  We simulate the acceleration processes of collisionless particles in a shock
structure with magnetohydrodynamical (MHD) fluctuations. The electromagnetic
field is represented as a sum of MHD shock solution ($\Mag_0, \Ele_0$) and
torsional Alfven modes spectra ($\delta \Mag, \delta \Ele $). We represent
fluctuation modes in logarithmic wavenumber space. Since the electromagnetic
fields are represented analytically, our simulations can easily cover as large
as eight orders of magnitude in resonant frequency, and do not suffer from
spatial limitations of box size or grid spacing. We deterministically calculate
the particle trajectories under the Lorenz force for time interval of up to ten
years, with a time step of $\sim 0.5 \sec$. This is sufficient to resolve
Larmor frequencies without a stochastic treatment. Simulations show that the
efficiency of the first order Fermi acceleration can be parametrized by the
fluctuation amplitude $\eta \equiv < \delta B^2 > ^{\frac 1 2} {B_0}^{-1}$ .
Convergence of the numerical results is shown by increasing the number of wave
modes in Fourier space while fixing $\eta$. Efficiency of the first order Fermi
acceleration has a maximum at $ \eta \simeq 10^1$. The acceleration rate
depends on the angle between the shock normal and $\Mag_0$, and is highest when
the angle is zero. Our method will provide a convenient tool for comparing
collisionless turbulence theories with, for example, observations of bipolar
structure of super nova remnants (SNRs) and shell-like synchrotron-radiating
structure.
