Parallel diffusion of charged particles by MHD turbulence : Comparison with Quasi-linear theory

We discuss parallel diffusion of charged particles by performing one-dimensional test particle simulations, using a one-dimensional, time stationary, slab model for the MHD turbulence. Parallel diffusion coefficient is evaluated numerically and its dependence to various turbulence parameters is considered, including the turbulence amplitude, the field power spectrum index $gamma$, and an index to denote wave phase coherence in turbulence. It is known that the parallel diffusion coefficient derived within the framework of the quasi-linear theory diverges when $gamma ge 2$ in slab geometry, due to the lack of the waves which can resonate linearly with particles with $90^o$ pitch angle. By introducing the concept of \u27effective pitch angle\u27, we define a modified quasi-linear parallel diffusion coefficient, which agrees well with the numerical simulation results. Implications to the observed mean free path of energetic particles in the solar wind are discussed