Trajectory response fit LOCO Simultaneous fit of the

Trajectory response fit (LOCO) Simultaneous fit of the trajectories using as variables : • Model parameters (via selected MAD parameters : strengths…). For TI 8 : • 2 strenghts of the main arc quads (QD/F). • 1 or 2 additional quads. • BPM gain factors. • Corrector gain factors. It is also possible to add tilts of BPMs, correctors… Fit quality of TI 8 data is rather good (but not perfect) : • Typical noise (pilot) ~ 0. 25 mm. • Average BPM gain ~ 0. 9 – assumes the average corrector field is OK. • BPM gain spread ~ 5% - need to evaluate contribution of the noise. 6/17/2021 TI 8 commissioning / J. Wenninger 1

Fit example First measurement : • First H corrector does not fit when only QD/F are allowed as free parameters. • Fitting one additional quad at a time, the fit gives a consistent/reasonable result only for QTLF 4004 : -20%. Histogram : data 6/17/2021 Second measurement : • QTLF 4004 strength increased by 20%. • Model fits now … * + Line : model fit TI 8 commissioning / J. Wenninger 2

Arc cell phase advance H plane : V plane : • right on ! Histogram : data H plane 6/17/2021 • 1% error on phase advance (larger than nominal). • Clearly visible on the plots : the V phase advance / cell is not 90 deg. * + Line : model fit V plane TI 8 commissioning / J. Wenninger 3

Dispersion fits Fit data to model assuming all errors come from initial conditions. In that case : where the fit constants A and B are related to the error on the initial dispersion (DD 0, DD’ 0) : Data sets : 1. Dispersion measurement during response measurement, QTLF 4004 ~ back to nominal (sunday night). 2. Data from the energy acceptance measurement, both quads down by 20%. 6/17/2021 TI 8 commissioning / J. Wenninger 4

H dispersion fit results Data set 2 : • Fit of first points is poor ! • If more weight is given to first points : D 0 increases to ~ 0. 1 m. Data set 1 Both measuremens are corrected for : • BPM gains (resp. fit) ~ 10% average. • 10% scale error of dp/p estimated using SPS orbit (SPS BPM scale). 6/17/2021 TI 8 commissioning / J. Wenninger 5

H dispersion The same data as on previous slide, but this time plot directly the measured dispersion and the fit … Data set 1 Blue : data 6/17/2021 Data set 2 Red : model fit TI 8 commissioning / J. Wenninger 6

V dispersion fit results Consistent with zero – in any case rather small and consistent with small (~ cm) SPS V dispersion. 6/17/2021 TI 8 commissioning / J. Wenninger 7