| Summary: | Recently, Bell [2] has reanalysed the problem of wave excitation by cosmic rays propagating in the pre-cursor region of a supernova remnant shock front. He pointed out a strong, nonresonant, current-driven instability previously overlooked in kinetic treatments [1, 5] and suggested that it can substantially amplify the ambient magnetic field. Magnetic field amplification is also an important issue regarding the formation and structure of relativistic shock fronts, particularly in relation to models of gamma-ray bursts [4]. We have generalised the linear analysis to apply to this case, assuming a relativistic background plasma and a monoenergetic, unidirectional incoming proton beam. We find essentially the same nonresonant instability noticed by Bell, and show that also under GRB conditions, it grows much faster than the resonant waves.We quantify the extent to which thermal effects in the background plasma limit the maximum growth rate.
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