Toroidal Magnetic Field Generation in the Magnetosphere of Crab Pulsar

Plasma mechanism for the generation of toroidal magnetic field in the magnetosphere of Crab pulsar is presented. The mechanism is based on the development of parametric type instability in the relativistic electron-positron plasma of the pulsar magnetosphere. As a result of plasma corotation with pulsar and its magnetic field, the effect of plasma radial braking takes place and the time dependence of plasma particle radial velocity is harmonic. This triggers the development of parametric type instability in the relativistic plasma of the pulsar magnetosphere. The energy for this process is drawn from the slowing down of pulsar rotation.     

Theory of the radio emission of pulsars

A consistent theory of excitation, stabilization, and propagation of electromagnetic oscillations in a relativistic one-dimensional electron-positron plasma flowing along curved magnetic field lines is presented. It is shown that in such a medium which is typical of the magnetosphere of a neutron star there exist unstable natural modes of oscillations. Nonlinear saturation of the instability leads to an effective energy conversion into transverse oscillations capable of leaving the magnetosphere of a pulsar. The polarization spectrum and the directivity pattern of generated radiation are determined. A comparison with observations has shown that the theory makes it possible to explain practically all the basic characteristics of observed pulsar radio emission.     

3-D Rpic Simulations of Relativistic Jets: Particle Acceleration, Magnetic Field Generation, and Emission

We have applied numerical simulations and modeling to the particle acceleration, magnetic field generation, and emission from relativistic shocks. We investigate the nonlinear stage of theWeibel instability and compare our simulations with the observed gamma-ray burst emission. In collisionless shocks, plasma waves and their associated instabilities (e.g., the Weibel, Buneman and other two-stream instabilities) are responsible for particle (electron, positron, and ion) acceleration and magnetic field generation. 3-D relativistic electromagnetic particle (REMP) simulations with three different electron-positron jet velocity distributions and also with an electron-ion plasma have been performed and show shock processes including spatial and temporal evolution of shocks in unmagnetized ambient plasmas. The growth time and nonlinear saturation levels depend on the initial jet parallel velocity distributions. Simulations show that the Weibel instability created in the collisionless shocks accelerates jet and ambient particles both perpendicular and parallel to the jet propagation direction. The nonlinear fluctuation amplitude of densities, currents, electric, and magnetic fields in the electron-positron shocks are larger for smaller jet Lorentz factor. This comes from the fact that the growth time of the Weibel instability is proportional to the square of the jet Lorentz factor. We have performed simulations with broad Lorentz factor distribution of jet electrons and positrons, which is assumed to be created by photon annihilation. Simulation results with this broad distribution show that the Weibel instability is excited continuously by the wide-range of jet Lorentz factor from lower to higher values. In all simulations the Weibel instability is responsible for generating and amplifying magnetic fields perpendicular to the jet propagation direction, and contributes to the electron’s (positron’s) transverse deflection behind the jet head. This small scale magnetic field structure contributes to the generation of “jitter” radiation from deflected electrons (positrons), which is different from synchrotron radiation in uniform magnetic fields. The jitter radiation resulting from small scale magnetic field structures may be important for understanding the complex time structure and spectral evolution observed in gamma-ray bursts or other astrophysical sources containing relativistic jets and relativistic collisionless shocks. The detailed studies of shock microscopic process evolution may provide some insights into early and later GRB afterglows.     

Variations of cosmic-ray energy in interplanetary space

A consistent theory of energy exchange between high-energy charged cosmic-ray particles and the random inhomogeneities of a magnetic field frozen in the moving solar wind plasma is developed. It is shown that the mode of the particle energy variations at a given law of plasma velocity variation in space is determined by the specific form of the particle distribution function. The equation for the density of cosmic-ray energy is obtained. Consideration is given to the generation of a charged particle energy spectrum in the course of multiple scatterings by the random inhomogeneities of the magnetic field.     

Nonlinear Drift-Alfvén Waves in Relativistically Hot Nonuniform Electron-Positron Plasmas

The magnetic viscosity tensor is derived for a magnetized relativistic collisionless plasma with temperature gradients. By means of this tensor we deduce the nonlinear equations for drift–Alfvén waves in a relativistic electron-positron low plasma with density and temperature gradients. It is shown that our new equations have solutions in the form of dipolar vortices. The present results should be relevant to a number of astrophysical objects with strong electron-positron pair production, e.g. in pulsars as well as in accretion disks and jets.     

Polarization spectra of synchrotron radiation and the plasma composition of relativistic jets

We investigate the problem of determining the plasma composition of relativistic jets in blazars and microquasars from the polarization frequency spectra of their synchrotron radiation. The effect of plasma composition on this radiation is attributable to a change in the structure of the ordinary and extraordinary waves in plasma, depending on the presence of a nonrelativistic electron-proton component in it and on the type of relativistic particles (electrons, positrons). The structure of the normal waves determines the properties of the observed radiation and primarily the shape of the polarization frequency spectrum. Our analytic calculations of the polarization spectra for simple models of jets with a uniform magnetic field and with a magnetic-field shear revealed characteristic features in the polarization spectra. These features allow us to differentiate between the synchrotron radiation from an admixture of relativistic particles in a cold plasma and the radiation from a relativistic plasma. However, definitive conclusions regarding the relativistic plasma composition (electrons or electron-positron pairs) can be reached only by a detailed analysis of the polarization frequency spectra that will be obtained in future radioastronomical studies with high angular and frequency resolutions.     

Cosmic rays from collapsing magnetized stars

We examine the acceleration of cosmic rays in the magnetospheres of collapsing stars with initial dipole magnetic fields and various initial energy distributions of charged particles in their magnetospheres (the exponential, relativistic Maxwellian, and Boltzmann distributions were considered). When a magnetized star contracts at the gravitational collapse stage, its magnetic field grows considerably. Such a variable magnetic field generates an eddy electric field. Our calculations suggest that this electric field can accelerate charged particles to relativistic energies. In this way collapsing stars can be sources of high-energy cosmic rays in our Galaxy as well as in other galaxies.     

The example of effective plasma acceleration in a magnetosphere

The problem of effective transform of Poynting flux energy into the kinetic energy of relativistic plasma outflow in a magnetosphere is considered. In this article we present an example of such acceleration. In order to perform it, we use the approach of ideal axisymmetric magnetohydrodynamics (MHD). For highly magnetized plasma outflow we show that a linear growth of Lorentz factor with a cylindrical distance from the rotational axis is a general result for any field configuration in the sub-magnetosonic flow. In the far region the full magnetohydrodynamics problem for one-dimensional flow is considered. It turns out that the effective plasma outflow acceleration is possible in the paraboloidal magnetic field. It is shown that such an acceleration is due to the drift of charged particles in the crossed electric and magnetic field. The clear explanation of the absence of acceleration in the monopole magnetic field if given.      

Tearing instability in the pulsar magnetosphere

Equations governing the coupling of the scalar and vector potentials for a resistive electron-positron plasma in a strong magnetic field are derived. It is shown that in the presence of magnetic shear, a tearing instability may occur. The latter can lead to magnetic field line reconnection and the formation of magnetic islands which could affect the dynamics of the pulsar magnetosphere.     

Filamentation Instability of Nonlinear Alfvén Waves and Plasma Heating associated with Recombination Effect

We investigate plasma heating associated with the effect of recombination and the filamentation instability of Alfvén waves propagating along homogeneous magnetic field in low-beta plasmas, by using an MHD simulation code. The linear instability of Alfvén waves leading to the filamentation is investigated by imposing small density perturbations across a magnetic field. We show results of the nonlinear stage of the above filamentation instability and the plasma heating through a two-dimensional simulation. It is shown that the plasma heating is caused by localized heating and whole heating, which are associated with the filamentation instability and the effect of recombination, respectively. We discuss the implication of these results for plasma heating processes observed in the chromosphere of the Sun.     

Generation of electromagnetic waves in the electron-positron plasma in the vicinity of a pulsar

The problem of the efficiency of the ion-synchrotron maser proposed by Hoshino and Arons is analyzed in a linear approximation. A hot, relativistic, electron-positron plasma penetrated by a relativistic ion beam is considered. At the front of the magnetosonic shock wave an electromagnetic wave is generated, which should be damped on positrons of the plasma. This should, in turn, result in synchrotron emission from energetic positrons in the high-frequency range, far above the natural frequencies of the plasma. It is shown that one must allow simultaneously for the conditions of resonance at a high harmonic of the ion-cyclotron frequency and at the fundamental of the electron-cyclotron frequency. Natural transverse waves are generated in the process, but within the framework of the linear theory there is no positron acceleration due to the kinetic energy of ions. Translated from Astrofizika, Vol. 43, No. 3, pp. 389-396, July–September, 2000.     

Parametric Decay of a Circularly Polarized Electromagnetic Wave in an Electron-Positron Magnetized Plasma

We study the parametric decays of an electromagnetic wave propagating along an external magnetic field in an electron-positron plasma. We include weakly relativistic effects on the particle motions in the wave field, and the nonlinear ponderomotive force. We find resonant and nonresonant wave couplings. These include, ordinary decay instabilities, in which the pump wave decays into an electro-acoustic mode and a sideband wave. There are also nonresonant couplings involving two sideband waves, and a nonresonant modulational instability in which the pump wave decays into two sideband modes. Depending on the parameters involved, there is a resonant modulational instability involving a forward propagating electro-acoustic mode and a sideband daughter wave.     

Inertia driven tearing modes in electron-positron plasmas

It is shown that the particle inertia can cause a tearing instability in an electron-positron collisionless plasma with sheared magnetic fields. An approximate analytical expression for the growth rate is obtained. It characterizes the magnetic reconnection timescale in a magnetized electronpositron plasma.     

Growth Rates of Envelope Modulations of Electromagnetic Waves in Relativistic Temperature Electron-Positron Plasmas, Stimulated by Weak Or Finite Phonon Damping

We study the modulational instability of an electron-positron plasma with relativistic temperatures and phonon damping. It is shown that when the phonon damping is O(1) or O(), a modulational instability appears even for classical temperatures. When the phonon damping is O(²)), we find that in the non-relativistic limit, previous results are recovered, and for ultrarelativistic temperatures, the instability occurs in a wider band around the relativistic plasma frequency.     

Acceleration of charged particles in the magnetosphere of a collapsing star and their nonthermal electromagnetic radiation

We investigate a transformation of a magnetic field and plasma in nonhomogeneous magnetospheres of collapsing stars with a dipole initial magnetic field and certain initial energy distributions of particles in the magnetosphere as the power low, relativistic Maxwell and Boltzmann. The betatron mechanism of the charged particles acceleration in a collapsing star’s magnetosphere is considered. When a magnetized star is compressed in the stage of the gravitational collapse, the magnetic field increases strongly. This variable magnetic field generates a vortical electric field. Our calculations show that this electric field will accelerate charged particles up to relativistic velocities. Thus, collapsing stars may be sources of high energy cosmic rays in our galaxy as in others. The acceleration of particles during the collapse happens mostly in polar regions of the magnetosphere that leads to polar relativistic streams (jets) formation. When moving in a magnetic field, these particles will generate nonthermal electromagnetic radiation in a broad electromagnetic wavelength band from radioto gamma rays. Thus, in the stage of the gravitational collapse, relativistic jets are formed in stellar magnetospheres. These jets are powerful sources of the nonthermal electromagnetic radiation.     

Fundamentals of collisionless shocks for astrophysical application, 2. Relativistic shocks

In this concise review of the recent developments in relativistic shock theory in the Universe we restrict ourselves to shocks that do not exhibit quantum effects. On the other hand, emphasis is given to the formation of shocks under both non-magnetised and magnetised conditions. We only briefly discuss particle acceleration in relativistic shocks where much of the results are still preliminary. Analytical theory is rather limited in predicting the real shock structure. Kinetic instability theory is briefed including its predictions and limitations. A recent self-similar relativistic shock theory is described which predicts the average long-term shock behaviour to be magnetised and to cause reasonable power-law distributions for energetic particles. The main focus in this review is on numerical experiments on highly relativistic shocks in (i) pair and (ii) electron-nucleon plasmas and their limitations. These simulations do not validate all predictions of analytic and self-similar theory and so far they do not solve the injection problem and the self-modification by self-generated cosmic rays. The main results of the numerical experiments discussed in this review are: (i) a confirmation of shock evolution in non-magnetised relativistic plasma in 3D due to either the lepton-Weibel instability (in pair plasmas) or to the ion-Weibel instability; (ii) the sensitive dependence of shock formation on upstream magnetisation which causes suppression of Weibel modes for large upstream magnetisation ratios σ>10⁻³; (iii) the sensitive dependence of particle dynamics on the upstream magnetic inclination angle θ _Bn , where particles of θ _Bn >34° cannot escape upstream, leading to the distinction between ‘subluminal’ and ‘superluminal’ shocks; (iv) particles in ultra-relativistic shocks can hardly overturn the shock and escape to upstream; they may oscillate around the shock ramp for a long time, so to speak ‘surfing it’ and thereby becoming accelerated by a kind of SDA; (v) these particles form a power-law tail on the downstream distribution; their limitations are pointed out; (vi) recently developed methods permit the calculation of the radiation spectra emitted by the downstream high-energy particles; (vii) the Weibel-generated downstream magnetic fields form large-amplitude vortices which could be advected by the downstream flow to large distances from the shock and possibly contribute to an extended strong field region; (viii) if cosmic rays are included, Bell-like modes can generate upstream magnetic turbulence at short and, by diffusive re-coupling, also long wavelengths in nearly parallel magnetic field shocks; (ix) advection of such large-amplitude waves should cause periodic reformation of the quasi-parallel shock and eject large-amplitude magnetic field vortices downstream where they contribute to turbulence and to maintaining an extended region of large magnetic fields.     

Self-modulation of pulsar radiation in strongly magnetized electron-positron plasmas

A nonlinear Schrödinger equation is obtained for linearly polarized electromagnetic waves propagating across the ambient magnetic field in an electron-positron plasma. The nonlinearities arising from wave intensity induced particle mass modulation, as well as harmonic generation are incorporated. Modulational instability and localization of pulsar radiation are investigated.     

Influence of electron-positron pair production on a pulsar magnetospheric structure

A self-consistent pulsar magnetospheric model with electron-positron pair production is considered. Unlike conventional models, the primary particles (electrons) are accelerated towards the neutron star and their curvature radiation towards a star generates electron-positron plasma near the neutron star. Inside an outflow channel, the generated plasma flows away from the pulsar magnetosphere. A part of the plasma electrons returns and, being accelerated towards the star, regenerate the plasma by their curvature radiation. It is shown that plasma production near the star causes an appearance of positron and electron equatorial belts. The plasma concentration and the flux of the returning electrons are estimated. The portion of the energy entering into the pulsar magnetosphere and its dependence on pulsar parameters are estimated.     

Electron surfing acceleration in oblique magnetic fields

Initially, inhomogeneous plasma jets, ejected by active galactic nuclei and associated with gamma-ray bursts, are thermalized by the formation of internal shocks. Jet subpopulations can hereby collide at Lorentz factors of a few. As the resulting relativistic shock expands into the upstream plasma, a significant fraction of the upstream ions is reflected. These ions, together with downstream ions that leak through the shock, form relativistic beams of ions that outrun the shock. The thermalization of these beams via the two-stream instability is thought to contribute significantly to plasma heating and particle acceleration by the shock. Here, the capability of a two-stream instability to generate relativistic field-aligned and cross-field electron flow, is examined for a magnetized plasma by means of a particle-in-cell (PIC) simulation. The electrons interact with the developing quasi-electrostatic waves and oblique magnetic fields. The simulation results bring forward evidence that such waves, by their non-linear interactions with the plasma, produce a highly relativistic field-aligned electron flow and electron energies, which could contribute to the radio synchrotron emissions from astrophysical jets, to ultrarelativistic leptonic subpopulations propagating with the jet and to the halo particles surrounding the accretion disc of the black hole.     

Propagation of Electromagnetic Waves in Pulsar Magnetospheres

We have developed a numerical code for the propagation of different electromagnetic modes in a pulsar magnetosphere filled by a relativistic, streaming electron-positron plasma in a strong, curved magnetic field. We determine the trajectories, limiting polarization and damping of the waves leaving the magnetosphere. This revised version was published online in July 2006 with corrections to the Cover Date.