C. B. Hededal

Magnetic Field Generation in Collisionless Shocks: Pattern Growth and Transport

We present results from three-dimensional particle simulations of collisionless shock formation, with relativistic counterstreaming ion-electron plasmas. Particles are followed over many skin depths downstream of the shock. Open boundaries allow the experiments to be continued for several particle crossing times. The experiments confirm the generation of strong magnetic and electric fields by a Weibel-like kinetic streaming instability and demonstrate that the electromagnetic fields propagate far downstream of the shock. The magnetic fields are predominantly transversal and are associated with merging ion current channels. The total magnetic energy grows as the ion channels merge and as the magnetic field patterns propagate downstream. The electron populations are quickly thermalized, while the ion populations retain distinct bulk speeds in shielded ion channels and thermalize much more slowly. The results help reveal processes of importance in collisionless shocks and may help to explain the origin of the magnetic fields responsible for afterglow synchrotron/jitter radiation from gamma-ray bursts.

Non-Fermi power-law acceleration in astrophysical plasma shocks

Collisionless plasma shock theory, which applies, for example, to the afterglow of gamma-ray bursts, still contains key issues that are poorly understood. In this Letter, we study charged particle dynamics in a highly relativistic collisionless shock numerically using ~109 particles. We find a power-law distribution of accelerated electrons, which upon detailed investigation turns out to originate from an acceleration mechanism that is decidedly different from Fermi acceleration. Electrons are accelerated by strong filamentation instabilities in the shocked interpenetrating plasmas and coincide spatially with the power-law-distributed current filamentary structures. These structures are an inevitable consequence of the now well-established Weibel-like two-stream instability that operates in relativistic collisionless shocks. The electrons are accelerated and decelerated instantaneously and locally: a scenery that differs qualitatively from recursive acceleration mechanisms such as Fermi acceleration. The slopes of the electron distribution power laws are in concordance with the particle power-law spectra inferred from observed afterglow synchrotron radiation in gamma-ray bursts, and the mechanism can possibly explain more generally the origin of nonthermal radiation from shocked interstellar and circumstellar regions and from relativistic jets.

Acceleration Mechanics in Relativistic Shocks by the Weibel Instability

Plasma instabilities (e.g., Buneman, Weibel, and other two-stream instabilities) created in collisionless shocks may be responsible for particle (electron, positron, and ion) acceleration. Using a three-dimensional relativistic electromagnetic particle code, we have investigated long-term particle acceleration associated with relativistic electron-ion or electron-positron jet fronts propagating into an unmagnetized ambient electron-ion or electron-positron plasma. These simulations have been performed with a longer simulation system than our previous simulations in order to investigate the nonlinear stage of the Weibel instability and its particle acceleration mechanism. The current channels generated by the Weibel instability are surrounded by toroidal magnetic fields and radial electric fields. This radial electric field is quasi stationary and accelerates particles that are then deflected by the magnetic field. Whether particles are accelerated or decelerated along the jet propagation direction depends on the velocity of particles and the sign of × in the moving frame of each particle. For the electron-ion case the large-scale current channels generated by the ion Weibel instability lead to more acceleration near the jet head. Consequently, the accelerated jet electrons in the electron-ion jet have a significant hump above a thermal distribution. However, in the electron-positron case, accelerated jet electrons have a smoother, nearly thermal distribution. In the electron-positron case, initial acceleration occurs as current channels form and then continues at a much lesser rate as the current channels and corresponding toroidal magnetic fields generated by the Weibel instability dissipate.

e PAIR LOADING AND THE ORIGIN OF THE UPSTREAM MAGNETIC FIELD IN GRB SHOCKS

We investigate here the effects of plasma instabilities driven by rapid e±-pair cascades, which arise in the environment of γ-ray burst (GRB) sources as a result of back-scattering of a seed fraction of the original spectrum. The injection of e± pairs induces strong streaming motions in the ambient medium. One therefore expects the pair-enriched medium ahead of the forward shock to be strongly sheared on length scales comparable to the radiation front thickness. Using three-dimensional particle-in-cell simulations, we show that plasma instabilities driven by these streaming e± pairs are responsible for the excitation of near-equipartition, turbulent magnetic fields. Our results reveal the importance of the electromagnetic filamentation instability in ensuring an effective coupling between e± pairs and ions, and may help explain the origin of large upstream fields in GRB shocks.

Particle Acceleration, Magnetic Field Generation, and Emission in Relativistic Shocks

Abstract Shock acceleration is a ubiquitous phenomenon in astrophysical plasmas. Plasma waves and their associated instabilities (e.g., Buneman, Weibel and other two-stream instabilities) created in collisionless shocks are responsible for particle (electron, positron, and ion) acceleration. Using a 3D relativistic electromagnetic particle code, we have investigated particle acceleration associated with a relativistic jet front propagating into an ambient plasma. We find small differences in the results for no ambient and modest ambient magnetic fields. Simulations show that the Weibel instability created in the collisionless shock front accelerates jet and ambient particles both perpendicular and parallel to the jet propagation direction. The small scale magnetic field structure generated by the Weibel instability is appropriate to the generation of “jitter” radiation from defected electrons (positrons) as opposed to synchrotron radiation. The jitter radiation resulting from small scale magnetic field structures may be important for understanding the complex time structure and spectral evolution observed in γ-ray bursts or other astrophysical sources containing relativistic jets and relativistic collisionless shocks.

Relativistic Shocks: Particle Acceleration, Magnetic Field Generation, and Emission

Shock acceleration is an ubiquitous phenomenon in astrophysical plasmas. Plasma waves and their associated instabilities (e.g., Buneman, Weibel and other two‐stream instabilities) created in collisionless shocks are responsible for particle (electron, positron, and ion) acceleration. Using a 3‐D relativistic electromagnetic particle (REMP) code, we have investigated particle acceleration associated with a relativistic jet front propagating into an ambient plasma with and without initial magnetic fields. We find small differences in the results for no ambient and modest ambient magnetic fields. Simulations show that the Weibel instability created in the collisionless shock front accelerates jet and ambient particles both perpendicular and parallel to the jet propagation direction. The non‐linear fluctuation amplitudes of densities, currents, electric, and magnetic fields in the electron‐positron shock are larger than those found in the electron‐ion shock at the same simulation time. This comes from the fac...

Simulation Study of Magnetic Fields Generated by the Electromagnetic Filamentation Instability

We have investigated the effects of plasma instabilities driven by rapid e± pair cascades, which arise in the environment of GRB sources as a result of back‐scattering of a seed fraction of the original spectrum. The injection of e± pairs induces strong streaming motions in the ambient medium. One therefore expects the pair‐enriched medium ahead of the forward shock to be strongly sheared on length scales comparable to the radiation front thickness. Using three‐dimensional particle‐in‐cell simulations, we show that plasma instabilities driven by these streaming e± pairs are responsible for the excitation of near‐equipartition, turbulent magnetic fields. Our results reveal the importance of the electromagnetic filamentation instability in ensuring an effective coupling between e± pairs and ions, and may help explain the origin of large upstream fields in GRB shocks.

Simulation Studies of Early Afterglows Observed with SWIFT

We have applied numerical simulations and modeling to the particle acceleration, magnetic field generation, and emission from relativistic shocks and plan to compare them 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. A 3‐D relativistic electromagnetic particle (REMP) code is used to study shock processes including spatial and temporal evolution of shocks in unmagnetized electron‐positron plasmas with three different jet velocity distributions. The “jitter” radiation from the shocks is different from synchrotron radiation. The dynamics of shock microscopic process evolution may provide some insight into early afterglows. Our simulation studies provide insight into new GRB observations with Swift.

In-situ Particle Acceleration in Collisionless Shocks

The outflows from gamma-ray bursts, active galactic nuclei and relativistic jets in general interact with the surrounding media through collisionless shocks. With three dimensional relativistic particle-in-cell simulations we investigate such shocks. The results from these experiments show that small-scale magnetic filaments with strengths of up to percents of equipartition are generated and that electrons are accelerated to power law distributions N(γ) ∝ γ−p in the vicinity of the filaments through a new acceleration mechanism. The acceleration is locally confined, instantaneous and differs from recursive acceleration processes such as Fermi acceleration. We find that the proposed acceleration mechanism competes with thermalization and becomes important at high Lorentz factors.

Particle Acceleration with Weibel Instability

We have applied numerical simulations and modeling to the particle acceleration, magnetic field generation, and emission from relativistic shocks and plan to compare them 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. A 3-D relativistic electromagnetic particle (REMP) code is used to study shock processes including spatial and temporal evolution of shocks in unmagnetized electron-positron plasmas with three different jet velocity distributions. The “jitter” radiation from the shocks is different from synchrotron radiation. The dynamics of shock microscopic process evolution may provide some insight into afterglows.