High gradient air core cavity for long bunch

High gradient low frequency RF cavities have been studied as an energy compressor for a short lived secondary particles with long bunch length. Although a ferro-magnetic loaded cavity can realize low resonant frequency in a reasonable cavity size, the high gradient requirement may not be compatible with it. This paper describes two types of high gradient air core (without ferro-magnetic load) cavities: simple but large (several meters) cavities and a set of high frequency (∼200 MHz) cavities that synthesizes the low frequency component as a beat.