Abstract:In the framework of classical mechanics, crystalline undulator radiation was discussed by using small amplitude and small period approximation. The results show that comparing with the large amplitude and large period approximation, small-amplitude and small period approximation have advantages of easy separation, high energy and low cost, etc. Selecting electron as shells is suitable for medium energy and high-energy, an electron source is economical and practical, and beam quality is good, etc. Selecting positron as shells is suitable for low or and medium energy. The results also indicate that the crystalline undulator radiation with the energy 100KeV can be gained using small-amplitude and small period approximation.