Pressure Profile in the experimental area of FCC-hh and FCC-ee calculated by an analytical code

Ultra high vacuum in the beam pipe is a basic requirement for the Future Circular Colliders (FCC). The dimension of the FCC and the high energy of the particles will make this requirement challenging. Simulations that predict the vacuum quality due to material and beam induced effects will allow to evaluate different designs and to choose an optimal solution. The mathematical model behind the simulations will be shown. Four coupled differential equations describe the mass conservation of the residual gas particles in the beam pipe. The sinks include all kind of distributed and local pumping. The sources are caused by synchrotron radiation, electron clouds, thermal outgassing and ion-induced desorption. The equation system is solved by an analytical method. This requires a transformation to first order equations for which a general valid solution exists. Adding a particular solution and the inclusion of appropriate boundary conditions define the solution function. The big advantage here is that an analytical simulation delivers fast results over large systems. The model has been implemented in a Python environment. It has been cross checked with programs like VASCO and MolFlow. Additionally, data obtained from the Large Hadron Collider’s (LHC) gauges were compared to the simulation output. This validates the program and gives trust to produce accurate vacuum forecasts for the FCC. Finally, simulations will be shown for the hadron-hadron collider FCC-hh. Possible designs will be evaluated for the long straight sections including an interaction point.