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.

With cooling, beam phase space density increases, which makes the beam motion intrinsically unstable. To suppress instabilities, dampers are required. With a progress of digital technology, digital dampers are getting to be more and more preferable. Conversion of an analog signal into digital one is described by a linear operator with explicit time dependence. Thus, the analog-digital converter (ADC) does not preserve a signal frequency. Instead, a monochromatic input signal is transformed into a mixture of all possible frequencies, combining the input one with multiples of the sampling frequency. Stability analysis has to include a cross-talk between all these combined frequencies. In this paper, we are analyzing a problem of stability for beam transverse microwave oscillations in a presence of digital damper; the impedance and the space charge are taken into account. The developed formalism is applied for antiproton beam in the Recycler Ring (RR) at Fermilab.

The design of transverse dampers for the Fermilab Recycler storage ring is described. An observed instability and analysis of subsequent measurements where used to identify the requirements. The digital approach being implemented is presented.

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 12th Beam Instrumentation Workshop addressed design principles and engineering issues of beam diagnostics and control instrumentation for charged particle accelerators and beam transport lines. The workshop provided a forum in which participants could exchange ideas and review instrumentation designs, and served as an introduction to relevant topics for engineers and scientists with the aid of tutorial sessions.