  As the second stage of the CEPC-SPPC project, SPPC (Super Proton-Proton
Collider) aims at exploring new physics beyond the Standard Model. The key
design goal for the SPPC accelerator complex is to reach 75 TeV in center of
mass energy with a circumference of 100 km for the collider and an injector
chain of four accelerators in cascade to support the collider. As an important
part of the SPPC conceptual study, the longitudinal beam dynamics was studied
systematically, which includes the dynamics in the collider and its complex
injector chain. First, the bunch filling scheme of the SPPC complex was
designed on the basis of various constraints such as the technical challenges
of the kicker magnets, limited extraction energy per injection and so on. Next,
the study on the longitudinal dynamics in the collider focused on the RF scheme
to meet the requirements for luminosity and mitigate relevant instabilities. A
higher harmonic RF system (800 MHz) together with the basic RF system (400 MHz)
to form a dual-harmonic RF system was employed to mitigate collective
instabilities and increase the luminosity by producing shorter bunches. In
addition, the longitudinal matchings between the bunches in the different
accelerator stages were studied, with special attention to the space charge
effects and the beam loading effect in the two lower energy rings (p-RCS and
MSS), which result in an optimization of the RF schemes. A set of
self-consistent beam and RF parameters for the SPPC complex was obtained. The
collider and the three proton synchrotrons of the injector chain have
unprecedented features, thus this study demonstrates how a future proton-proton
collider complex looks like.
