High gradient air core cavity for energy compression of long bunch

In order to achieve a smaller energy spread for secondary particles such as muons, so called phase rotation scheme is proposed: the energy spread is compressed by RF electric field after an appropriate length drift. Although longer drift time makes the final energy spread smaller, it requires very RF low frequency a few MHz. Because the secondary particles have short lifetime, high gradient electric field has to be generated. Cavities without ferro-magnetic load are described. (author)