  Turbulent motions in stellar convection zones generate acoustic energy, part
of which is then supplied to normal modes of the star. Their amplitudes result
from a balance between the efficiencies of excitation and damping processes in
the convection zones. We develop a formalism that provides the excitation rates
of non-radial global modes excited by turbulent convection. As a first
application, we estimate the impact of non-radial effects on excitation rates
and amplitudes of high-angular-degree modes which are observed on the Sun. A
model of stochastic excitation by turbulent convection has been developed to
compute the excitation rates, and it has been successfully applied to solar
radial modes (Samadi & Goupil 2001, Belkacem et al. 2006b). We generalize this
approach to the case of non-radial global modes. This enables us to estimate
the energy supplied to high-($\ell$) acoustic modes. Qualitative arguments as
well as numerical calculations are used to illustrate the results. We find that
non-radial effects for $p$ modes are non-negligible:
  - for high-$n$ modes (i.e. typically $n > 3$) and for high values of $\ell$;
the power supplied to the oscillations depends on the mode inertia.
  - for low-$n$ modes, independent of the value of $\ell$, the excitation is
dominated by the non-diagonal components of the Reynolds stress term. We
carried out a numerical investigation of high-$\ell$ $p$ modes and we find that
the validity of the present formalism is limited to $\ell < 500$ due to the
spatial separation of scale assumption. Thus, a model for very high-$\ell$
$p$-mode excitation rates calls for further theoretical developments, however
the formalism is valid for solar $g$ modes, which will be investigated in a
paper in preparation.
