Recent developments in computational and theoretical studies of alpha-
particle-driven Alfven turbulence in both the long (k(perpendicular-to
) rho(i) much less than 1) and the short (k (perpendicular-to) rho(i)
less-than-or-equal-to 1) wavelength regimes are reported. In the long
wavelength regime, a hybrid particle-fluid model is solved numerically
as well as analytically in a simple slab geometry. The dominant nonli
near interactions are found to be couplings between two Alfven waves t
o generate a zero-frequency electromagnetic convective cell and strong
E x B convection of resonant alpha particles, which result in signifi
cant changes in plasma equilibria. The fluctuation energies first incr
ease, then saturate and decay. The alpha-particle transport is convect
ive and significant but does not necessarily lead to an appreciable al
pha-particle loss. A mode-coupling theory is developed to explain the
simulation results. In the short wavelength regime, a reduced turbulen
ce model that describes the coupled nonlinear evolutions of fluctuatio
n spectrum \phi\k2 and alpha-particle density profile n(alpha)(r,t) in
the presence of an alpha-particle source S(alpha)(r,t) is solved nume
rically. A steady state is achieved. The nonlinear saturation is due t
o ion Compton scattering-induced energy transfer to higher wave number
s. Alpha-particle transport is significant, and a diffusion coefficien
t of D(alpha) congruent-to 0.5 m2/s for International Thermonuclear Ex
perimental Reactor (ITER)-like parameters is obtained. The effect of a
nomalous alpha-particle diffusion on alpha-particle power coupling to
bulk plasmas is also discussed.