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, the dynamics of an amplitude modulated R-D-MHD waves is governed by the cubic nonlinear Schroedinger equation. The latter has been derived by using the reductive perturbation technique and the two-timescale analysis which accounts for the harmonic generation nonlinearity in plasmas. The stability of the modulated wave envelope against non-resonant perturbations is studied. Finally, the possibility of localized envelope excitations is discussed.
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…
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 …
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…
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 …
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…
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 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)].
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 …
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…
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 …
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…
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…
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…
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…
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…
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…
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…
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.
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 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…
A nonlinear time dependent fluid simulation model is developed that describes the evolution of magnetohydrodynamic waves in the presence of collisional and charge exchange interactions of a partially ionized plasma. The partially ionized plasma consists of electrons, ions and a significant number of neutral atoms. In our model, the electrons and ions are described by a single fluid compressible magnetohydrodynamic (MHD) model and are coupled self-consistently to the neutral gas, described by the compressible hydrodynamic equations. Both the plasma and neutral fluids are treated with different …
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…
It is shown that low-collisionality plasmas cannot support linearly polarized shear-Alfvén fluctuations above a critical amplitude $δB_{\perp}/B_{0} \sim β^{\,-1/2}$, where $β$ is the ratio of thermal to magnetic pressure. Above this cutoff, a developing fluctuation will generate a pressure anisotropy that is sufficient to destabilize itself through the parallel firehose instability. This causes the wave frequency to approach zero, interrupting the fluctuation before any oscillation. The magnetic field lines rapidly relax into a sequence of angular zig-zag structures. Such a restrictive bound …
This work, which extends Squire et al. [ApJL, 830 L25 (2016)], explores the effect of self-generated pressure anisotropy on linearly polarized shear-Alfvén fluctuations in low-collisionality plasmas. Such anisotropies lead to stringent limits on the amplitude of magnetic perturbations in high-beta plasmas, above which a fluctuation can destabilize itself through the parallel firehose instability. This causes the wave frequency to approach zero, "interrupting" the wave and stopping its oscillation. These effects are explored in detail in the collisionless and weakly collisional "Braginskii" reg…
In this work, we derive a dispersion equation that describes the excitation of the oblique (or Alfvén) firehose instability in a plasma that contains both electron and ion species modelled by bi-kappa velocity distribution functions. The equation is obtained with the assumptions of low-frequency waves and moderate to large values of the parallel (respective to the ambient magnetic field) plasma beta parameter, but it is valid for any direction of propagation and for any value of the particle gyroradius (or Larmor radius). Considering values for the physical parameters typical to those found in…
Understanding the removal of energy from turbulent fluctuations in a magnetized plasma and the consequent energization of the constituent plasma particles is a major goal of heliophysics and astrophysics. Previous work has shown that nonlinear interactions among counterpropagating Alfven waves---or Alfven wave collisions---are the fundamental building block of astrophysical plasma turbulence and naturally generate current sheets in the strongly nonlinear limit. A nonlinear gyrokinetic simulation of a strong Alfven wave collision is used to examine the damping of the electromagnetic fluctuation…
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 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…
We present a theoretical framework for plasma turbulence in astrophysical plasmas (solar wind, interstellar medium, galaxy clusters, accretion disks). The key assumptions are that the turbulence is anisotropic with respect to the mean magnetic field and frequencies are low compared to the ion cyclotron frequency. The energy injected at the outer scale scale has to be converted into heat, which ultimately cannot be done without collisions. A KINETIC CASCADE develops that brings the energy to collisional scales both in space and velocity. Its nature depends on the physics of plasma fluctuations.…
Analytical expressions for the dispersion relations and polarizations of low-frequency waves in magnetized plasmas based on two-fluid model are obtained. The properties of waves propagating at different angles (to the ambient magnetic field $\mathbf{B}_{0}$) and β(the ratio of the plasma to magnetic pressures) values are investigated. It is shown that two linearly polarized waves, namely the fast and Alfvén modes in the low-β$\left( β\ll 1\right)$ plasmas, the fast and slow modes in the β\sim 1 plasmas, and the Alfvén and slow modes in the high-β$\left( β\gg 1\right)$ plasmas, become circularl…
Whistler-Alfvén turbulence in a non-neutral ultrarelativistic pair plasma
University of Wisconsin at Madison（威斯康星大学麦迪逊分校）；Space Science Institute（空间科学研究所）；University of Kansas（堪萨斯大学）；Massachusetts Institute of Technology（麻省理工学院）
Observations of interstellar scintillations at radio wavelengths reveal a Kolmogorov-like scaling of the electron density spectrum with a spectral slope of -5/3 over six decades in wavenumber space. A similar turbulent density spectrum in the solar wind plasma has been reported. The energy transfer process in the magnetized solar wind plasma over such extended length-scales remains an unresolved paradox of modern turbulence theories raising the especially intriguing question of how a compressible magnetized solar wind exhibits a turbulent spectrum that is a characteristic of an incompressible …
The characteristics of Alfvén waves propagating in a direction oblique to the ambient magnetic field in a stellar wind environment are discussed. A kinetic formulation for a magnetized dusty plasma is adopted considering Maxwellian distributions of electrons and ions, and immobile dust particles electrically charged by absorption of plasma particles and by photoionization. The dispersion relation is numerically solved and the results are compared with situations previously studied where dust particles were not charged by photoionization, which is an important process in a stellar wind of a rel…
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…
Alfvénic component of MHD turbulence damps Alfvénic waves. The consequences of this effect are important for many processes, from cosmic ray (CR) propagation to launching outflows and winds in galaxies and other magnetized systems. We discuss the differences in the damping of the streaming instability by turbulence and the damping of a plane parallel wave. The former takes place in the system of reference aligned with the local direction of magnetic field along which CRs stream. The latter is in the reference frame of the mean magnetic field and traditionally considered in plasma studies. We a…
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…
A Hamiltonian two-field gyrofluid model for kinetic Alfvén waves (KAWs) in a magnetized electron-proton plasma, retaining ion finite-Larmor-radius corrections and parallel magnetic field fluctuations, is used to study the inverse cascades that develop when turbulence is randomly driven at sub-ion scales. In the directions perpendicular to the ambient field, the dynamics of the cascade turns out to be nonlocal and the ratio $χ_f$ of the wave period to the characteristic nonlinear time at the driving scale affect some of its properties. For example, at small values of $χ_f$, parametric decay ins…
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…
Both global dynamics and turbulence in magnetized weakly collisional cosmic plasmas are described by general magnetofluid equations that contain pressure anisotropies and heat fluxes that must be calculated from microscopic plasma kinetic theory. It is shown that even without a detailed calculation of the pressure anisotropy or the heat fluxes, one finds the macroscale dynamics to be generically unstable to microscale Alfvenically polarized fluctuations. Two instabilities are considered in detail: the parallel firehose instability (including the finite-Larmor-radius effects that determine the …
Magnetic reconnection in strongly magnetized (low-beta), weakly collisional plasmas is investigated using a novel fluid-kinetic model [Zocco & Schekochihin, Phys. Plasmas 18, 102309 (2011)] which retains non-isothermal electron kinetics. It is shown that electron heating via Landau damping (linear phase mixing) is the dominant dissipation mechanism. In time, electron heating occurs after the peak of the reconnection rate; in space, it is concentrated along the separatrices of the magnetic island. For sufficiently large systems, the peak reconnection rate is $cE_{max}\approx 0.2v_AB_{y,0}$, whe…
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…
Weak turbulence of magnetohydrodynamic (MHD) waves in strongly magnetized plasma is studied when the thermal pressure is less than the magnetic field pressure. In this situation the main nonlinear mechanism is the resonance scattering of fast magneto-acoustic and Alfvenic waves on slow magneto-acoustic waves. As a result, the former waves serve as the high-frequency waves with respect to the latter ones so that the total number of HF waves - an adiabatic invariant - conserves additionally. In the weak turbulence regime this invariant is shown to generate the Kolmogorov type spectrum with a con…
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…
Astrophysical plasmas are turbulent and magnetized. The interaction between cosmic rays (CRs) and magnetohydrodynamic (MHD) turbulence is a fundamental astrophysical process. Based on the current understanding of MHD turbulence, we revisit the trapping of CRs by magnetic mirrors in the context of MHD turbulence. In compressible MHD turbulence, isotropic fast modes dominate both trapping and gyroresonant scattering of CRs. The presence of trapping significantly suppresses the pitch-angle scattering and the spatial diffusion of CRs along the magnetic field. The resulting parallel diffusion coeff…
A phenomenological turbulence model for kinetic Alfvén waves in a magnetizedcollisionless plasma, able to reproduce the non-universalpower-law spectra observed at the sub-ion scales in the solar wind and the terrestrial magnetosphere, is presented.The process of temperature homogenization along distortedmagnetic field lines, induced by Landau damping,affects the turbulencetransfer time and results in a steepening of the sub-ion power-law spectrumof critically-balanced turbulence, whose exponent is sensitive to the ratio between the Alfvén wave period and the nonlinear timescale. Transition fro…
