The Effect of Noise on Transverse Emittance Growth in the Tevatron

As particle densities in accelerators and storage rings increase, instabilities arise that dilute emittance or, at worst, actually drive the beam out of the machine. Beam feedback systems can extend the intensity threshold of these instabilities. These systems have pushed the intensity limits of many accelerators beyond their design intensity and have become a necessity for present day operation. For most beam feedback applications, the dominant design specification is the system gain required to counteract the instability growth rate. This gain is predominantly limited by the delay and dynamic range of the system. A secondary but significant design specification is the amount of noise power that is deposited in the beam. This noise will cause emittance growth over time periods on the order of minutes unless there is some other damping mechanism such as synchrotron radiation. Noise will have a minimal effect on fast cycling machines, but it could have a devastating effect on hadron storage rings that must maintain high luminosity. Instrumentation for measuring feedback system response functions has become increasingly powerful in the last four years, and feedback designers have taken advantage of this when designing new feedback systems for existing machines. By measuring the system response at low beam intensity, the stability of the system at higher intensities can be extrapolated. The theory and application of this technique are well documented. This paper documents the extrapolation of noise properties of the feedback system from the system response measurements. First, a theory for determining relative emittance growth rate as a function of the system response is derived. Second, the theory is tested in the Fermilab Tevatron storage ring. The paper will show how the measured relative growth rates compare between feedback loops open and closed, and it will show how closely these rates compare with theory.