  We present preliminary results of Particle-In-Cell simulations of magnetic
turbulence production by isotropic cosmic-ray ions streaming upstream of
supernova remnant shocks. The studies aim at testing the MHD predictions by
Bell (2004, 2005) of a strong amplification of short-wavelength nonresonant
wave modes and at studying the subsequent evolution of the magnetic turbulence
and its backreaction on cosmic ray trajectories. The detailed knowledge of the
upstream turbulence properties is crucial to ascertain all aspects of the shock
acceleration process - the transport properties of cosmic rays, the shock
structure, thermal particle injection and heating processes. An amplification
of magnetic field would also facilitate the acceleration of particles beyond
the "knee" in the cosmic-ray spectrum. Our kinetic approach is particularly
suited to address the backreaction on the cosmic rays, and it allows us to test
Bell's prediction of the eventual formation of extended filamentary structure
in the cosmic-ray distribution and also to arrive at a reliable estimate of the
total saturation magnetic-field level. The parameters chosen for the
simulations are favorable for the rapid excitation of purely growing modes. We
confirm the generation of the turbulent magnetic field due to the drift of
cosmic-ray ions in the upstream plasma, but show that the growth rate of the
field perturbations is much slower than estimated using the MHD approach and
the amplitude of the turbulence saturates at about dB/B~1. The magnetic field
also remains below equipartition with the upstream plasma.
