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Magnetic field evolution in relativistic unmagnetized collisionless shocks  [PDF]
Uri Keshet,Boaz Katz,Anatoly Spitkovsky,Eli Waxman
Physics , 2008, DOI: 10.1088/0004-637X/693/2/L127
Abstract: We study relativistic unmagnetized collisionless shocks using unprecedentedly large particle-in-cell simulations of two-dimensional pair plasma. High energy particles accelerated by the shock are found to drive magnetic field evolution on a timescale >10^4 plasma times. Progressively stronger magnetic fields are generated on larger scales in a growing region around the shock. Shock-generated magnetic fields and accelerated particles carry >1% and >10% of the downstream energy flux, respectively. Our results suggest limits on the magnetization of relativistic astrophysical flows.
Ion acceleration in non-relativistic astrophysical shocks  [PDF]
L. Gargaté,A. Spitkovsky
Physics , 2011, DOI: 10.1088/0004-637X/744/1/67
Abstract: We explore the physics of shock evolution and particle acceleration in non-relativistic collisionless shocks using multidimensional hybrid simulations. We analyze a wide range of physical parameters relevant to the acceleration of cosmic rays (CRs) in astrophysical non-relativistic shock scenarios, such as in supernova remnant (SNR) shocks. We explore the evolution of the shock structure and particle acceleration efficiency as a function of Alfv\'enic Mach number and magnetic field inclination angle $\theta$. We show that there are fundamental differences between high and low Mach number shocks in terms of the electromagnetic turbulence generated in the pre-shock zone and downstream; dominant modes are resonant with the streaming CRs in the low Mach number regime, while both resonant and non-resonant modes are present for high Mach numbers. Energetic power law tails for ions in the downstream plasma can account for up to 15% of the incoming upstream flow energy, distributed over $\sim5%$ of the particles in a power law with slope $-2\pm0.2$ in energy. The energy conversion efficiency (for CRs) peaks at $\theta=15^\circ$ to $30^\circ$ and $M_A=6$, and decreases for higher Mach numbers, down to $\sim2%$ for $M_A=31$. Accelerated particles are produced by Diffusive Shock Acceleration (DSA) and by Shock Drift Acceleration (SDA) mechanisms, with the SDA contribution to the overall energy gain increasing with magnetic inclination. We also present a direct comparison between hybrid and fully kinetic particle-in-cell results at early times; the agreement between the two models justifies the use of hybrid simulations for longer-term shock evolution. In SNR shocks, particle acceleration will be significant for low Mach number quasi-parallel flows ($M_A < 30$, $\theta< 45$). This finding underscores the need for effective magnetic amplification mechanism in SNR shocks.
Simulations and Theory of Ion Injection at Non-relativistic Collisionless Shocks  [PDF]
Damiano Caprioli,Ana-Roxana Pop,Anatoly Spitkovsky
Physics , 2014, DOI: 10.1088/2041-8205/798/2/L28
Abstract: We use kinetic hybrid simulations (kinetic ions - fluid electrons) to characterize the fraction of ions that are accelerated to non-thermal energies at non-relativistic collisionless shocks. We investigate the properties of the shock discontinuity and show that shocks propagating almost along the background magnetic field (quasi-parallel shocks) reform quasi-periodically on ion cyclotron scales. Ions that impinge on the shock when the discontinuity is the steepest are specularly reflected. This is a necessary condition for being injected, but it is not sufficient. Also by following the trajectories of reflected ions, we calculate the minimum energy needed for injection into diffusive shock acceleration, as a function of the shock inclination. We construct a minimal model that accounts for the ion reflection from quasi-periodic shock barrier, for the fraction of injected ions, and for the ion spectrum throughout the transition from thermal to non-thermal energies. This model captures the physics relevant for ion injection at non-relativistic astrophysical shocks with arbitrary strengths and magnetic inclinations, and represents a crucial ingredient for understanding the diffusive shock acceleration of cosmic rays.
Dynamical efficiency of collisionless magnetized shocks in relativistic jets  [PDF]
M. A. Aloy,P. Mimica
Physics , 2010, DOI: 10.1063/1.3625603
Abstract: The so-called internal shock model aims to explain the light-curves and spectra produced by non-thermal processes originated in the flow of blazars and gamma-ray bursts. A long standing question is whether the tenuous collisionless shocks, driven inside a relativistic flow, are efficient enough to explain the amount of energy observed as compared with the expected kinetic power of the outflow. In this work we study the dynamic efficiency of conversion of kinetic-to- thermal/magnetic energy of internal shocks in relativistic magnetized outflows. We find that the collision between shells with a non-zero relative velocity can yield either two oppositely moving shocks (in the frame where the contact surface is at rest), or a reverse shock and a forward rarefaction. For moderately magnetized shocks (magnetization {\sigma} ~ 0.1), the dynamic efficiency in a single two-shell interaction can be as large as 40%. Hence, the dynamic efficiency of moderately magnetized shocks is larger than in the corresponding unmagnetized two-shell interaction. We find that the efficiency is only weakly dependent on the Lorentz factor of the shells and, thus internal shocks in the magnetized flow of blazars and gamma-ray bursts are approximately equally efficient.
Particle Acceleration in Relativistic Magnetized Collisionless Pair Shocks: Dependence of Shock Acceleration on Magnetic Obliquity  [PDF]
Lorenzo Sironi,Anatoly Spitkovsky
Physics , 2009, DOI: 10.1088/0004-637X/698/2/1523
Abstract: We investigate shock structure and particle acceleration in relativistic magnetized collisionless pair shocks by means of 2.5D and 3D particle-in-cell simulations. We explore a range of inclination angles between the pre-shock magnetic field and the shock normal. We find that only magnetic inclinations corresponding to "subluminal" shocks, where relativistic particles following the magnetic field can escape ahead of the shock, lead to particle acceleration. The downstream spectrum in such shocks consists of a relativistic Maxwellian and a high-energy power-law tail with exponential cutoff. For increasing magnetic inclination in the subluminal range, the high-energy tail accounts for an increasing fraction of particles (from ~1% to ~2%) and energy (from ~4% to ~12%). The spectral index of the power law increases with angle from -2.8+-0.1 to -2.3+-0.1. Particle energization is driven by the Diffusive Shock Acceleration process for nearly parallel shocks, and switches to Shock-Drift Acceleration for larger subluminal inclinations. For "superluminal" shocks, the downstream particle spectrum does not show any significant suprathermal tail. As seen from the upstream frame, efficient acceleration in relativistic (Lorentz factor gamma0 > 5) magnetized (sigma > 0.03) flows exists only for a very small range of magnetic inclination angles (< 34/gamma0 degrees), so relativistic astrophysical pair shocks have to be either nearly parallel or weakly magnetized to generate nonthermal particles. These findings place constraints on the models of AGN jets, Pulsar Wind Nebulae and Gamma Ray Bursts that invoke particle acceleration in relativistic magnetized shocks. (Abridged)
Strong Relativistic Collisionless Shock  [PDF]
Andrei Gruzinov
Physics , 2001,
Abstract: A direct numerical simulation of a strong relativistic collisionless shock propagating into an unmagnetized medium has been performed in two spatial dimensions. It is found that: (i) collisionless shock exists, (ii) particle acceleration is insignificant, (iii) the shock does not generate ``quasi-static'' magnetic fields, contrary to recent claims by other authors. All our results agree with a simple plasma-physical model of collisionless shocks. On the other hand, astrophysical evidence indicates that shocks do accelerate charged particles, and GRB phenomenology indicates that shocks do generate strong magnetic fields. The conflict between the simplest plasma-physical model and astronomical observations of collisionless shocks is discussed.
Weibel-instability-mediated collisionless shocks in laboratory with ultraintense lasers  [PDF]
F. Fiuza,R. A. Fonseca,J. Tonge,W. B. Mori,L. O. Silva
Physics , 2012, DOI: 10.1103/PhysRevLett.108.235004
Abstract: The formation of non-relativistic collisionless shocks in laboratory with ultrahigh intensity lasers is studied via \emph{ab initio} multi-dimensional particle-in-cell simulations. The microphysics behind shock formation and dissipation, and the detailed shock structure are analyzed, illustrating that the Weibel instability plays a crucial role in the generation of strong subequipartition magnetic fields that isotropize the incoming flow and lead to the formation of a collisionless shock, similarly to what occurs in astrophysical scenarios. The possibility of generating such collisionless shocks in laboratory opens the way to the direct study of the physics associated with astrophysical shocks.
Magnetic Fields In Relativistic Collisionless Shocks  [PDF]
Rodolfo Santana,Rodolfo Barniol Duran,Pawan Kumar
Physics , 2013, DOI: 10.1088/0004-637X/785/1/29
Abstract: We present a systematic study on magnetic fields in Gamma-Ray Burst (GRB) external forward shocks (FSs). There are 60 (35) GRBs in our X-ray (optical) sample, mostly from Swift. We use two methods to study epsilon_B (fraction of energy in magnetic field in the FS). 1. For the X-ray sample, we use the constraint that the observed flux at the end of the steep decline is $\ge$ the X-ray FS flux. 2. For the optical sample, we use the condition that the observed flux arises from the FS (optical sample light curves decline as ~t^-1, as expected for the FS). Making a reasonable assumption on E (jet isotropic equivalent kinetic energy), we converted these conditions into an upper limit (measurement) on epsilon_B n^{2/(p+1)} for our X-ray (optical) sample, where n is the circumburst density and p is the electron index. Taking n=1 cm^-3, the distribution of epsilon_B measurements (upper limits) for our optical (X-ray) sample has a range of ~10^-8 -10^-3 (~10^-6 -10^-3) and median of ~few x 10^-5 (~few x 10^-5). To characterize how much amplification is needed, beyond shock compression of a seed magnetic field ~10 muG, we expressed our results in terms of an amplification factor, AF, which is very weakly dependent on n (AF propto n^0.21 ). The range of AF measurements (upper limits) for our optical (X-ray) sample is ~ 1-1000 (~10-300) with a median of ~50 (~50). These results suggest that some amplification, in addition to shock compression, is needed to explain the afterglow observations.
The Maximum Energy of Accelerated Particles in Relativistic Collisionless Shocks  [PDF]
Lorenzo Sironi,Anatoly Spitkovsky,Jonathan Arons
Physics , 2013, DOI: 10.1088/0004-637X/771/1/54
Abstract: The afterglow emission from gamma-ray bursts (GRBs) is usually interpreted as synchrotron radiation from electrons accelerated at the GRB external shock, that propagates with relativistic velocities into the magnetized interstellar medium. By means of multi-dimensional particle-in-cell simulations, we investigate the acceleration performance of weakly magnetized relativistic shocks, in the magnetization range 0
Steady-state structure of relativistic collisionless shocks  [PDF]
David Medvigy,Abraham Loeb
Physics , 2000,
Abstract: We explore analytically the structure of relativistic shock and solitary wave solutions in collisionless plasmas. In the wave frame of reference, a cold plasma is flowing from one end and impacting on a low velocity plasma. First we show that under astrophysical conditions, a cold electron-positron plasma is unstable with respect to a two-stream instability in the interface between these regions. The instability heats the inflowing cold plasma rapidly, on a timescale comparable to the inverse of its plasma frequency. We then derive time-independent equations to describe the resulting hot state of the pair plasma, and describe the conditions under which the spatially uniform solution is the unique stable solution for the post shock conditions. We also examine plasmas composed of cold protons and hot electrons, and show that the spatially uniform solution is the unique stable solution there as well. We state the shock jump conditions which connect a cold, electron-proton plasma to a hot electron-proton plasma. The generic feature evident in all of these models is that the plasma's initial, directed kinetic energy gets almost completely converted into heat. The magnetic field plays the role of catalyst which can induce the plasma instability, but our solutions indicate that the macroscopic field only gets amplified by a factor of approximately three in the frame of the shock.
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