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It is well-recognized that the presence of magnetic fields will lead toanisotropic energy cascade and dissipation of astrophysical turbulence. Withthe diffusion approximation and linear dissipation rates, we study the cascadeand damping of Alfv\'en-cyclotron fluctuations in solar plasmas numerically.For an isotropic case the steady-state turbulence spectra are nearly isotropicin the inertial range and can be fitted by a single power-law function with aspectral index of -3/2, similar to the Iroshnikov-Kraichnan phenomenology.Beyond the MHD regime the kinetic effects make the spectrum softer at higherwavenumbers. In the dissipation range the turbulence spectrum cuts off at thewavenumber, where the damping rate becomes comparable to the cascade rate, andthe cutoff wavenumber changes with the wave propagation direction. The angleaveraged turbulence spectrum of the isotropic model resembles a brokenpower-law. Taking into account the Doppler effects, the model naturallyreproduces the broken power-law turbulence spectra observed in the solar windand predicts that a higher break frequency always comes along with a softerdissipation range spectrum that may be caused by the increase of the turbulenceintensity, the reciprocal of the plasma \beta, and/or the angle between thesolar wind velocity and the mean magnetic field. These predictions can betested by detailed comparisons with more accurate observations.

Cascade and Damping of Alfv\'en-Cyclotron Fluctuations: Application to Solar Wind Turbulence