Which acceleration process for UHE-Cosmic Rays in Gamma Ray Bursts ?

In this paper, we have made an accurate investigation of proton acceleration in GRBs and we have predicted a possible signature of cosmic rays, in a sufficiently baryon-loaded fireball, via GeV $\gamma$-ray emission produced by $\pi^{0}$-meson decay. If two ungrounded assumptions are removed, namely, Bohm's scaling and a slow magnetic field decrease, the usual Fermi processes are unable to generate ultra high energy cosmic rays (UHECRs) in GRBs. We propose to develop another scenario of relativistic Fermi acceleration in the internal shock stage. We present the results of a realistic Monte-Carlo simulation of a multi-front acceleration which clearly shows the possible generation of UHECR. The amount of energy converted into UHECRs turns out to be a sizeable fraction of the magnetic energy.