We present a short summary of use of longitudinal and transverse dampers in the Tevatron Run II operation (2001-2006).

This book presents the developments in accelerator physics and technology implemented at the Tevatron proton-antiproton collider, the world’s most powerful accelerator for almost twenty years prior to the completion of the Large Hadron Collider. The book covers the history of collider operation and upgrades, novel arrangements of beam optics and methods of orbit control, antiproton production and cooling, beam instabilities and feedback systems, halo collimation, and advanced beam instrumentation. The topics discussed show the complexity and breadth of the issues associated with modern hadron accelerators, while providing a systematic approach needed in the design and construction of next generation colliders. This book is a valuable resource for researchers in high energy physics and can serve as an introduction for students studying the beam physics of colliders.

The longitudinal and transverse coupling impedances of the Tevatron vacuum chamber are estimated and summed up. The resistive-wall impedances of the beam pipe and the laminations in the Lambertson magnets dominate below (approximately) 50 MHz. Then come the inductive parts of the bellows and BPM's. The longitudinal and transverse collective instabilities, for both single bunch and multi bunches, are studied using Run II parameters. As expected the transverse coupled-bunch instability driven by the resistive-wall impedance is the most severe collective instability. However, it can be damped by a transverse damper designed for the correction of injection offsets. The power of such a damper has been studied.

The brightness of the antiproton beam in Fermilab's 8 GeV Recycler ring is limited by a transverse instability. This instability has occurred during the extraction process to the Tevatron for large stacks of antiprotons even with dampers in operation. This paper describes observed features of the instability, introduces the threshold phase density to characterize the beam stability, and finds the results to be in agreement with a resistive wall instability model. Effective exclusion of the longitudinal tails from Landau damping by decreasing the depth of the RF potential well is observed to lower the threshold density by up to a factor of two.

Transverse instabilities of the antiproton beam have been observed in the Recycler ring soon after its commissioning. After installation of transverse dampers, the threshold for the instability limit increased significantly but the instability is still found to limit the brightness of the antiprotons extracted from the Recycler for Tevatron shots. In this paper, we describe observations of the instabilities during the extraction process as well as during dedicated studies. The measured instability threshold phase density agrees with the prediction of the rigid beam model within a factor of 2. Also, we conclude that the instability threshold can be significantly lowered for a bunch contained in a narrow and shallow potential well due to effective exclusion of the longitudinal tails from Landau damping.