Energetic particle transport in a finite amplitude magnetosonic and Alfveni
c turbulence is considered using the Monte Carlo particle simulations, whic
h involve integration of particle equations of motion. We show that in the
low-beta plasma the cosmic-ray acceleration can be the most important dampi
ng process for magnetosonic waves. Assuming such conditions we derive the m
omentum diffusion coefficient D-p, for relativistic particles in the presen
ce of anisotropic finite-amplitude turbulent wave fields, for hat and Kolmo
gorov-type turbulence spectra, respectively. We confirm the possibility of
larger values of D-p occurring due to transit-time damping resonance intera
ction in the presence of isotropic fast-mode waves in comparison to the Alf
ven waves of the same amplitude (cf. Schlickeiser and Miller, 1997). The im
portance of quasi-perpendicular fast-mode waves is stressed for the acceler
ation of high velocity particles.