charged heavy ion fluids, and superthermal distributed electrons and positrons. In the nonlinear regime, the Korteweg-de Vries (K-dV) and modified K-dV(MK-dV) equations describing the propagation of HIA waves are derived. The latter admits a solitary wave solution with both positive and negative potentials (for K-dV equation) and only po…
Alfvénic-type turbulence in strongly magnetized, low-beta pair plasmas is investigated. A coupled set of equations for the evolution of the magnetic and flow potentials are derived, covering both fluid and kinetic scales. In the fluid (MHD) range those equations are the same as for electron-ion plasmas, so turbulence at those scales is expected to be of the Alfvénic nature, exhibiting critical balance, dynamic alignment, and transition to a tearing mediated regime at small scales. The critical scale at which a transition to a tearing-mediated range occurs is derived, and the spectral slope in …
The linear and nonlinear properties of the Rao-dust-magnetohydrodynamic (R-D-MHD) waves in a dusty magnetoplasma are studied. By employing the inertialess electron equation of motion, inertial ion equation of motion, Ampère's law, Faraday's law, and the continuity equation in a plasma with immobile charged dust grains, the linear and nonlinear propagation of two-dimensional R-D-MHD waves are investigated. In the linear regime, the existence of immobile dust grains produces the Rao cutoff frequency, which is proportional to the dust charge density and the ion gyrofrequency. On the other hand, t…
It is often asserted or implicitly assumed, without justification, that the results of two-dimensional investigations of plasma turbulence are applicable to the three-dimensional plasma environments of interest. A projection method is applied to derive two scalar equations that govern the nonlinear evolution of the Alfvenic and pseudo-Alfvenic components of ideal incompressible magnetohydrodynamic (MHD) plasma turbulence. The mathematical form of these equations makes clear the inherently three-dimensional nature of plasma turbulence, enabling an analysis of the nonlinear properties of two-dim…
A generalized hydrodynamical model has been used to study low frequency modes in a strongly coupled, cold, magnetized dusty plasma. Such plasmas exhibit elastic properties due to strong correlations among dust particles and the tensile stresses imparted by the magnetic field. It has been shown that longitudinal compressional Alfven modes and elasticity modified transverse shear mode exist in such a medium. The features of these collective modes are established and discussed.
Large amplitude kinetic Alfvénon (exact Alfvén soliton) matching condition is investigated in quasineutral electron-ion and electron-positron-ion plasmas immersed in a uniform magnetic field. Using the standard pseudopotential method, the magnetohydrodynamics (MHD) equations are exactly solved and a global allowed matching condition for propagation of kinetic solitary waves is derived. It is remarked that, depending on the plasma parameters, the kinetic solitons can be sub- or super-Alfvénic, in general. It is further revealed that, either upper or lower soliton speed-limit is independent of f…
One-dimensional PIC Simulation of Induced Compton Scattering in Magnetized Electron-Positron Pair Plasma
Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所引力物理与量子信息中心）；Department of Physics, Kyoto University（京都大学物理学系）；Graduate School of System Informatics, Kobe University（神户大学系统信息学研究）
In a magnetized plasma, both the transverse and longitudinal Alfvén waves carry an average energy density that, for each mode of oscillation, resembles the classical energy of a harmonic oscillator with unit mass and angular frequency that depends on the background magnetic field and plasma density. We employ this fact to introduce a pair of canonical variables for the underlying classical system, and then use the canonical quantization procedure to express the Alfvén wave velocity (or the corresponding plasma displacement vector) in terms of creation and annihilation operators. We thus introd…
We have derived the full set of MHD equations for incompressible shear flow of a magnetized fluid and considered their solution in the wave-vector space. The linearized equations give the famous amplification of slow magnetosonic waves and describe the magnetorotational instability. The nonlinear terms in our analysis are responsible for the creation of turbulence and self-sustained spectral density of the MHD (Alfven and pseudo-Alfven) waves. Perspectives for numerical simulations of weak turbulence and calculation of the effective viscosity of accretion disks are shortly discussed in k-space…
Beam instabilities in the strongly magnetized electron-positron plasma of pulsar magnetospheres are considered. We analyze the resonance conditions and estimate the growth rates of the Cherenkov and cyclotron instabilities of the ordinary (O), extraordinary (X) and Alfvén modes in two limiting regimes: kinetic and hydrodynamic. As a preliminary step, we reconsider wave dispersion and polarization properties in a one dimensional pair plasma taking into account relativistic thermal effects. We then find the location of the Cherenkov and cyclotron resonance of the X, O and Alfvén waves with the p…
The formation of small but finite amplitude electrostatic shocks in the propagation of quantum ion-acoustic waves (QIAWs) obliquely to an external magnetic field is reported in a quantum electron-positron-ion (e-p-i) plasma. Such shocks are seen to have double-layer (DL) structures composed of the compressive and accompanying rarefactive slow-wave fronts. Existence of such DL shocks depends critically on the quantum coupling parameter $H$ associated with the Bohm potential and the positron to electron density ratio $δ$. The profiles may, however, steepen initially and reach a steady state with…
Interchange drive and cross-field transport of density filaments in quasi-neutral inhomogeneously magnetized electron-positron plasmas is shown to be strongly reduced by the presence of minority ions. Two mechanisms are identified for the reduction in radial propagation and plasma transport: effective mass related inertia, and collisionality dependent Boltzmann spin-up of the filaments. Numerical results are obtained with a three-dimensional full-F multi-species gyrofluid model.
The existence of the dust acoustic wave (DAW) in a strongly magnetized electron-positron (pair)-dust plasma is demonstrated. In the DAW, the restoring force comes from the pressure of inertialess electrons and positrons, and the dust mass provides the inertia. The waves could be of interest in astrophysical settings such as the supernovae and pulsars, as well as in cluster explosions by intense laser beams in laboratory plasmas.
The properties of nucleus-acoustic (NA) solitary waves (SWs) and double layers (DLs) in a four-component magnetized degenerate quantum plasma system (containing non-degenerate inertial light nuclei, both non-relativistically and ultra-relativistically degenerate electrons and positrons, and immobile heavy nuclei) are theoretically investigated by the reductive perturbation method. The Korteweg-de Vries (K-dV), the modified K-dV (MK-dV), and the Gardner equations are derived to examine the basic features (viz. amplitude, speed, and width) of NA SWs and DLs. It is found that the effects of the u…
A rigorous theoretical investigation has been made on the nonlinear propagation of dust-ion-acoustic shock waves in a multi-component magnetized pair-ion plasma having inertial warm positive and negative ions, inertialess non-thermal electrons and positrons, and static negatively charged massive dust grains. The Burgers' equation is derived by employing reductive perturbation method. The plasma model supports both positive and negative shock structures in the presence of static negatively charged massive dust grains. It is found that the steepness of both positive and negative shock profiles d…
We discuss complete theory of spin-1/2 electron-positron quantum plasmas, when electrons and positrons move with velocities mach smaller than the speed of light. We derive a set of two fluid quantum hydrodynamic equations consisting of the continuity, Euler, spin (magnetic moment) evolution equations for each species. We explicitly include the Coulomb, spin-spin, Darwin and annihilation interactions. The annihilation interaction is the main topic of the paper. We consider contribution of the annihilation interaction in the quantum hydrodynamic equations and in spectrum of waves in magnetized e…
A set of fluid equations, taking into account the spin properties of the electrons and positrons in a magnetoplasma, are derived. The magnetohydrodynamic limit of the pair plasma is investigated. It is shown that the microscopic spin properties of the electrons and positrons can lead to interesting macroscopic and collective effects in strongly magnetized plasmas. In particular, it is found that new Alfvenic solitary structures, governed by a modified Korteweg-de Vries equation, are allowed in such plasmas. These solitary structures vanish if the quantum spin effects are neglected. Our results…
We present a new model for simulating the electromagnetic fluctuations with frequencies much lower than the ion cyclotron frequency in plasmas confined in general magnetic configurations. This novel model (termed as GK-E&B) employs nonlinear gyrokinetic equations formulated in terms of electromagnetic fields along with momentum balance equations for solving fields. It, thus, not only includes kinetic effects, such as wave-particle interaction and microscopic (ion Larmor radius scale) physics; but also is computationally more efficient than the conventional formulation described in terms of pot…
Alfvén wave collisions are the primary building blocks of the non-relativistic turbulence that permeates the heliosphere and low-to-moderate energy astrophysical systems. However, many astrophysical systems such as gamma-ray bursts, pulsar and magnetar magnetospheres, and active galactic nuclei have relativistic flows or energy densities. To better understand these high energy systems, we derive reduced relativistic MHD equations and employ them to examine weak Alfvénic turbulence, dominated by three-wave interactions, in reduced relativistic magnetohydrodynamics, including the force-free, inf…
The evolution of a linearly-polarized, long-wavelength Alfvén wave --propagating in a collisionless magnetized plasma with a sheared parallel-directed velocity flow-- is here studied by means of two-dimensional hybrid Vlasov-Maxwell (HVM) simulations. The unperturbed sheared flow has been represented by an exact solution of the HVM set of equations (Malara {\it et al.}, Phys. Rev. E 97, 053212), this avoiding spurious oscillations that would arise from the non-stationary initial state and inevitably affect the dynamics of the system. We have considered the evolution of both a small and a moder…
In this paper, the evolution of the induced axial magnetization due to the propagation of an electromagnetic (em) wave along the static background magnetic field in a two-component plasma has been investigated using the Block equation. The evolution process induces a strong magnetic anisotropy in the plasma medium, depending nonlinearly on the incident wave amplitude. This induced magnetic anisotropy can modify the dispersion relation of the incident em wave, which has been obtained in this paper. In the low frequency Alfven wave limit, this dispersion relation shows that the resulting phase v…
Alfvén waves as excited in black hole accretion disks and neutron star magnetospheres are the building blocks of turbulence in relativistic, magnetized plasmas. A large reservoir of magnetic energy is available in these systems, such that the plasma can be heated significantly even in the weak turbulence regime. We perform high-resolution three-dimensional simulations of counter-propagating Alfvén waves, showing that an $E_{B_{\perp}}(k_{\perp}) \propto k_{\perp}^{-2}$ energy spectrum develops as a result of the weak turbulence cascade in relativistic magnetohydrodynamics and its infinitely ma…
We extend the classical two-fluid magnetohydrodynamic (MHD) formalism to include quantum effects such as electron Fermi pressure, Bohm pressure and spin couplings. At scales smaller than the electron skin-depth, the Hall effect and electron inertia must be taken into account, and can overlap with the quantum effects. We write down the full set of two-fluid quantum MHD (QMHD) and analyze the relative importance ofthese effects in the high density environments of neutron star atmospheres and white dwarf interiors, finding that for a broad range of parameters all these effects are operative. Of a…
The interaction of laser with plasmas leads to many interesting phenomena which includes laser energy absorption, mode conversion, energetic particle generation etc. In this work, the excitation of Korteweg - de Vries (KdV) Alfven solitons in plasma is demonstrated with the help of 2-D Particle - In - Cell (PIC) simulations. For this purpose, the propagation of a pulsed $CO_2$ (with a wavelength of $10 μm$) laser normally incident on an overdense plasma target is considered in the presence of an external magnetic field. The magnitude of the external magnetic field is chosen so as to have the e…
The density fluctuation spectrum in the solar wind reveals a Kolmogorov-like scaling with a spectral slope of -5/3 in wavenumber space. The energy transfer process in the magnetized solar wind, characterized typically by MHD turbulence, over extended length-scales remains an unresolved paradox of modern turbulence theories, raising the question of how a compressible magnetofluid exhibits a turbulent spectrum that is characteristic of an incompressible hydrodynamic fluid. To address these questions, we have undertaken three-dimensional time dependent numerical simulations of a compressible magn…
The density fluctuation spectrum in the solar wind reveals a Kolmogorov-like scaling with a spectral slope of -5/3 in wavenumber space. The energy transfer process in the magnetized solar wind, characterized typically by MHD turbulence, over extended length-scales remains an unresolved paradox of modern turbulence theories, raising the question of how a compressible magnetofluid exhibits a turbulent spectrum that is characteristic of an incompressible hydrodynamic fluid. To address these questions, we have undertaken three-dimensional time dependent numerical simulations of a compressible magn…
The effects of charge exchange on waves propagating in weakly ionized plasmas are discussed. It is shown that for low-frequency processes, ions and neutrals should be treated as a single fluid with some effective charge on all of them. We have derived a new momentum equation which should be used in such an environment. As a result, the low-frequency magnetic waves can propagate even if particles are not magnetized, which is entirely due to the charge exchange and the fact that it is not possible to separate particles into two different populations as charged and neutral species. So there can b…
The saturation mechanism of the Weibel instability is investigated theoretically by considering the evolution of currents in numerous cylindrical beams that are generated in the initial stage of the instability. Based on a physical model of the beams, it is shown that the magnetic field strength attains a maximum value when the currents in the beams evolve into the Alfven current and that there exist two saturation regimes. The theoretical prediction of the magnetic field strength at saturation is in good agreement with the results of two-dimensional particle-in-cell simulations for a wide ran…
The nonlinear interaction between counterpropagating Alfven waves is the physical mechanism underlying the cascade of energy to small scales in astrophysical plasma turbulence. Beginning with the equations for incompressible MHD, an asymptotic analytical solution for the nonlinear evolution of these Alfven wave collisions is derived in the weakly nonlinear limit. The resulting qualitative picture of nonlinear energy transfer due to this mechanism involves two steps: first, the primary counterpropagating Alfven waves interact to generate an inherently nonlinear, purely magnetic secondary fluctu…
