Acceleration of the beam-induced tail ions by second harmonic ICRF waves is analytically investigated. The pitch-angle-averaged distribution function of ions is obtained by use of a local Fokker-Planck equation with the beam source and quasi-linear r.f. diffusion terms. The beam-induced tail is extended to the energy region above the injection energy by r.f.-induced diffusion. A simple scaling of the 'extended-tail temperature' with respect to the deposited r.f. power density is presented. Comparison is made with numerical results by a two-dimensional Fokker-Planck code. It is found that the analytical results are in good agreement with the numerical results for the beam injection nearly-perpendicular to the magnetic field. The scaling is also consistent with the data of combined heating experiments in JT-60.