The Effect of Turbulence at Small Wavenumbers on Particle Diffusion

The reduced perpendicular power spectrum of slab- and of two-dimensional turbulence is generally assumed to be Kolmogorov with spectral index -5/3 at higher wavenumbers, becoming independent of wavenumber at small wavenumbers (see, e.g. Bieber et al. 1994, ApJ, 420). In some theories this assumptions leads to tractable expressions for the parallel- and the perpendicular mean free paths. Here we relax this assumption and consider two alternatives: The spectral index changes from -5/3 to -1 to 0, or from -5/3 to -1 to +3 at progressively smaller wavenumbers. The main difference between these two spectra is therefore that the first one remains flat at small wavenumbers while the second one goes to zero. The spectra are normalized such that they coincide at high wavenumbers and yield the same variance. They are then used in quasi-linear theory for parallel diffusion and non-linear guiding center theory for perpendicular diffusion (Matthaeus et. al. 2003, ApJL, 590), and weakly nonlinear theory for both parallel and perpendicular diffusion (Shalchi et al. 2004, ApJ, 616). We show that in all cases the parallel mean free path shows little effect of the change at small wavenumbers while the perpendicular mean free path typically increases.