  We perform 2.5D hybrid simulations with massless fluid electrons and kinetic
particle-in-cell ions to study the temporal evolution of ion temperatures,
temperature anisotropies and velocity distribution functions in relation to the
dissipation and turbulent evolution of a broad-band spectrum of parallel and
obliquely propagating Alfv\'en-cyclotron waves. The purpose of this paper is to
study the relative role of parallel versus oblique Alfv\'en-cyclotron waves in
the observed heating and acceleration of minor ions in the fast solar wind. We
consider collisionless homogeneous multi-species plasma, consisting of
isothermal electrons, isotropic protons and a minor component of drifting
$\alpha$ particles in a finite-$\beta$ fast stream near the Earth. The kinetic
ions are modeled by initially isotropic Maxwellian velocity distribution
functions, which develop non-thermal features and temperature anisotropies when
a broad-band spectrum of low-frequency non-resonant, $\omega \leq 0.34
\Omega_p$, Alfv\'en-cyclotron waves is imposed at the beginning of the
simulations. The initial plasma parameter values, such as ion density,
temperatures and relative drift speeds, are supplied by fast solar wind
observations made by the \textit{Wind} spacecraft at 1AU. The imposed
broad-band wave spectra is left-hand polarized and resembles \textit{Wind}
measurements of Alfv\'enic turbulence in the solar wind. The imposed magnetic
field fluctuations for all cases are within the inertial range of the solar
wind turbulence and have a Kraichnan-type spectral slope $\alpha=-3/2$. We vary
the propagation angle from $\theta= 0^\circ$ to $\theta=30^\circ$ and
$\theta=60^\circ$, and find that the minor ion heating is most efficient for
the highly-oblique waves propagating at $60^\circ$, whereas the protons exhibit
perpendicular cooling at all propagation angles.
