Meeting on muon collider lattice (impact of larger β* and smaller L*) held on 26th November 2024

Present: C. Carli, K. Oide, J. Keintzel, P. Raimondi, G. Roy, K. Skoufaris, M. Vanwelde

The presentation by Marion focused on a study of the impact of (slightly) larger β^* (and rms bunch length) on the dynamic and momentum acceptances. This was triggered by the observation that a lattice with acceptable dynamic aperture over the required momentum range has not been found even for a perfect machine without imperfections with a β^* = 1.5 mm. Extrapolations allowed to expect that slightly relaxing on β^* allows to design lattices with an acceptable dynamic and momentum acceptance for a perfect machine and to finally start studies on the proposed periodic machine deformations (machine "wobbling" to mitigate peak radiation at the locations, where neutrinos from muon decays reach Earth's surface) and imperfections as alignment tolerances, impact of unwanted multipolar components and magnet strength variations (power supply ripple).

The main difficulty of the study was to ensure similar optimization procedures for all of the cases (β^*s) considered. The smooth behaviour of lattice properties (peak betatron functions, Montague W functions, dynamic apertures ..) plotted versus momentum offset indicate that this has been achieved. Only parameters for the case for β^* = 3 mm are not located on a smooth curve.

Updating the study to take into account the most recent input on maximum quadrupole gradients and aperture communicated by the magnet WG (assuming that the few final focus quadrupoles can be constructed with larger amount of HTS materiel than the many magnets required for the rest of the machine) gave very similar results. The conclusion of a similar study on with a shorter L^* is that only a modest improvement can be gained.

Main points from the discussions:

• Discussion on working point triggered by a comment by Katsunobu: the present working is mainly the result of putting togethe the different pieces of the lattoce with little margin to move easily (no zero dispersion straight sections other than around the IPs, where the phase advances can be adjusted without impact on the dispersion). It is important that develop designs allowing to adjust the working point over a reasonable region. The working points of the latest designs (for whole ring and not per IP) might be reasonable. Beam-beam studies should be carried out to optimize the working point.
• Pantaleo recommends changes around the IP:
  • A bending close to the IP (large Twiss betas such that a small deflection has significant effect) has a significant effect on the dispersion in the CC section. Smearing out of the neutrino radiation should be taken out into account to ensure that this is not an issue. 
  • Test whether a sextupole in the region with the doublet at the end of the long straight section housing the IP close to the the start of the CC section allows mitigating the third order chromatoc effects seen in the plots of the tunes versus momentum offset.
• Kyriacos mentions that slightly asymmetric β^* might be envisaged to limit maxima of the Montague W functions.
• Discussion on not that small β_h at the location of the sextupoles for the vertical local correction of chromatic effects: the reason is that the dispersion needed for the correction is not independant from the horizontal betatron function. 
• Ghislain recommends to test whether Resonance Driving Term (RDT) studies, which can easily be done with MAD-NG would allow to gain insight on non-linear behaviour and, in turn, to increase the off and on momentum dynamic apertures.