Ion Dynamics and Acceleration in Relativistic Shocks

Martins, S. F.; Fonseca, Ricardo; Silva, L. O.; Mori, W. B.

doi:10.1088/0004-637x/695/2/l189

Cited by 168 publications

(194 citation statements)

References 29 publications

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“…The broad range of unstable modes excited in the process should here produce the turbulence needed for first-order Fermi acceleration. PIC simulations [73][74][75][76][77] have been highly instrumental in validating this scenario for relativistic and nonrelativistic shocks. Beamplasma instabilities are thus a key part of the loop: Particle acceleration→ beam-plasma instabilities→ magnetic turbulence→ particle acceleration.…”

Section: Gamma Ray Bursts and High Energy Cosmic Raysmentioning

confidence: 99%

Multidimensional electron beam-plasma instabilities in the relativistic regime

2010

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The interest in relativistic beam-plasma instabilities has been greatly rejuvenated over the past two decades by novel concepts in laboratory and space plasmas. Recent advances in this long-standing field are here reviewed from both theoretical and numerical points of view. The primary focus is on the two-dimensional spectrum of unstable electromagnetic waves growing within relativistic, unmagnetized, and uniform electron beam-plasma systems. Although the goal is to provide a unified picture of all instability classes at play, emphasis is put on the potentially dominant waves propagating obliquely to the beam direction, which have received little attention over the years. First, the basic derivation of the general dielectric function of a kinetic relativistic plasma is recalled. Next, an overview of two-dimensional unstable spectra associated with various beam-plasma distribution functions is given. Both cold-fluid and kinetic linear theory results are reported, the latter being based on waterbag and Maxwell-Jüttner model distributions. The main properties of the competing modes ͑developing parallel, transverse, and oblique to the beam͒ are given, and their respective region of dominance in the system parameter space is explained. Later sections address particle-in-cell numerical simulations and the nonlinear evolution of multidimensional beam-plasma systems. The elementary structures generated by the various instability classes are first discussed in the case of reduced-geometry systems. Validation of linear theory is then illustrated in detail for large-scale systems, as is the multistaged character of the nonlinear phase. Finally, a collection of closely related beam-plasma problems involving additional physical effects is presented, and worthwhile directions of future research are outlined.

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Section: Gamma Ray Bursts and High Energy Cosmic Raysmentioning

confidence: 99%

Multidimensional electron beam-plasma instabilities in the relativistic regime

2010

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“…The role of the Weibel instability in forming the shock transition in weakly magnetized plasmas has recently been established through several numerical experiments (Nishikawa et al 2003(Nishikawa et al , 2005Silva & Fonseca 2003;Frederiksen et al 2004;Keshet et al 2009;Martins et al 2009). Numerical simulations of relativistic shocks have shown that the relatively less energetic upstream electrons are significantly heated to energies comparable to the energy of ions as they cross the foreshock, which appears to be in agreement with electromagnetic observations of supernova remnants and gamma-ray burst afterglows where the high energy radiation is believed to be synchrotron radiation originating from the gyration of high-energy electrons in magnetic fields significantly higher than the interstellar magnetic field (Panaitescu & Kumar 2002;Piran 2005;Gehrels & Mészáros 2012).…”

Section: Introductionmentioning

confidence: 99%

Electron Heating in a Relativistic, Weibel-Unstable Plasma

Kumar

Eichler

Gedalin

2015

ApJ

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The dynamics of two initially unmagnetized relativistic counter-streaming homogeneous ion-electron plasma beams are simulated in two dimensions (2D) using the particle-in-cell (PIC) method. It is shown that current filaments, which form due to the Weibel instability, develop a large-scale longitudinal electric field in the direction opposite to the current carried by the filaments as predicted by theory. This field, which is partially inductive and partially electrostatic, is identified as the main source of net electron acceleration, greatly exceeding that due to magnetic field decay at later stages. The transverse electric field, although larger than the longitudinal field, is shown to play a smaller role in heating electrons, contrary to previous claims. It is found that in one dimension, the electrons become strongly magnetized and are not accelerated beyond their initial kinetic energy. Rather, the heating of the electrons is enhanced by the bending and break up of the filaments, which releases electrons that would otherwise be trapped within a single filament and slow the development of the Weibel instability (i.e., the magnetic field growth) via induction as per Lenz's law. In 2D simulations, electrons are heated to about one quarter of the initial kinetic energy of ions. The magnetic energy at maximum is about 4%, decaying to less than 1% by the end of the simulation. The ions are found to gradually decelerate until the end of the simulation, by which time they retain a residual anisotropy of less than 10%.

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“…However, such a strong magnetic field determines the particle trajectories downstream and has the potential to modify the signatures of the collisionless shock. Collisionless shocks have been studied for many decades, mainly in the context of space and astrophysics [1][2][3][4]. Recently, shock acceleration raised significant interest in the quest for a laser-based ion acceleration scheme due to an experimentally demonstrated high beam quality [5][6][7][8].…”

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confidence: 99%

Electromagnetic Field Generation in the Downstream of Electrostatic Shocks Due to Electron Trapping

et al. 2014

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A new magnetic field generation mechanism in electrostatic shocks is found, which can produce fields with magnetic energy density as high as 0.01 of the kinetic energy density of the flows on time scales ∼10 4 ω −1 pe . Electron trapping during the shock formation process creates a strong temperature anisotropy in the distribution function, giving rise to the pure Weibel instability. The generated magnetic field is well confined to the downstream region of the electrostatic shock. The shock formation process is not modified, and the features of the shock front responsible for ion acceleration, which are currently probed in laserplasma laboratory experiments, are maintained. However, such a strong magnetic field determines the particle trajectories downstream and has the potential to modify the signatures of the collisionless shock. Collisionless shocks have been studied for many decades, mainly in the context of space and astrophysics [1][2][3][4]. Recently, shock acceleration raised significant interest in the quest for a laser-based ion acceleration scheme due to an experimentally demonstrated high beam quality [5][6][7][8].Interpenetrating plasma slabs of hot electrons and cold ions are acting to set up the electrostatic fields via longitudinal plasma instabilities. The lighter electrons leaving the denser regions are held back by the electric fields, which pull the ions. Particles are trapped in the associated electrostatic potential, which steepens and eventually reaches a quasisteady-state collisionless electrostatic shock. Most of the theoretical work dates back to the 1970s [9-13] relying on the pseudo-Sagdeev potential [14] and progress has been mainly triggered by kinetic simulations [15][16][17][18].The short formation time scales and the one dimensionality of the problem make it easily accessible with theory and computer simulations. However, long time shock evolution was often one dimensional or electrostatic codes were used, and the role of electromagnetic modes was mostly neglected. More advanced multidimensional simulations have shown the importance of electromagnetic modes also in this context, due to transverse modes which are excited on the ion time scale [19,20]. We show that in the case of very high electron temperatures associated with the formation of electrostatic shocks [21], electromagnetic modes become important on electron time scales, creating strong magnetic fields in the downstream of the shock.With the increase in laser energy and intensity, the possibility to drive electrostatic shocks has become important for laboratory experiments of electrostatic shocks. Recent laser-driven shock experiments showed the appearance of an electromagnetic field structure [22][23][24], which was attributed to the ion-filamentation instability [25] that evolves on time scales of ten thousands of the inverse electron plasma frequency, ω −1 pe . As a main outcome of this Letter, we show that these structures can already be seeded and produced on tens of ω −1 pe and remain in a quasisteady state over t...

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Ion Dynamics and Acceleration in Relativistic Shocks

Cited by 168 publications

References 29 publications

Multidimensional electron beam-plasma instabilities in the relativistic regime

Multidimensional electron beam-plasma instabilities in the relativistic regime

Electron Heating in a Relativistic, Weibel-Unstable Plasma

Electromagnetic Field Generation in the Downstream of Electrostatic Shocks Due to Electron Trapping

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