To improve output performance of salient-pole synchronous machines, the authors previously proposed permanent-magnet-assisted salient-pole synchronous machines (PMa-SMs) that have permanent magnets (PMs) between the field poles. They verified the PM effect of increasing the output power and the terminal voltage by finite element analysis (FEA) and experiments under steady states. In this paper, demagnetization in the PMs due to sudden three-phase short circuits is evaluated by FEA. The results have shown that irreversible demagnetization arises in the PMs by the sudden short-circuiting at the rated voltage. Moreover, additional damper bars on the PMs are proposed and the effect on the PM demagnetization is investigated by FEA. It has been found that adding the damper bars on the outer surfaces of the PMs is effective to reduce the PM demagnetization.