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Collisionless relativistic shocks have been the focus of intense theoreticaland numerical investigations in recent years. The acceleration of particles,the generation of electromagnetic microturbulence and the building up of ashock front are three interrelated essential ingredients of a relativisticcollisionless shock wave. In this paper we investigate two issues of importancein this context: (1) the transport of suprathermal particles in the excitedmicroturbulence upstream of the shock and its consequences regarding particleacceleration; (2) the preheating of incoming background electrons as they crossthe shock precursor and experience relativistic oscillations in themicroturbulent electric fields. We place emphasis on the importance of themotion of the electromagnetic disturbances relatively to the background plasmaand to the shock front. This investigation is carried out for the two majorinstabilities involved in the precursor of relativistic shocks, thefilamentation instability and the oblique two stream instability. Finally, weuse our results to discuss the maximal acceleration at the external shock of agamma-ray burst; we find in particular a maximal synchrotron photon energy ofthe order of a few GeV.

Particle transport and heating in the microturbulent precursor of relativistic shocks