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The thesis contributes to the future operation of the Super Proton Synchrotron at CERN and to the numerous efforts that ensure the long-term physics performance of the Large Hadron Collider. An increased mitigation of higher order electromagnetic modes in the travelling wave acceleration system of the SPS is required to ensure delivery of the high intensity particle beam desired in the future. The proposed solutions are developed from theory as well as simulations and tested in measurements.