Touschek scattering can have a detrimental effect on lifetime of the electron beam, even for a high-energy ring like the ESRF. In particular, Touschek lifetime is critical for time-structured modes of operation (single bunch, 16-bunch). It can be minimised by achieving a large momentum acceptance.

For a long time, the comparison between experimental off-momentum lattice characteristics (orbit, tunes, ß-functions, synchrotron frequency) and predictions from tracking software had shown significant discrepancies at large p/p values. Several effects have been investigated to account for this divergence:

- Tracking: off-momentum tracking always implies some approximations in the description of elements. However similar results are obtained from different tracking software (BETA, MAD).
- Non-linear effects due to higher-order field components of magnetic elements: even a significant scaling of the measured multipolar components does not remove the discrepancy.
- Approximation of the thin sextupoles by a single thin lens or by a succession of thin lenses. Given the variation of ß-functions along sextupoles, this turns out to be the most significant effect.

Starting from this revised description of the optics, a new sextupole model has been established that relates sextupole strengths and currents. It results from a global fit on all sextupoles to minimise the differences between measured and predicted tune shifts with energy over a wide range of p/p values and a large number of sextupole settings. The very non-linear, off-momentum behaviour of the lattice is now well reproduced in simulations, as illustrated in Figure 176. This gives us confidence in the fact that the model may be used for pursuing the optimisation of the energy acceptance of the machine.

Fig. 176: Comparison of measured (plain) and predicted (dashed) tune shifts with energy.