Abstract

X-ray observations of synchrotron rims in supernova remnant (SNR) shocks show evidence of efficient electron acceleration and strong magnetic field amplification (a factor of similar to 100 between the upstream and downstream medium). This amplification may be due to plasma instabilities driven by shock-accelerated particles or cosmic rays (CRs), as they propagate ahead of the shocks. One candidate process is the cosmic ray current-driven (CRCD) instability caused by the electric current of unmagnetized CRs (i.e., CRs whose Larmor radii are much larger than the length scale of the CRCD modes) propagating parallel to the upstream magnetic field. Particle-in-cell (PIC) simulations have shown that the back-reaction of the amplified field on CRs would limit the amplification factor of this instability to less than similar to 10 in galactic SNRs (not including the additional field compression at the shock). In this paper, we study the possibility of further amplification driven near shocks by magnetized CRs, whose Larmor radii are smaller than the length scale of the field that was previously amplified by the CRCD instability. We find that additional amplification can occur due to a new instability, driven by the CR current perpendicular to the field, which we term the perpendicular current-driven instability (PCDI). We derive the growth rate of this instability and, using PIC simulations, study its non-linear evolution. We show that the maximum amplification of PCDI is determined by the disruption of CR current, which happens when CR Larmor radii in the amplified field become comparable to the length scale of the instability. We find that, in regions close to the shock, PCDI grows on scales smaller than the scales of the CRCD instability, and, therefore, it results in larger amplification of the field (amplification factor up to similar to 45). One possible observational signature of PCDI is the characteristic dependence of the amplified field on the shock velocity, B(2) proportional to v(sh)(2), which contrasts with the one corresponding to the CRCD instability acting alone, B(2) proportional to v(sh)(2). Our results strengthen the idea of CRs driving a significant part of the magnetic field amplification observed in SNR shocks.