Résumé
The recent observations of sharp X-ray filaments in many young supernova remnants like CasA, Kepler or Tycho or in older ones like SN1006 led to the conclusion of an amplification of the magnetic field in regards to its standard interstellar medium values. This magnetic field is hardly of external origin and is certainly produced through the acceleration of cosmic-rays around the blast wave. The streaming instability driven by the upstream cosmic-ray gradient is one of the favourite way to generate the magnetic fluctuations to the required level. Recent theoretical progresses conclude that aside the usual resonant interaction an efficient non-resonant regime could be at the origin of the high magnetic fields in supernova blast waves. The present work, investigate this issue. In particular it shown that both non-resonant and resonant regimes should operate in supernova shocks. We discuss the saturation mechanisms of these regimes. We show that the turbulence spectrum is probably highly anisotropic both up- and downstream and we examine the consequences of anisotropy on the values of the magnetic field in the post shock regions as well as the cosmic-ray acceleration process.