A procedure to set phase and amplitude of the RF in the SNS linac´s superconducting cavities

This paper describes a procedure to set the phase and amplitude of the RF fields in the Spallation Neutron Source (SNS) linac´s superconducting cavities. The linac uses superconducting cavities to accelerate the H^- ion beam from the normal conducting linac at 185 MeV to a final energy of ~1 GeV. There are two types of cavities in the linac, 33 cavities with a geometric beta of 0.61 and 48 cavities with a geometric beta of 0.81. The correct phase setting of any single superconducting cavity depends on the RF phase and amplitude of all the preceding superconducting cavities. For the beam to be properly accelerated it must arrive at each cavity with a relative phase (φ _s), called the synchronous phase, of about -20 degrees. That is, it must arrive early with respect to the phase at which it would gain the maximum energy by 20 degrees. This timing provides the longitudinal focusing. Beam particles arriving slightly later gain more energy and move faster relative to the synchronous beam particle. The problem is to set the phase and amplitude of each cavity in the linac; so that the synchronous particle arrives at each cavity with the correct phase. The amplitude of each superconducting cavity will be adjusted as high as possible constrained only by the available RF power and the breakdown field of the cavity