  Energetic particle populations in nuclear fusion experiments can destabilize
Alfv\' en Eigenmodes through inverse Landau damping and couplings with gap
modes in the shear Alfv\' en continua. We use the reduced MHD equations to
describe the linear evolution of the poloidal flux and the toroidal component
of the vorticity in a full 3D system, coupled with equations of density and
parallel velocity moments for the energetic particles. We add the Landau
damping and resonant destabilization effects by a closure relation. We apply
the model to study the Alfv\' en modes stability in Large Helical Device (LHD)
inward-shifted configurations, performing a parametric analysis in a range of
realistic values of energetic particle $\beta$ ($\beta_{f}$), ratios of the
energetic particle thermal/Alfv\' en velocities ($V_{th}/V_{A0}$), magnetic
Lundquist numbers ($S$) and toroidal modes ($n$). The $n = 1$ and $n = 2$ TAE
are destabilized although $n = 3$ and $n = 4$ TAE are weakly perturbed. The
most unstable configurations are associated with density gradients of energetic
particles in the plasma core: TAE are destabilized even for small energetic
particle populations if their thermal velocity is lower than $0.4$ times the
Alfv\' en velocity. The frequency range of MHD bursts measured in LHD are
$50-70$ kHz for $n=1$ and $60-80$ kHz for $n=2$ TAE, consistent with the model
predictions.
