  Bunch splitting is an RF manipulation method of changing the bunch structure,
bunch numbers and bunch intensity in the high-intensity synchrotrons that serve
as the injector for a particle collider. An efficient way to realize bunch
splitting is to use the combination of different harmonic RF systems, such as
the two-fold bunch splitting of a bunch with a combination of fundamental
harmonic and doubled harmonic RF systems. The two-fold bunch splitting and
three-fold bunch splitting methods have been experimentally verified and
successfully applied to the LHC/PS. In this paper, a generalized multi-fold
bunch splitting method is given. The five-fold bunch splitting method using
specially designed multi-harmonic RF systems was studied and tentatively
applied to the medium-stage synchrotron (MSS), the third accelerator of the
injector chain of the Super Proton-Proton Collider (SPPC), to mitigate the
pileup effects and collective instabilities of a single bunch in the SPPC. The
results show that the five-fold bunch splitting is feasible and both the bunch
population distribution and longitudinal emittance growth after the splitting
are acceptable, e.g., a few percent in the population deviation and less than
10% in the total emittance growth.
