Transport Equation for MHD Turbulence: Application to Particle Production at Interplanetary Shocks

The aim of the present paper is to unify the various transport equations for turbulent waves that are used in different areas of space physics. Here, we mostly focus on the magnetohydrodynamic (MHD) turbulence, in particular the Alfvénic turbulence. The applied methods, however, are general and can be extended to other forms of turbulence, for example the acoustic turbulence, or Langmuir plasma waves. With minor modifications, the derivations followed here can be extended for relativistic motions, thus making it possible to apply them to the wave transport in astrophysical objects with high plasma speeds (radio-jets), or strong gravity (black hole surroundings). The transport equation is incorporated into the numerical model of the solar energetic particle acceleration at the front of interplanetary shock wave. The resulting turbulence spectra upstream and downstream the shock are presented and their contribution to the particle acceleration is evaluated.