New approach to LHC optics commissioning for the nonlinear era

In 2017, optics commissioning strategy for low-${\beta }^{*}$ operation of the CERN Large Hadron Collider (LHC) underwent a major revision. This was prompted by a need to extend the scope of beam-based commissioning at high energy, beyond the exclusively linear realm considered previously, and into the nonlinear regime. It also stemmed from a recognition that, due to operation with crossing angles in the experimental insertions, the linear and nonlinear optics quality were intrinsically linked through potentially significant feed-down at these locations. Following the usual linear optics commissioning therefore, corrections for (normal and skew) sextupole and (normal and skew) octupole errors in the high-luminosity insertions were implemented. For the first time, the LHC now operates at top energy with beam-based corrections for nonlinear dynamics, and for the effect of the crossing scheme on beta-beating and dispersion. The new commissioning procedure has improved the control of various linear and nonlinear characteristics of the LHC, yielding clear operational benefits.

Figure 1

Distortion of tune footprint through the ${\beta }^{*}$ squeeze. Displayed footprints are defined by first-order detuning coefficients obtained via simulation. Simulations consist of an effective model of normal octupole errors in IR1 (ATLAS) and IR5 (CMS) which reproduces the observed detuning, together with Landau octupoles powered as per operation for luminosity production in 2016. Grey regions show the desired footprint, expected in the absence of the IR contribution. Red regions show the inferred footprint if IR-octupole errors are uncompensated.

Figure 2

$\beta$-beat in LHC Beam 1 before and after application of global optics correction at flat orbit in 2017.

Figure 3

Measurements of chromatic coupling before (red) and after (blue) compensation with skew sextupole correctors in the LHC arcs. Plots are shown for Beam 1 (top) and Beam 2 (bottom).

Figure 4

Linear and nonlinear corrector layout in LHC experimental IRs [47].

Figure 5

Amplitude detuning measured with flat orbit in 2016, for LHC Beam 2 at ${\beta }^{*}=0.4\mathrm{m}$ with Landau octupoles powered off (red). Simulated detuning is shown in gray, for models based upon the measured magnetic errors. Sixty instances of the magnetic errors are simulated, corresponding to the uncertainty in the magnetic measurements.

Figure 6

Measured tune (black) as a function of the vertical crossing angle in the ATLAS (IR1) insertion, compared to predictions based upon magnetic measurements (red).

Figure 7

Beam-based correction for normal octupole errors in the ATLAS (IR1) and CMS (IR5) insertions, compared to expected corrections based upon magnetic measurement. Sixty instances of model-based corrections are shown corresponding to the uncertainty in the magnetic measurements.

Figure 8

Improvement in online tune measurement quality upon application of corrections for normal octupole errors in the ATLAS (IR1) and CMS (IR5) insertions.

Figure 9

Improvement in online coupling measurement upon application of normal octupole corrections in the ATLAS (IR1) and CMS (IR5) insertions.

Figure 10

Example of amplitude detuning measurements at ${\beta }^{*}=0.3\mathrm{m}$ after IR-octupole correction (blue), and ${\beta }^{*}=0.4\mathrm{m}$ before correction (red).

Figure 11

Example of tune shift with crossing angle with (blue) and without (red) correction of normal octupole errors.

Figure 12

Histogram of the $|f_{4000}^{\prime }|$ ac-dipole resonance driving term, related to the $4Q_x$ resonance, measured in LHC BPMs with and without correction of normal octupole errors in the ATLAS (IR1) and CMS (IR5) insertions.

Figure 13

Change in fractional intensity determined from Beam-Current Transformer data, for the two minutes prior (red), and following (blue), application of normal octupole corrections in IR1 (ATLAS) and IR5 (CMS). Measurements performed at ${\beta }^{*}=0.14\mathrm{m}$ during dedicated tests of the ATS optics [67, 68].

Figure 14

Tune shift of LHC Beam 1 as a function of the horizontal crossing angle in CMS (IR5). Red data show the tune shift measured after application of normal octupole corrections, but before correction of normal sextupole. The fit to the measured data is also shown in red. Blue data corresponds to the tune shift measured after application of normal sextupole corrections. The gray line indicates the expected variation of tune after normal sextupole correction.

Figure 15

Beam-based corrections for the normal sextupole errors applied in the CMS (IR5) insertion, compared to the expected corrections based upon magnetic measurements. Sixty instances of the model-based corrections are shown, corresponding to the uncertainty in the magnetic measurements.

Figure 16

Histograms of Beam 1 (top) and Beam 2 (bottom) beta-beating measured at LHC BPMs, before (blue) and after (red) normal sextupole compensation in IR5 (CMS).

Figure 17

Measurement of $f_{1001}$ at 100 (light red) and $150\mu \mathrm{rad}$ (light blue) crossing angles. The values plotted are the difference of the real (top) and imaginary (bottom) parts of the RDT with respect to measurement at flat orbit, for all BPMs around the ring. Simulated RDT shifts for a model which includes normal sextupole and skew octupole corrector powering which best reproduced the crossing angle scan are shown (dark red/dark blue).

Figure 18

Required global coupling correction [70] of Beam 2 as a function of vertical crossing angle in the ATLAS (IR1) insertion. Measurements before normal sextupole and skew octupole correction are for ${\beta }^{*}=0.4\mathrm{m}$ (red), and after correction for ${\beta }^{*}=0.25\mathrm{m}$ (green). The postcorrection measurement extrapolated to ${\beta }^{*}=0.4\mathrm{m}$ is shown (gray). The correction strength is defined as $|C^{-}|=\sqrt{{\mathrm{CORR}}_{\Re e}^2+{\mathrm{CORR}}_{\Im m}^2}$ where ${\mathrm{CORR}}_{\Re e}$ and ${\mathrm{CORR}}_{\Im m}$ are skew-quadrupole knobs acting orthogonally on the real and imaginary parts of $f_{1001}$ at a specific location in the ring [70].

Figure 19

Beam- and model-based correction for normal sextupole errors in the ATLAS IR (IR1), compared to the expected corrections based upon magnetic measurements.

Figure 20

Tune shift of LHC Beam 1 (left) and LHC Beam 2 (right) as a function of vertical crossing angle in IR1 (ATLAS). Red data shows the tune shift measured after application of normal octupole corrections, but before correction of normal/skew sextupole or skew octupole. The fit to the measured data is also shown in red. Blue data corresponds to the tune shift measured after application of normal/skew sextupole, and skew octupole corrections. The gray line indicates the expected variation of tune after correction, based upon the red fit and expected performance of the skew sextupole correction. The green line represents the expected variation after correction, where the skew octupole corrector misalignment inferred from $Q$-shift during its application has been incorporated as a source of linear tune variation.

Figure 21

Change to $Q_y$ of Beam 2 upon application of skew-octupole correction for feed-down to $|C^{-}|$, with a $150\mu \mathrm{rad}$ vertical crossing angle in IR1 (ATLAS).

Figure 22

Beam- and model-based correction of skew sextupole errors in the ATLAS (IR1) insertion.

Figure 23

Histograms of beta-beating measured at LHC BPMs, before (blue) and after (red) skew sextupole compensation in IR1 (ATLAS).

Figure 24

Histogram of the $|f_{0030}^{\prime }|$ ac-dipole resonance driving term, related to the $3Q_y$ resonance, measured in LHC BPMs with and without correction of skew sextupole errors in the ATLAS (IR1) insertion.

Figure 25

Beta-beating (top,center) and normalized dispersion (bottom) of LHC Beam 2, measured at flat orbit after application of global linear optics corrections, and at the operational crossing scheme after application of all nonlinear corrections in 2017.

Figure 26

Orbit leakage during K-modulation measurements performed in the operational configuration of the ${\beta }^{*}=0.3\mathrm{m}$.

Figure 27

Vertical $\beta$-beat of LHC Beam 1 before and after reoptimization of linear optics corrections at the operational configuration of the crossing scheme.

Figure 28

$\beta$-beat in Beam 1 measured for flat orbit and the operational configuration at ${\beta }^{*}=0.4\mathrm{m}$ in 2017.

Figure 29

$\beta$-beat in Beam 2 measured for at flat orbit and the operational configuration at ${\beta }^{*}=0.4\mathrm{m}$ in 2017.

Figure 30

Normalized dispersion at flat orbit for Beam 1 (top) and Beam 2 (bottom), measured for flat orbit and for the operational configuration at ${\beta }^{*}=0.4\mathrm{m}$ in 2017.