Sporadic transverse instabilities have been observed at the Fermilab Recycler Ring leading to increase in transverse emittances and beam loss. The driving source of these instabilities has been attributed to the resistive-wall impedance with space-charge playing an important role in suppressing Landau damping. Growth rates of the instabilities are computed. Remaining problems are discussed.

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 resistive wall instability is analyzed for antiprotons in the Recycler Ring. Damper requirements are formulated.

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.

Sporadic transverse instabilities have been observed at the Fermilab Recycler Ring leading to increase in transverse emittances and beam loss. The driving source of these instabilities has been attributed to the resistive-wall impedance with space-charge playing an important role in suppressing Landau damping. Growth rates of the instabilities have been computed. Remaining problems are discussed.

Transverse beam instability of a coasting beam with a digital damper is examined. Threshold of instability is calculated in specific cases with Landau damping taken into account. The results are applied to the Fermilab Recycler Ring. Some improvement of existing RR damper is proposed.

Transverse instability of a bunched beam in a ring accelerator is considered. An emphasis is given to an investigation of rigid modes at space charge dominating beam coupling impedance and about linear synchrotron oscillations. The theory is applied to the Fermilab Recycler [1] which is treated as a proton accumulator in context of Proton Plan II [2]. It is shown that the instability growth time can reach about 0.3 ms, and chromaticity about -7 to -10 is required to suppress it. The suppression by means of 26 MHz damper is considered also, and required parameters of the damper are provided. Arguments are adduced that obtained stability conditions are not only necessary but also sufficient, because other modes except the rigid ones are more stable.