Generation of Mesoscale Magnetic Fields and the Dynamics of Cosmic Ray   Acceleration
  The problem of the cosmic ray origin is discussed in connection with their acceleration in supernova remnant shocks. The diffusive shock acceleration mechanism is reviewed and its potential to accelerate particles to the maximum energy of (presumably) galactic cosmic rays ($10^{18}eV $) is considered. It is argued that to reach such energies, a strong magnetic field at scales larger than the particle gyroradius must be created as a result of the acceleration process, itself. One specific mechanism suggested here is based on the generation of Alfven wave at the gyroradius scale with a subsequent transfer to longer scales via interaction with strong acoustic turbulence in the shock precursor. The acoustic turbulence in turn, may be generated by Drury instability or by parametric instability of the Alfven waves. 
P.H. Diamond and M.A. Malkov (UCSD)