  (Abridged) X-ray observations of synchrotron rims in supernova remnant (SNR)
shocks show evidence of strong magnetic field amplification (a factor of ~100
between the upstream and downstream medium). This amplification may be due to
plasma instabilities driven by shock-accelerated cosmic rays (CRs). One
candidate is the cosmic ray current-driven (CRCD) instability (Bell 2004),
caused by the electric current of large Larmor radii CRs 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 ~10 in galactic SNRs. 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 and
saturation. We find that PCDI increases the amplification of the field
(amplification factor up to ~45, not including the shock compression) and
discuss its observational signatures. Our results strengthen the idea of CRs
driving a significant part of the magnetic field amplification observed in SNR
shocks.
