Résumé
Supernova blast wave shock is a very important site of cosmic-ray
acceleration. However, the detailed physical process of acceleration, in
particular, non-linear interplay between cosmic-ray streaming and magnetic
field amplification has not been studied under a realistic environment. In this
paper, using a unique and novel numerical method, we study cosmic-ray
acceleration at supernova blast wave shock propagating in the interstellar
medium with well-resolved magnetic field amplification by non-resonant hybrid
instability (or Bell instability). We find that the magnetic field is mildly
amplified under typical ISM conditions that leads to maximum cosmic-ray energy
~30 TeV for supernova remnants with age ~1000 years consistent with gamma-ray
observations. The strength of the amplified magnetic field does not reach
so-called saturation level, because cosmic-ray electric current towards the
shock upstream has finite spatial extent, by which Bell instability cannot
experience many e-folding times.