On-line dispersion estimation and correction scheme for the Compact Linear Collider

The Compact Linear Collider (CLIC) has stringent component alignment tolerances in order to preserve the ultralow emittance of the utilized particle beams. Beam-based alignment techniques have been designed to relax these tolerances to realizable values. In this paper, a scheme is presented that is capable of mitigating besides the effects of static misalignments also dynamic misalignments caused by ground motion. It is based on the well-known dispersion-free steering (DFS) algorithm, with the peculiarity that it can perform its correction during the usual operation (on-line). This is enabled by performing the necessary dispersion measurements by introducing only negligibly small beam energy changes (per mille level). It has been found that this on-line correction becomes sensitive to the imperfections of transverse wakefields and structure tilts. These sensitivities have been studied via analytical models and in simulations and appropriate countermeasures to improve the robustness of the method have been proposed. The correction performance and robustness properties of the improved algorithm have been studied in detail with respect to all relevant static and dynamic imperfections in a realistic scenario. The presented scheme is not only a potentially important operational tool for CLIC, but the findings with respect to robustness properties for different imperfections are of general interest for the application of the dispersion-free steering algorithm.

Figure 1

Illustration of the basic principle of dispersion-free steering, where two beams with the same offset $\mathrm{\Delta }{x}_1$ in a quadrupole magnet are deflected differently, if they have different beam energies $E_1$ and $E_2$.

Figure 2

Structure of the overall beam-based alignment scheme for the CLIC main linac.

Figure 3

Simulated dispersion due to a dipole kick created by the 1000th quadrupole magnet of the main linac of CLIC, which is vertically misaligned. Different energy changes $\delta$ result in different measured dispersion patterns, especially far downstream of the kick (nonlinear regime).

Figure 4

Dispersion due to typical wakefields after rf alignment in the CLIC main linac for different global energy changes $\delta$ from 0.05% to 5% employed for the dispersion measurement.

Figure 5

Dispersion due to typical residual transverse wakefields after rf alignment in the CLIC main linac for global and local energy changes $\delta$ of 1 per mille. The local energy change is adjusted to correct bin 25, which is marked in the plot with the two vertical black lines.

Figure 6

Comparison of physical dispersion (black) and the dispersion measured (red) by the DFS algorithm, due to structure tilts in the main linac of CLIC. The data have been created with simulations for the DFS bin 25.

Figure 7

DFS performance with respect to the vertical emittance growth $\mathrm{\Delta }{\epsilon }_y$ relative to the nominal emittance ${\epsilon }_0$ of 10 nm for a scheme with a global energy change $\delta$ of 5% for different values of the DFS parameter $\omega$. The performance is evaluated for different imperfection, where an optimal weight ${\omega }_{\text{opt}}$ of about 2 has been found (vertical dashed line).

Figure 8

Sensitivity of DFS to residual wakefields with respect to the vertical emittance growth $\mathrm{\Delta }{\epsilon }_y$ relative to the nominal emittance ${\epsilon }_0$ of 10 nm for a scheme with a global energy change for different WFM resolutions. The CLIC specification for ${\sigma }_{\mathrm{WFM}}$ is $3.5\mu \mathrm{m}$ and is indicated with the vertical dashed line.

Figure 9

DFS performance with respect to the vertical emittance growth $\mathrm{\Delta }{\epsilon }_y$ relative to the nominal emittance ${\epsilon }_0$ of 10 nm as a function of the parameter $\omega$ for a scheme with a local energy change $\delta$ of 0.1% in each bin introduced by using the PETS on/off mechanism. The emittance growth for BPM offsets (black line) is unacceptably high and hence not visible in this plot.

Figure 10

DFS performance with respect to the vertical emittance growth $\mathrm{\Delta }{\epsilon }_y$ relative to the nominal emittance ${\epsilon }_0$ of 10 nm as a function of the DFS parameter $\omega$ for a scheme with a local energy change $\delta$ created by changing the accelerating gradients of structures belonging to one decelerator by 4%. The performance is evaluated for different imperfection, where an optimal weight ${\omega }_{\text{opt}}$ of about 1 has been found (vertical dashed line).

Figure 11

Probability $\mathrm{p}$ of not reaching a certain correction level after the DFS correction, where the values are given relative to the nominal emittance ${\epsilon }_0$ of 10 nm. The static imperfections in Table 1 as well as BPM and quadrupole magnet rolls are included. Two correction schemes are tested: the local scheme with a change the acceleration gradients per decelerator of 4% (loc.), and the global scheme with an acceleration gradient change of 5% (glob.). The results after each of the three iterations of the corrections are shown.