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Magnetic-field generation by a relativistic ion beam propagating through anelectron-ion plasma along a homogeneous magnetic field is investigated with2.5D high-resolution particle-in-cell (PIC) simulations. The studies testpredictions of a strong amplification of short-wavelength modes of magneticturbulence upstream of nonrelativistic and relativistic parallel shocksassociated with supernova remnants, jets of active galactic nuclei, andgamma-ray bursts. We find good agreement in the properties of the turbulenceobserved in our simulations compared with the dispersion relation calculatedfor linear waves with arbitrary orientation of ${\vec k}$. Depending on theparameters, the backreaction on the ion beam leads to filamentation of theambient plasma and the beam, which in turn influences the properties of themagnetic turbulence. For mildly- and ultra-relativistic beams, the instabilitysaturates at field amplitudes a few times larger than the homogeneous magneticfield strength. This result matches our recent studies of nonrelativisticallydrifting, hot cosmic-ray particles upstream of supernova-remnant shocks whichindicated only a moderate magnetic-field amplification by nonresonantinstabilities. We also demonstrate that the aperiodic turbulence generated bythe beam can provide efficient particle scattering with a rate compatible withBohm diffusion. Representing the ion beam as a constant external current, i.e.excluding a backreaction of the magnetic turbulence on the beam, we observenon-resonant parallel modes with wavelength and growth rate as predicted byanalytic calculations. In this unrealistic setup the magnetic field isamplified to amplitudes far exceeding the homogeneous field, as observed inrecent MHD and PIC simulations.

Aperiodic magnetic turbulence produced by relativistic ion beams