The steady-state energy distribution function of alpha (α)-particles is derived in an analytical form by directly solving the Fokker-Planck (FP) equation in an approximate manner under the assumption that the functional dependence of the α-particle confinement time τα(E) on its energy is given by τα(E) ∝ E-ℓ (ℓ is a constant). In addition, a new retardation theory is proposed on the basis of the FP equation under the same assumption. Finally, this proposed retardation theory is applied to dynamic problems of an α-particle-heated DT-reactor through the introduction of what is called a "dynamic response (matrix) function", the result of which enables us to discuss quantitatively problems such as thermal instability and control without numerical analysis of the FP equation.