A Summary on Landau Octupoles for the LHC

The justification and calculation of a Landau octupole scheme for LHC version 5 may be found in ref. [1]. This approach takes advantage of the analysis of 2D Landau damping documented in ref. [2], which shows that the stability is improved as compared to the usual 1D approach. The stability of single and multi-bunch modes for reduced beam intensity in several realistic operational LHC configurations is estimated and reported in ref. [3]. We summarise briefly in this note the above-mentioned studies and provide some missing information, such as the instability growth rates of multi-bunch modes vs chromaticity, to clarify the requirements. After discussing the stability of single bunch head-tail modes, comparing their real coherent tune shifts with tune spreads of different origin, we present stability diagrams of multi-bunch modes having complex coherent tune shifts and discuss Landau octupole schemes making use of arc octupoles or b4 spool-pieces.