Uncoupled achromatic condition of a dog-leg system with the presence of RF cavities

To merge the beam from either of the two injectors to the main linac, a dog-leg system will be employed in the second Medium Energy Beam Transport （MEBT2） line of the China ADS driving accelerator. The achromatic condition has to be guaranteed to avoid beam center excursion against energy jitter. RF cavities were found to be indispensable to control the bunch length growth in the dog-leg system of MEBT2. The full uncoupling between transverse and longitudinal plane is desired to minimize the growth of projected rms emittances. The uncoupled achromatic condition of this dogleg system with the presence of RF bunching cavities will be deduced using the transfer matrices method. It is found that, to fulfill the uncoupling condition, the distance between the bunching cavities is uniquely determined by the maximum energy gain of the RF cavities. The theoretical analysis is verified by the simulation code TraceWin. The space charge effect on the uncoupled achromatic condition and the beam emittance growth will Mso be discussed.