Coherent betatron instability in the Tevatron

The instability was first observed during the recent 1987-88 Tevatron fixed target run. In this operating mode 1000 consecutive bunches are loaded into the machine at 150 GeV with a bunch spacing of 18.8 x 10-9 sec (53 MHz). The normalized transverse emittance is typically 15 π x 10-6 m rad in each plane with a longitudinal emittance of about 1.5 eV-sec. The beam is accelerated to 800 GeV in 13 sec. and then it is resonantly extracted during a 23 sec flat top. As the run progressed the bunch intensities were increased until at about 1.4 x 1010 ppb (protons per bunch) we experienced the onset of a coherent horizontal oscillation taking place in the later stages of the acceleration cycle (>600 GeV). This rapidly developing coherent instability results in a significant emittance growth, which limits machine performance and in a catastrophic scenario it even prevents extraction of the beam. In this paper the authors present a simple analytic description of the observed instability. The authors will show that a combination of a resistive wall coupled bunch effect and a single bunch slow head-tail instability is consistent with the above observations. Finally, a systematic numerical analysis of our model (growth-time vs chromaticity plots) points to the existence of the ι ≥ 1 slow head-tail modes as a plausible mechanism for the observed coherent instability. This last claim, as mentioned before, does not have conclusive experimental evidence, although it is based on a very good agreement between the measured values of the instability growth-time and the ones calculated on the basis of the model