High-Density and High-Intensity Beams at the CERN PS

Abstract

The production of high-density and high-intensity beams has been a constant activity at the CERN Proton Synchrotron (PS) since many years. This paper is a status report of the present situation, including also a discussion of ongoing studies and future activities. Abstract. The production of high-density and high-intensity beams has been a constant activity at the CERN Proton Synchrotron (PS) since many years. This paper is a status report of the present situation, including also a discussion of ongoing studies and future activities.

Landau damping of the weak head-tail instability for beams with quadratic amplitude-dependent betatron tunes and binomial amplitude distributions

“…We can see that modes 5,6, and 7 are unstable and they have the largest growth rates. The rise times of these three modes range from 200-285 ms, which are close to the observed [1] rise times 100-200 ms. However, we are not able to compare the frequency shifts with measurements as there are no data available.…”

“…This is clearly demonstrated by the observation of the high-order modes l = 5, 6, and 7 at the CERN PS [1].…”

“…Using the beam parameters in [1] and also the impedance formula, we calculated Ω 0 for modes 2 to 10. For each mode, only the frequency with index n=0 was calculated, since this index value gives the largest frequency shift (∆f Hz) and growth rate (k s −1 ), roughly two orders of magnitude larger than that of the next index value (n=1).…”

“…When we compared with the rise times obtained using the approximate mode spectra in Ref. [1], they differ by as much as a factor of two. This shows that the approximate spectra are inaccurate and the exact spectra h lk (ω) should be used instead if a bunch has the binomial profile.…”

“…The results can be represented in a "stability diagram" with the standard interpretation but with the axes representing the real and imaginary parts of the eigen-values. As a numerical example, we determine the octupole strength needed to damp the reported high-order modes observed [1] in the CERN PS for bunches with "LHC characteristics". …”