does not substantially change the results presented in the following section, despite being computationally more expensive. The turbulence power spectrum (Fig. \[Pspectrum\]) is assumed to be scale-invariant, or Kolmogorov, in all the three space-dimensions: $$G(k) \propto k^{-\beta -2 },$$ where $\beta = 5/3$ is the one-dimensional power-law Kolmogorov index and the additional $2$ accounts for the dimensionality of the turbulence. At scales larger than $k_{\rm min} ^{-1}$ ($k_{0} < k < k_{\rm min}$, with $k_{\rm min}/k_{0} = 10^2$ ), the power spectrum is simply taken as constant consistently with the solar wind large-scale power spectrum (see, e.g., @Jokipii.Coleman:68).

The method of particle propagation follows the widely used approach in [@Giacalone.Jokipii:99] and @Fraschetti.Giacalone:12. The fluctuating field comprises $N_m$ transverse wave modes at every point occupied by the particle with random amplitude, phase, orientation and polarization. The magnitudes of the wavenumber $k_i$ of the $N_m$ modes are logarithmically equispaced, $\Delta k/ k =$ constant. We sampled the power spectrum over a discrete number of $N_m^* = 188$ modes. Numerical calculations show that the diffusion coefficients are not affected by the sampling resolution in $k-$space with $N_m > N_m^*$ [@Fraschetti.Giacalone:12]. However, the fluctuation $\delta {\bf B}$ is calculated here with a space-dependent amplitude 