Measurement of rf voltage in long traveling wave accelerating structures with application to the CERN Super Proton Synchrotron

Since its inauguration in 1976, the Super Proton Synchrotron (SPS) at CERN relies on a traveling wave system for particle acceleration instead of making use of standing wave cavities that are more common in circular accelerators. These traveling wave structures (TWSs) are essentially periodically loaded waveguides operated at a fundamental frequency of about 200 MHz. In the frame of the LHC injector upgrade project, the SPS accelerating system is presently improved to better cope with the increased beam intensity required for the future High Luminosity LHC era. The available accelerating voltage provided by the TWSs by means of radio-frequency (rf) generators is a fundamental and valuable input for machine operation and particle tracking codes used to simulate beam phenomena in the SPS. Measurement of the voltage with well known nonresonant and on-axis perturbation methods is however infeasible due to the extreme mechanical length of the SPS structures. It is shown that a good estimate of the rf voltage can be obtained from off-axis measurement samples in each accelerating gap in addition to the in- and output reflection coefficients of the structures. The rf voltage for the LHC proton beam delivered by the system configuration that was installed during the first and second exploitation run of the LHC is measured by this method, not including the beam loading. The impact on the fundamental accelerating mode and the rf voltage of additional higher order mode (HOM) couplers, which are also required for the upgrade of the acceleration system, is assessed by the proposed method as well.