Scaling Law of Beam Break-Up for the Single Ultrashort Bunch in RF Linac

Femtosecond bunch is a hot topic in the present world accelerator research community. The high peak current bunch will lead to the beam breakup phenomenon. In this paper, the scaling law with current for the single ultrashort bunch beam breakup in the radio frequency linear accelerator is proposed and obtained. The scaling power factor is roughly estimated to be 1/6, 1/6 and 1/3 for the geometry wake, the surface roughness wake and the resistance wake respectively.