This paper summarizes recent progresses in our theoretical understanding of particle acceleration at relativistic shock waves and it discusses two salient consequences: (1) the maximal energy of accelerated particles; (2) the impact of the shock-gene
rated micro-turbulence on the multi-wavelength light curves of gamma-ray burst afterglows.
The physics of instabilities in the precursor of relativistic collisionless shocks is of broad importance in high energy astrophysics, because these instabilities build up the shock, control the particle acceleration process and generate the magnetic
fields in which the accelerated particles radiate. Two crucial parameters control the micro-physics of these shocks: the magnetization of the ambient medium and the Lorentz factor of the shock front; as of today, much of this parameter space remains to be explored. In the present paper, we report on a new instability upstream of electron-positron relativistic shocks and we argue that this instability shapes the micro-physics at moderate magnetization levels and/or large Lorentz factors. This instability is seeded by the electric current carried by the accelerated particles in the shock precursor as they gyrate around the background magnetic field. The compensation current induced in the background plasma leads to an unstable configuration, with the appearance of charge neutral filaments carrying a current of the same polarity, oriented along the perpendicular current. This ``current-driven filamentation instability grows faster than any other instability studied so far upstream of relativistic shocks, with a growth rate comparable to the plasma frequency. Furthermore, the compensation of the current is associated with a slow-down of the ambient plasma as it penetrates the shock precursor (as viewed in the shock rest frame). This slow-down of the plasma implies that the ``current driven filamentation instability can grow for any value of the shock Lorentz factor, provided the magnetization sigma <~ 10^{-2}. We argue that this instability explains the results of recent particle-in-cell simulations in the mildly magnetized regime.
Recent analytical and numerical work argue that successful relativistic Fermi acceleration requires a weak magnetization of the unshocked plasma, all the more so at high Lorentz factors. The present paper tests this conclusion by computing the afterg
low of a gamma-ray burst outflow propagating in a magnetized stellar wind using ab initio principles regarding the microphysics of relativistic Fermi acceleration. It is shown that in magnetized environments, one expects a drop-out in the X-ray band on sub-day scales as the synchrotron emission of the shock heated electrons exits the frequency band. At later times, Fermi acceleration becomes operative when the blast Lorentz factor drops below a certain critical value, leading to the recovery of the standard afterglow light curve. Interestingly, the observed drop-out bears resemblance with the fast decay found in gamma-ray bursts early X-ray afterglows.
Fermi acceleration can develop efficiently at relativistic collisionless shock waves provided the upstream (unshocked) plasma is weakly magnetized. At low magnetization, the large size of the shock precursor indeed provides enough time for electromag
netic micro-instabilities to grow and such micro-instabilities generate small scale turbulence that in turn provides the scattering required. The present paper extends our previous analysis on the development of these micro-instabilities to account for the finite angular dispersion of the beam of reflected and accelerated particles and to account for the expected heating of the upstream electrons in the shock precursor. We show that the oblique two stream instability may operate down to values of the shock Lorentz factor gamma_{sh}~10 as long as the electrons of the upstream plasma remain cold, while the filamentation instability is strongly inhibited in this limit; however, as electrons get heated to relativistic temperatures, the situation becomes opposite and the two stream instability becomes inhibited while the filamentation mode becomes efficient, even at moderate values of the shock Lorentz factor. The peak wavelength of these instabilities migrates from the inertial electron scale towards the proton inertial scale as the background electrons get progressively heated during the crossing of the shock precursor. We also discuss the role of current driven instabilities upstream of the shock. In particular, we show that the returning/accelerated particles give rise to a transverse current through their rotation in the background magnetic field. We find that the compensating current in the background plasma can lead to a Buneman instability which provides an efficient source of electron heating. [Abridged]
