The Tevatron Tune Tracker PLL — Theory, Implementation and Measurements

ABSTRACT: The Tevatron tune tracker is based on the idea that the trans-verse phase response of the beam can be measured quickly and accurately enough to allow us to track the betatron tune with a phase locked loop (PLL). The goal of this paper is to show the progress of the PLL project at Fermilab. We will divide this paper into three parts: theory, implementation and measurements. In the theory section, we will use a simple linear model to show that our design will track the betatron tune under conditions that occur in the Tevatron. In the im-plementation section we will break down and examine each part of the PLL and in some cases calculate the actual PLL parameters used in our system from beam measurements. And finally in the measurements section we will show the results of the PLL performance. FERMILAB-TM-2275-A