Has the next particle accelerator been designed yet? As I understand it is called the Future Circular Collider. Where are we at in the process of this?
First of all, apart from the FCC there is two other options respectively rival projects on the table. These are a high-energy upgrade of the LHC (CMS energy 27TeV instead of 14TeV called HE-LHC) and the Chinese CEPC (Chinese electron positron collider, circumference ~100km) which aims in a first step at an CMS energy $e^+e^-$ of 240GeV (being a Higgsfactory based on the $e^+e^-\rightarrow Zh$ process), but which is meant to be later upgraded to a hadron machine.
Actually all 3 possibilities have at least their Conceptual Design Report (CDR) at least partly ready, the CDR of CERN is aimed to be fully accomplished by the end of 2018 for both options FCC and HE-LHC. Large parts of the CDRs can already be consulted on the internet: http://cepc.ihep.ac.cn for the CEPC and https://readthedocs.web.cern.ch/display/SUS/FCC+CDR for CERN, but the access is password protected.