Multidimensional simulations of magnetic field amplification and electron acceleration to near-energy equipartition with ions by a mildly relativistic quasi-parallel plasma collision

The energetic electromagnetic eruptions observed during the prompt phase of gamma-ray bursts are attributed to synchrotron emissions. The internal shocks moving through the ultrarelativistic jet, which is ejected by an imploding supermassive star, are the likely source of this radiation. Synchrotron emissions at the observed strength require the simultaneous presence of powerful magnetic fields and highly relativistic electrons. We explore with one and three-dimensional relativistic particle-in-cell simulations the transition layer of a shock, that evolves out of the collision of two plasma clouds at a speed 0.9c and in the presence of a quasi-parallel magnetic field. The cloud densities vary by a factor of 10. The number densities of ions and electrons in each cloud, which have the mass ratio 250, are equal. The peak Lorentz factor of the electrons is determined in the 1D simulation, as well as the orientation and the strength of the magnetic field at the boundary of the two colliding clouds. The relativistic masses of the electrons and ions close to the shock transition layer are comparable as in previous work. The 3D simulation shows rapid and strong plasma filamentation behind the transient precursor. The magnetic field component orthogonal to the initial field direction is amplified in both simulations to values that exceed those expected from the shock compression by over an order of magnitude. The forming shock is quasi-perpendicular due to this amplification. The simultaneous presence of highly relativistic electrons and strong magnetic fields will give rise to significant synchrotron emissions.Comment: 8 pages, 5 figures. This work was presented at 21st International Conference on Numerical Simulation of Plasmas (ICNSP'09). Accepted for publication IEEE Trans. on Plasma Scienc

The influence of the mass-ratio on the acceleration of particles by filamentation instabilities

Almost all sources of high energy particles and photons are associated with jet phenomena. Prominent sources of such highly relativistic outflows are pulsar winds and Active Galactic Nuclei. The current understanding of these jets assumes diluted plasmas which are best described as kinetic phenomena. In this kinetic description particle acceleration to ultra-relativistic speeds can occur in completely unmagnetized and neutral plasmas through insetting effects of instabilities. Even though the morphology and nature of particle spectra are understood to a certain extent, the composition of the jets is not known yet. While Poynting-flux dominated jets are certainly composed of electron-positron plasmas, the understanding of the governing physics in AGN jets is mostly unclear. In this article we investigate how the constituting elements of an electron-positron-proton plasma behave differently under the variation of the fundamental mass-ratio m_p/m_e. We studied initially unmagnetized counterstreaming plasmas using fully relativistic three-dimensional particle-in-cell simulations to investigate the influence of the mass-ratio on particle acceleration and magnetic field generation in electron-positron-proton plasmas. We covered a range of mass-ratios m_p/m_e between 1 and 100 with a particle number composition of n_{p^+}/n_{e^+} of 1 in one stream, only protons are injected in the other, whereas electrons are present in both to guarantee charge neutrality in the simulation box. We find that with increasing proton mass the instability takes longer to develop and for mass-ratios > 20 the particles seem to be accelerated in two phases which can be accounted to the individual instabilities of the different species. This means that for high mass ratios the coupling between electrons/positrons and the heavier protons, which occurs in low mass-ratios, disappears.Comment: 15 pages, 6 figure

Magnetic field amplification and electron acceleration to near-energy equipartition with ions by a mildly relativistic quasi-parallel plasma protoshock

The prompt emissions of gamma-ray bursts are seeded by radiating ultrarelativistic electrons. Internal shocks propagating through a jet launched by a stellar implosion, are expected to amplify the magnetic field & accelerate electrons. We explore the effects of density asymmetry & a quasi-parallel magnetic field on the collision of plasma clouds. A 2D relativistic PIC simulation models the collision of two plasma clouds, in the presence of a quasi-parallel magnetic field. The cloud density ratio is 10. The densities of ions & electrons & the temperature of 131 keV are equal in each cloud. The mass ratio is 250. The peak Lorentz factor of the electrons is determined, along with the orientation & strength of the magnetic field at the cloud collision boundary. The magnetic field component orthogonal to the initial plasma flow direction is amplified to values that exceed those expected from shock compression by over an order of magnitude. The forming shock is quasi-perpendicular due to this amplification, caused by a current sheet which develops in response to the differing deflection of the incoming upstream electrons & ions. The electron deflection implies a charge separation of the upstream electrons & ions; the resulting electric field drags the electrons through the magnetic field, whereupon they acquire a relativistic mass comparable to the ions. We demonstrate how a magnetic field structure resembling the cross section of a flux tube grows in the current sheet of the shock transition layer. Plasma filamentation develops, as well as signatures of orthogonal magnetic field striping. Localized magnetic bubbles form. Energy equipartition between the ion, electron & magnetic energy is obtained at the shock transition layer. The electronic radiation can provide a seed photon population that can be energized by secondary processes (e.g. inverse Compton).Comment: 12 pages, 15 Figures, accepted to A&

Two-stream-like instability in dilute hot relativistic beams and astrophysical relativistic shocks

Relativistic collisionless shocks are believed to be efficient particle accelerators. Nonlinear outcome of the interaction of accelerated particles that run ahead of the shock, the so-called "precursor", with the unperturbed plasma of the shock upstream, is thought to facilitate additional acceleration of these particles and to possibly modify the hydrodynamic structure of the shock. We explore here the linear growth of kinetic modes appearing in the precursor-upstream interaction in relativistic shocks propagating in non and weakly magnetized plasmas: electrostatic two-stream parallel mode and electrostatic oblique modes. These modes are of particular interest because they are the fastest growing modes known in this type of system. Using a simplified distribution function for a dilute ultra-relativistic beam that is relativistically hot in its own rest frame, yet has momenta that are narrowly collimated in the frame of the cold upstream plasma into which it propagates, we identify the fastest growing mode in the full $k$-space and calculate its growth rate. We consider all types of plasma (pairs and ions-electrons) and beam (charged and charge-neutral). We find that unstable electrostatic modes are present in any type of plasma and for any shock parameters. We further find that two modes, one parallel ($k_\perp=0$) and the other one oblique ($k_\perp \sim k_\|$), are competing for dominance and that either one may dominate the growth rate in different regions of the phase space. The dominant mode is determined mostly by the perpendicular spread of the accelerated particle momenta in the upstream frame, which reflects the shock Lorentz factor. The parallel mode becomes more dominant in shocks with lower Lorentz factors (i.e., with larger momentum spreads). We briefly discuss possible implications of our results for external shocks in gamma-ray burst sources

Particle-in-cell simulation of a mildly relativistic collision of an electron-ion plasma carrying a quasi-parallel magnetic field: Electron acceleration and magnetic field amplification at supernova shocks

Plasma processes close to SNR shocks result in the amplification of magnetic fields and in the acceleration of electrons, injecting them into the diffusive acceleration mechanism. The acceleration of electrons and the B field amplification by the collision of two plasma clouds, each consisting of electrons and ions, at a speed of 0.5c is investigated. A quasi-parallel guiding magnetic field, a cloud density ratio of 10 and a plasma temperature of 25 keV are considered. A quasi-planar shock forms at the front of the dense plasma cloud. It is mediated by a circularly left-hand polarized electromagnetic wave with an electric field component along the guiding magnetic field. Its propagation direction is close to that of the guiding field and orthogonal to the collision boundary. It has a low frequency and a wavelength that equals several times the ion inertial length, which would be indicative of a dispersive Alfven wave close to the ion cyclotron resonance frequency of the left-handed mode (ion whistler), provided that the frequency is appropriate. However, it moves with the super-alfvenic plasma collision speed, suggesting that it is an Alfven precursor or a nonlinear MHD wave such as a Short Large-Amplitude Magnetic Structure (SLAMS). The growth of the magnetic amplitude of this wave to values well in excess of those of the quasi-parallel guiding field and of the filamentation modes results in a quasi-perpendicular shock. We present evidence for the instability of this mode to a four wave interaction. The waves developing upstream of the dense cloud give rise to electron acceleration ahead of the collision boundary. Energy equipartition between the ions and the electrons is established at the shock and the electrons are accelerated to relativistic speeds.Comment: 16 pages, 18 figures, Accepted for publication by Astron & Astrophy

Particle transport and heating in the microturbulent precursor of relativistic shocks

Collisionless relativistic shocks have been the focus of intense theoretical and numerical investigations in recent years. The acceleration of particles, the generation of electromagnetic microturbulence and the building up of a shock front are three interrelated essential ingredients of a relativistic collisionless shock wave. In this paper we investigate two issues of importance in this context: (1) the transport of suprathermal particles in the excited microturbulence upstream of the shock and its consequences regarding particle acceleration; (2) the preheating of incoming background electrons as they cross the shock precursor and experience relativistic oscillations in the microturbulent electric fields. We place emphasis on the importance of the motion of the electromagnetic disturbances relatively to the background plasma and to the shock front. This investigation is carried out for the two major instabilities involved in the precursor of relativistic shocks, the filamentation instability and the oblique two stream instability. Finally, we use our results to discuss the maximal acceleration at the external shock of a gamma-ray burst; we find in particular a maximal synchrotron photon energy of the order of a few GeV.Comment: 14 pages, 6 figures. Revised versio

Particle Acceleration, Magnetic Field Generation, and Associated Emission in Collisionless Relativistic Jets

Nonthermal radiation observed from astrophysical systems containing relativistic jets and shocks, e.g., active galactic nuclei (AGNs), gamma-ray bursts (GRBs), and Galactic microquasar systems usually have power-law emission spectra. Recent PIC simulations using injected relativistic electron-ion (electro-positron) jets show that acceleration occurs within the downstream jet. Shock acceleration is a ubiquitous phenomenon in astrophysical plasmas. Plasma waves and their associated instabilities (e.g., the Buneman instability, other two-streaming instability, and the Weibel instability) created in the shocks are responsible for particle (electron, positron, and ion) acceleration. The simulation results show that the Weibel instability is responsible for generating and amplifying highly nonuniform, small-scale magnetic fields. These magnetic fields contribute to the electron's transverse deflection behind the jet head. The ``jitter'' radiation from deflected electrons has different properties than synchrotron radiation which assumes a uniform magnetic field. This jitter radiation may be important to understanding the complex time evolution and/or spectral structure in gamma-ray bursts, relativistic jets, and supernova remnants.Comment: 4 pages, 3 figures, contributed talk at the workshop: High Energy Phenomena in Relativistic Outflows (HEPRO), Dublin, 24-28 September 2007. Fig. 3 is replaced by the correct versio

Conditions for the onset of the current filamentation instability in the laboratory

Current Filamentation Instability (CFI) is capable of generating strong magnetic fields relevant to explain radiation processes in astrophysical objects and lead to the onset of particle acceleration in collisionless shocks. Probing such extreme scenarios in the laboratory is still an open challenge. In this work, we investigate the possibility of using neutral $e^{-}$ $e^{+}$ beams to explore the CFI with realistic parameters, by performing 2D particle-in-cell simulations. We show that CFI can occur unless the rate at which the beam expands due to finite beam emittance is larger than the CFI growth rate and as long as the role of competing electrostatic two-stream instability (TSI) is negligible. We also show that the longitudinal energy spread, typical of plasma based accelerated electron-positron fireball beams, plays a minor role in the growth of CFI in these scenarios

Relativistic Particle-In-Cell Simulation Studies of Prompt and Early Afterglows from GRBs

Nonthermal radiation observed from astrophysical systems containing relativistic jets and shocks e.g. gamma-ray bursts (GRBs) active galactic nuclei (AGNs) and microquasars commonly exhibit power-law emission spectra. Recent PIC simulations of relativistic electron-ion (or electron-positron) jets injected into a stationary medium show that particle acceleration occurs within the downstream jet. In collisionless relativistic shocks particle (electron, positron and ion) acceleration is due to plasma waves and their associated instabilities (e.g. the Weibel (filamentation) instability) created in the shock region. The simulations show that the Weibel instability is responsible for generating and amplifying highly non-uniform small-scale magnetic fields. These fields contribute to the electron's transverse deflection behind the jet head. The resulting ``jitter'' radiation from deflected electrons has different properties compared to synchrotron radiation which assumes a uniform magnetic field. Jitter radiation may be important for understanding the complex time evolution and/or spectra in gamma-ray bursts, relativistic jets in general and supernova remnants.Comment: 19 pages,7 figures, contributed talk at Seventh European Workshop on Collisionless Shocks, Paris, 7- 9 November 2007. High resolution version can be obtained at http://gammaray.nsstc.nasa.gov/~nishikawa/shockws07.pd