Instability Thresholds in the IOTA Ring at Fermilab

Nonlinear focusing elements enhance the stability of particle beams in high-energy colliders through Landau Damping, via the tune spread these elements introduce. Here we discuss the experiment at Fermilab's Integrable Optics Test Accelerator (IOTA) which aims to investigate the influence of such nonlinear focusing elements, particularly octupoles, on the transverse stability of the beam. In this experiment, we employ an active transverse feedback system, an anti-damper, as a controlled source of impedance to induce a coherent instability in the beam. By utilizing the anti-damper, we examine the impact of nonlinear focusing octupoles on the beam's transverse stability. The stability diagram, a tool to determine the system's stability, is therefore measured directly using this newly demonstrated method, which was first explored at the LHC. The experiment at IOTA adds insight to this stability diagram measurement method by aiming to map out the entire stability diagram by investigating a large phase range of the anti-damper. This experiment also aims to obtain the beam distribution function from the direct measurement of a stability diagram, a procedure never done before. From this experiment in IOTA, we present the first results of stability diagram analysis and present plans for further investigation.