Power scalability of single-frequency single-mode Yb-doped fiber amplifiers is significant for their applications. Considering their potential applications in radiation environments, the influence of radiation-induced attenuation (RIA) on the power scalability of signal-frequency single-mode Yb-doped fiber amplifiers is studied in this work. A theoretical model for predicting the power limitation of single-frequency single-mode Yb-doped fiber amplifiers is proposed by considering the limitations of pump brightness, stimulated Brillion scattering (SBS), and transverse mode instability (TMI), and taking RIA into account. It is revealed that RIA can not only greatly lower the power limit, but also make it more difficult to achieve power limitation. The analytic formula of power limit is deduced. It is found that the effect of RIA on the power limitation is mainly determined by the optimal length with no RIA. It is suggested that the reduction of power limitation caused by RIA can be weakened by shortening the optimum length of Yb-doped fiber.

The requirement of Yb-doped fiber for achieving certain target power is also discussed and the needed ranges of core diameter and fiber length are given analytically. It is found that the RIA will increase the difficulty in achieving the target power by limiting the option of Yb-doped fibers. In spite of that, it is also found that such an effect of RIA can be weakened by increasing the core absorption coefficient and pump brightness. Moreover, the numerical model and related formula can also reveal the influence of radiation dose by fitting the relationship between RIA and radiation dose through using the empirical expressions such as power law. They can provide significant guidance for designing and utilizing single-frequency single-mode Yb-doped fiber amplifiers in radiation environments.