A kinetic approach to non resonant modes and growth rates of streaming instability: consequences for shock acceleration

We show here that a purely kinetic approach to the excitation of waves by cosmic rays in the vicinity of a shock front leads to predict the appearance of a non-alfvenic fastly growing mode which is the same that was found by Bell (2004) by treating the plasma in the MHD approximation. The kinetic approach we present is more powerful in that it allows us to investigate different models for the compensation of the cosmic ray current in the background upstream plasma.