Nonlinear correction schemes for the phase 1 LHC insertion region upgrade and dynamic aperture studies

The phase 1 LHC interaction region (IR) upgrade aims at increasing the machine luminosity essentially by reducing the beam size at the interaction point. This requires a total redesign of the full IR. A large set of options has been proposed with conceptually different designs. This paper reports on a general approach for the compensation of the multipolar errors of the IR magnets in the design phase. The goal is to use the same correction approach for the different designs. The correction algorithm is based on the minimization of the differences between the IR transfer map with errors and the design IR transfer map. Its performance is tested using the dynamic aperture as a figure of merit. The relation between map coefficients and resonance terms is also given as a way to target particular resonances by selecting the right map coefficients. The dynamic aperture is studied versus magnet aperture using recently established relations between magnetic errors and magnet aperture.

Figure 1

Evaluation of the various orders of ${\chi }_q^2$ (upper plot) before (blue markers) and after (red markers) correction. Sixty realizations of the random magnetic errors are used. The layout is the low-${\beta }_{\max }$, whose optical functions are also reported (lower plot).

Figure 2

Evaluation of the various orders of ${\chi }_q^2$ (upper plot) before (blue markers) and after (gray and red markers) correction. The red markers represent a nonoptimized (in terms of correctors location) compensation scheme. Sixty realizations of the random magnetic errors are used. The layout is the symmetric one, whose optical functions are also reported (lower plot).

Figure 3

Comparison of the minimum dynamic aperture for the LHC IR upgrade layouts low-${\beta }_{\max }$ and symmetric with and without correction of the nonlinear magnetic errors in the low-beta quadrupoles.

Figure 4

DA as a function of the low-beta quadrupoles aperture. The scan over the aperture of ${\mathrm{Q}}_1$ is shown in the upper plot (nominal aperture 150 mm), while ${\mathrm{Q}}_2$ and ${\mathrm{Q}}_3$ are considered in the lower plot (nominal aperture 220 mm). The layout is the so-called compact one.

Figure 5

Behavior of the average (over realizations) DA as a function of quadrupole apertures: (top) ${\mathrm{Q}}_1$ and (bottom) ${\mathrm{Q}}_2$ and ${\mathrm{Q}}_3$. A fit of the function $f(\varphi )=a{\varphi }^{-3}+b$ is shown for all cases.