Collisionless shocks are commonly argued to be the sites of cosmic-ray (CR) acceleration. We study the influence of CRs on weakly magnetized relativistic collisionless shocks and apply our results to external shocks in gamma-ray burst (GRB) afterglows. The common view is that the transverse Weibel instability (TWI) generates a small-scale magnetic field that facilitates collisional coupling and thermalization in the shock transition. The TWI field is expected to decay rapidly, over a finite number of proton plasma skin depths from the transition. However, the synchrotron emission in GRB afterglows suggests that a strong and persistent magnetic field is present in the plasma that crosses the shock; the origin of this field is a key open question. Here we suggest that the common picture involving TWI demands revision. Namely, the CRs drive turbulence in the shock upstream on scales much larger than the skin depth. This turbulence generates a large-scale magnetic field that quenches TWI and produces a magnetized shock. The new field efficiently confines CRs and enhances the acceleration efficiency. The CRs modify the shocks in GRB afterglows at least while they remain relativistic. The origin of the magnetic field that gives rise to the synchrotron emission is plausibly in the CR-driven turbulence. We do not expect ultra-high-energy cosmic-ray production in external GRB shocks.
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