Tune tracking with a PLL in the Tevatron

The Tevatron tune tracker is based on the idea that the phase of the transverse frequency response of the beam can be measured quickly and accurately enough so that the phase at the betatron tune resonance can be tracked by a phase locked loop (PLL). In this paper, a mathematical model of this idea is discussed and is used as the basis for the realization of the tune tracker hardware. The tune tracker has been successfully tested under different beam conditions and is now operational in the Tevatron