 | Layout of the PS ring including the combined-function main magnets (red and blue rectangles for the focusing and defocusing parts, respectively) and the location of the key elements for MTE. The ten different sectors of the PS are indicated by the numbers and the radial offset between the rectangles accounts for the four different magnet types (see~\cite{Burnet:1359959} for a recent more detailed information). For the wire scanners (elements with a name starting with WS), the measurement plane is marked in brackets. The number in the element name indicates the straight section number. |
 | Top: Example of the measured diamond detector signal $\ell_\mathrm{m}(t)$ recorded in SS15. The losses generated by the island sweeping through the blade of the dummy septum cause the first spike, while the second spike represents the losses of the core. Bottom: detailed views of the island and core losses (left and right plot, respectively) together with a fitted Gaussian model (from~\cite{PhysRevAccelBeams.22.104002}). |
 | Charge collected by the diamond detector per primary proton, as a function of impacting particle's position on the dummy septum blade, in the presence and without fringe field. Typical difference between the case with and without the fringe field is of the order of $9$\%. |
 | Comparison of the simulated signal profile (red band, left axis) with the number of simulated lost protons (blue line, right axis) as a function of time for the extraction of the island for the diamond detector in SS15. These data are compared with the measured beam losses recorded on the $15^{th}$ of November 2017 at 21:34:54 with a beam intensity of $1.85 \times 10^{13}$~protons (black line, left axis). The band of the simulated signal includes the cable attenuation (see next section) and the statistical uncertainty of the simulation. The lost proton profile is computed from simulation (refer to the text for more detail). In the studies reported in the rest of the paper, only the raising edge of the loss profile is taken into account, i.e. the portion of the signal in the shaded area is excluded. |
 | Peak value of the measured losses as a function of the beam intensity for the core and island. Data from numerical simulations carried out with FLUKA are also shown, including the uncertainty on the cable attenuation (band). |
 | Left: Phase-space representation at SS15 of the core and islands. The stable fixed points (SFP) are highlighted with a magenta dot, except for the rightmost, which represents the extracted island, that is represented as a cyan dot. The vertical line indicates the position of the dummy septum. Right: relationship between the horizontal position inside the extracted island referred to the position of the SFP and the corresponding action value. For each value of $x-x_\mathrm{SFP}$ the orbit of this initial condition is computed and its action estimated. |
 | Left: Phase-space representation at SS15 of the core and islands. The stable fixed points (SFP) are highlighted with a magenta dot, except for the rightmost, which represents the extracted island, that is represented as a cyan dot. The vertical line indicates the position of the dummy septum. Right: relationship between the horizontal position inside the extracted island referred to the position of the SFP and the corresponding action value. For each value of $x-x_\mathrm{SFP}$ the orbit of this initial condition is computed and its action estimated. |
 | Left: Distribution of the normalised beam emittance for the core and the island as a function of the total beam intensity. No visible trend is observed. The reconstruction of the normalised beam emittances is performed according to the method described in the text. For the sake of comparison, emittance measurements performed in the SPS after injection are also shown. Right: comparison between the reconstructed normalised emittance of the island and the emittance distribution obtained from the sensitivity analysis on the nonlinear PS model. |
 | Left: Distribution of the normalised beam emittance for the core and the island as a function of the total beam intensity. No visible trend is observed. The reconstruction of the normalised beam emittances is performed according to the method described in the text. For the sake of comparison, emittance measurements performed in the SPS after injection are also shown. Right: comparison between the reconstructed normalised emittance of the island and the emittance distribution obtained from the sensitivity analysis on the nonlinear PS model. |
 | Horizontal beta-function (top-left), dispersion function (top-right), and position of the SFP and the dummy septum location (bottom) as a function of the euclidean distance of the sextupolar and octupolar components of the synthetic non-linear PS models from the nominal one. The horizontal continuous lines in the top plots represent a variation of $\pm 10\%$ around the nominal value of the parameter. The tolerance for the SFP position is set to $\pm$ \SI{1.5}{\milli\meter} around the nominal value. |
 | Horizontal beta-function (top-left), dispersion function (top-right), and position of the SFP and the dummy septum location (bottom) as a function of the euclidean distance of the sextupolar and octupolar components of the synthetic non-linear PS models from the nominal one. The horizontal continuous lines in the top plots represent a variation of $\pm 10\%$ around the nominal value of the parameter. The tolerance for the SFP position is set to $\pm$ \SI{1.5}{\milli\meter} around the nominal value. |