Cosmic Ray transport in turbulent magnetic field
  Cosmic ray (CR) transport and acceleration is determined by the properties of
magnetic turbulence. Recent advances in MHD turbulence call for revisions in
the paradigm of cosmic ray transport. We use the models of magnetohydrodynamic
turbulence that were tested in numerical simulation, in which turbulence is
injected at large scale and cascades to to small scales. We shall address the
issue of the transport of CRs, both parallel and perpendicular to the magnetic
field. We shall demonstrate compressible fast modes are dominant cosmic ray
scatterer from both quasilinear and nonlinear theories. We shall also show that
the self-generated wave growth by CRs are constrained by preexisting turbulence
and discuss the process in detail in the context of shock acceleration at
supernova remnants and their implications. In addition, we shall dwell on the
nonlinear growth of kinetic gyroresonance instability of cosmic rays induced by
large scale compressible turbulence. This gyroresonance of cosmic rays on
turbulence is demonstrated an important scattering mechanism in addition to
direct interaction with the compressible turbulence. The feedback of the
instability on large scale turbulence should be included in future simulations.
