The CMS Precision Proton Spectrometer timing system performance in Run 2, future upgrades and sensor radiation hardness studies.

Central exclusive processes can be studied in CMS by combining the information of the central detector with the Precision Proton Spectrometer (PPS). PPS detectors, placed symmetrically at more than 200 m from the interaction point, can detect the scattered protons that survive the interaction. PPS has taken data at high luminosity while fully integrated in the CMS experiment. The total amount of collected data corresponds to more than 100 fb$^{-1}$ during the LHC Run 2. PPS consists of 3D silicon tracking stations as well as timing detectors that measure both the position and direction of protons and their time-of-flight with high precision. The detectors are hosted in special movable vacuum chambers, the Roman Pots, which are placed in the primary vacuum of the LHC beam pipe. The sensors reach a distance of few mm from the beam. Detectors have to operate in vacuum and must be able to sustain highly non-uniform irradiation: sensors used in Run 2 have accumulated an integrated dose with a local peak of $\sim 5 \cdot 10^{15}$ protons/cm$^2$. The timing system is made with high purity scCVD diamond sensors. A new architecture with two diamond crystals read out in parallel by the same electronic channel has been used to enhance the detector performance. In this paper, after a general overview of the PPS detector, we describe the timing system in detail. The sensor and the dedicated amplification chain are described, together with the signal digitization technique. Performance of the detector in Run 2 is reported. Recently the sensors used in Run 2 have been tested for efficiency and timing performance in a dedicated test beam at DESY. Preliminary results on radiation damage are reported. Important upgrades of the timing system are ongoing for the LHC Run 3, with the goal of reaching an ultimate timing resolution better than 30 ps; they are also discussed here.