Upgrade of MAD-X for HL-LHC project and FCC studies

The design efforts for the High Luminosity upgrade project of the Large Hadron Collider (HL-LHC) and for the FCC-ee studies required significant extensions of the MAD-X code, widely used for designing and simulating particle accelerators. The modelling of synchrotron radiation effects has recently been reviewed, improved, and tested on the lattices of ESRF, LEP, and CLIC Final Focus System. The results were cross checked with several codes, such as AT, PLACET, Geant4, and MAD8. The implementation of space charge has been deeply restructured into a fully modular design. The linear coupling calculation has been completely reviewed and improved to ensure its robustness in the presence of strong coupling effects as is the case for some HL-LHC studies. The slicing module has been generalized to allow for generating thick slices of bending magnets, quadrupoles and solenoids. The $\texttt{SBEND}$ element has been extended to take into account not only the bending angle, but also the integrated dipole strength. Patches have been added to the list of supported elements. Finally, the PTC program inside MAD-X has been extended to provide the tracking of resonance driving terms along lattices, as well as an AC dipole element