The alpha particle power coupling efficiency to the bulk plasma,alphaidentical to P(coupled)/P(birth), is reduced when the energetic alpha particles are subject to anomalous radial diffusion, Dan, caused by alpha particle instabilities. Ifis appreciably smaller than 1, this has a strong effect on the ignition margin MIPalpha(coupled)/Ploss of a tokamak plasma. First, a simple analytical form ofis found to be= 1 - (SD/L), whereL2/4Dis the spatial loss time andSDis the slowing down time. The power coupling efficiencydecreases with increasing Teand increases with ne. Second, a reduced time dependent alpha particle kinetic equation containing the term.Dn, where Dcan be a non-linear function ofn/, is derived and solved using a multiple energy group method. An Alfven wave turbulence theory by Gang (Phys. Fluids B 4 (1992) 3152) is used to parametrize Dfrom first principles. When Dan3 m2/s,is reduced to 0.95. The consequence for the accessible operating regimes of an ITER-like fusion device are also discussed
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