  With the diffusion approximation, we study the cascade and damping of
Alfv\'{e}n-cyclotron fluctuations in solar plasmas numerically. Motivated by
wave-wave couplings and nonlinear effects, we test several forms of the
diffusion tensor. For a general locally anisotropic and inhomogeneous diffusion
tensor in the wave vector space, the turbulence spectrum in the inertial range
can be fitted with power-laws with the power-law index varying with the wave
propagation direction. For several locally isotropic but inhomogeneous
diffusion coefficients, the steady-state turbulence spectra are nearly
isotropic in the absence of damping and can be fitted by a single power-law
function. However, the energy flux is strongly polarized due to the
inhomogeneity that leads to an anisotropic cascade. Including the anisotropic
thermal damping, the turbulence spectrum cuts off at the wave numbers, where
the damping rates become comparable to the cascade rates. The combined
anisotropic effects of cascade and damping make this cutoff wave number
dependent on the wave propagation direction, and the propagation direction
integrated turbulence spectrum resembles a broken power-law, which cuts off at
the maximum of the cutoff wave numbers or the $^4$He cyclotron frequency.
Taking into account the Doppler effects, the model can naturally reproduce the
broken power-law wave spectra observed in the solar wind and predicts that a
higher break frequency is aways accompanied with a greater spectral index
change that may be caused by the increase of the Alfv\'{e}n Mach number, the
reciprocal of the plasma beta, and/or the angle between the solar wind velocity
and the mean magnetic field. These predictions can be tested by future
observations.
