Basic Bell-MHD Turbulence
  Nonresonant current instability was identified by Bell (2004) as an important
mechanism for magnetic field amplification in supernova remnants. In this paper
we focus on studying the nonlinear stage of this instability using the
incompressible MHD formulation. We demonstrate that the evolution of magnetic
turbulence driven by the Bell instability resembles turbulence driven on large
scales. More importantly, we demonstrate that the energy-containing scale for
magnetic fields is proportional to the square root of magnetic energy density.
Given the observational constraints of the possible field amplification, this
new relation allows us to directly estimate the maximum energy of particles
scattered by such fields and this estimate is normally below the average
particle energy. This implies that, without taking into account the feedback to
cosmic rays, the typical scales of Bell fields, in either linear or nonlinear
regime, will be too small to affect high energy particle acceleration. We
mention several scenarios of back-reaction to cosmic rays that could be
important.
