On the efficiency of Fermi acceleration at relativistic shocks

It is shown that Fermi acceleration at an ultra-relativistic shock wave cannot operate on a particle for more than 1 1/2 Fermi cycle (i.e., u -> d -> u -> d) if the particle Larmor radius is much smaller than the coherence length of the magnetic field on both sides of the shock, as is usually assumed. This conclusion is shown to be in excellent agreement with recent numerical simulations. We thus argue that efficient Fermi acceleration at ultra-relativistic shock waves requires significant non-linear processing of the far upstream magnetic field with strong amplification of the small scale magnetic power. The streaming or transverse Weibel instabilities are likely to play a key role in this respect.Comment: 4 pages, 2 figures; to appear in ApJ Letter

A fast current-driven instability in relativistic collisionless shocks

We report here on a fast current-driven instability at relativistic collisionless shocks, triggered by the perpendicular current carried by the supra-thermal particles as they gyrate around the background magnetic field in the shock precursor. We show that this instability grows faster than any other instability studied so far in this context, and we argue that it is likely to shape the physics of the shock and of particle acceleration in a broad parameter range.Comment: 6 pages, 5 figures -- version to appear in EP

On electromagnetic instabilities at ultra-relativistic shock waves

(Abridged) This paper addresses the issue of magnetic field generation in a relativistic shock precursor through micro-instabilities. The level of magnetization of the upstream plasma turns out to be a crucial parameter, notably because the length scale of the shock precursor is limited by the Larmor rotation of the accelerated particles in the background magnetic field and by the speed of the shock wave. We discuss in detail and calculate the growth rates of the following beam plasma instabilities seeded by the accelerated and reflected particle populations: for an unmagnetized shock, the Weibel and filamentation instabilities, as well as the Cerenkov resonant longitudinal and oblique modes; for a magnetized shock, the Weibel instability and the resonant Cerenkov instabilities with the longitudinal electrostatic modes, as well as the Alfven, Whisler and extraordinary modes. All these instabilities are generated upstream, then they are transmitted downstream. The modes excited by Cerenkov resonant instabilities take on particular importance with respect to the magnetisation of the downstream medium since, being plasma eigenmodes, they have a longer lifetime than the Weibel modes. We discuss the main limitation of the wave growth associated with the length of the precursor and the magnetisation of the upstream medium for both oblique and parallel shock waves. We also characterize the proper conditions to obtain Fermi acceleration. We recover some results of most recent particle-in-cell simulations and conclude with some applications to astrophysical cases of interest, pulsar winds and gamma-ray burst external shock waves in particular. (Abridged)Comment: 14 pages, 2 figures; v2: enlarged discussion on the limitations of the growths of instabilities for oblique and parallel relativistic shock waves, typos correcte

Particle acceleration at relativistic shock waves

Relativistic sources, e.g. gamma-ray bursts, pulsar wind nebulae and powerful active galactic nuclei produce relativistic outflows that lead to the formation of collisionless shock waves, where particle acceleration is thought to take place. Our understanding of relativistic shock acceleration has improved in the past decade, thanks to the combination of analytical studies and high level numerical simulations. In ultra-relativistic shocks, particle acceleration is made difficult by the generically transverse magnetic field and large advection speed of the shocked plasma. Fast growing microturbulence is thus needed to make the Fermi process operative. It is thought, and numerical simulations support that view, that the penetration of supra-thermal particles in the shock precursor generates a magnetic turbulence which in turn produces the scattering process needed for particle acceleration through the Fermi mechanism. Through the comparison of the growth timescale of the microinstabilities in the shock precursor and the precursor crossing timescale, it is possible to delimit in terms of magnetization and shock Lorentz factor the region in which micro-turbulence may be excited, hence whether and how Fermi acceleration is triggered. These findings are summarized here and astrophysical consequences are drawn.Comment: based on talks given at KIAA "Cosmic ray" workshop, at SF2A2011 and at WISAP2011; 16 pages, 1 figure. To be published in the proceedings of the WISAP 2011 Eilat meeting, eds M. Mond and P.-L. Sule

Oblique Mixed Shocks in Extragalactic Jets

Full version with figures freely available on ADS at http://cdsads.u-strasbg.fr/cgi-bin/nph-iarticle_query?1991ApJ...367...86F&data_type=PDF_HIGH&type=PRINTERAnalytical calculations of the spectra obtained from first-order Fermi acceleration mechanism with oblique shocks are presented. They are a generalization of the quasiparallel configuration, where the streaming instability modifies the acceleration process, and of the quasiperpendicular configuration, where the magnetic pressure is significant. We show that influence of the streaming instability on the compression ratio of the fluid is always negligible, it changes the spectal index only through the modification of the effective compression ratio of the scattering centers. The observational constraints on the cut-off frequency imply that the magnetic turbulence in extragalactic jets must be weak and most probably of Kraichnan type. The application of our calculations to the jet of 3C 273 shows that the theory of diffusive acceleration in oblique shocks works quite well with a non-relativistic flow velocity, and yields narrow ranges for the different parameters

Fermi Acceleration at relativistic Shocks

International audienceAfter a successful development of theoretical and numerical works on Fermi acceleration at relativistic shocks, some difficulties recently raised with the scattering issue, a crucial aspect of the process. Most pioneering works were developed assuming the scattering off magnetic fluctuations as given. Even in that case, when a mean field is considered, its orientation is mostly perpendicular to the shock normal in the front frame, and this tends to quench the scattering process. Solving this difficulty leads to address the issue of the generation of very intense magnetic fluctuations at short wave lengths. The relativistic motion of the shock front let the cosmic rays to visit upstream during a very short time only, making this generation of magnetic fluctuations very challenging. Anyway there is some hope to solve the problem. Thanks to a recent work by Spitkovsky (2008) \cite{AS}, we know that the process works without any mean field and now we have to investigate up to which intensity the mean field can be amplified for allowing Fermi process with appropriate fast instabilities. In this presentation, the collisionless shock structure in relativistic regime is sketched, the scattering issue is presented, and the instabilities that can provide the expected magnetic field amplification are presented as well. Although there exists observational evidence that particles are accelerated in relativistic flows and are distributed according to a power law suggesting a Fermi process, the drastic conditions for Fermi process to work are not always clearly fulfilled