Emittance Dominated Long Bunches in Dual Harmonic RF Systems

The storage of long bunches for long time intervals needs flattened stationary buckets with large bucket height. In the case of small energy spread with a cooled beam, the Coulomb interaction cannot be ignored. The properties of the dual harmonic RF systems are discussed for the emittance dominated long bunches below transition. The external voltage has to be increased to compensate the Coulomb interaction to keep bunch length unchanged. The longitudinal motion of the initially mismatched beam has been studied for both single and dual harmonic RF system. Bucket height of the single harmonic system is too small even for 20 % mismatch. Halo formation and debunching can be seen after a few synchrotron periods for single particles with large amplitude. The simulation results by using ORBIT code for the FAIR-HESR synchrotron has been given together with theoretical analysis.