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The relation between the spatial diffusion coefficient along the magnetic field, <I>k</I><em>II</em>, and the momentum diffusion coefficient, D<em><I>p</I></em>, for relativistic cosmic ray particles is modelled using Monte Carlo simulations. Wave fields with vanishing wave helicity and cross-helicity, constructed by superposing 'Alfvén-like' waves are considered. As the result, particle trajectories in high amplitude wave fields and then - by averaging over these trajectories - the values of transport coefficients are derived. The modelling is performed at various wave amplitudes, from δ <i>B</i>/<i>B</i><em><sub>0</sub></em> = 0.15 to 2.0, and for a number of wave field types. At our small amplitudes approximately the quasi-linear theory (QLT) estimates for <I>k</I><sub><em>II</em> </sub> and D<I><em><sub>p</sub></em></I> are reproduced. However, with growing wave amplitude the simulated results show a small divergence from the QLT ones, with <I>k</I><sub><em>II</em> </sub>decreasing slower than theoretical prediction and the opposite being true for D<I><em><sub>p</sub></em></I>. The wave field form gives only a slight influence on the wave-particle interactions at large wave amplitudes δ <i>B</i>/<i>B</i><em><sub>0 </sub></em>~ 1. The parameter characterizing the relative efficiency of the second-order to the first-order acceleration at shock waves, D<I><em><sub>p</sub></em></I> <I>κ</I><sub><em>II</em> </sub> is given in the QLT approximation by the Skilling formula V<em><sup>2</sup><sub>A </sub></em>p<em><sup>2 </sup></em>/ 9. In simulations together with increasing δ <i>B</i> it increases above this scale in all the cases under our study. Consequences of the present results for the second-order Fermi acceleration at shock waves are briefly addressed.