Linear and second order optics corrections for the KEK Accelerator Test Facility final focus beam line

In this paper, the linear and second order optics corrections for the KEK Accelerator Test Facility (ATF2) final focus beam line are described. The beam optics of the ATF2 beam line is designed based on a local chromaticity correction scheme similar to the ILC final focus system. Beam measurements in 2012 revealed skew sextupole field errors that were much larger than expected from magnetic field measurements. The skew sextupole field error was a critical limitation of the beam size at the ATF2 virtual interaction point (IP). Therefore, four skew sextupole magnets were installed to correct the field error in August 2012. By using the four skew sextupole magnets, the predicted tolerances of the skew sextupole field errors of the ATF2 magnets were increased. Furthermore, analyzing field maps of the sextupole magnets identified the source of the skew sextupole field error. After the field error source was removed, the IP vertical beam size could more easily be focused to less than 65 nm.

Figure 1

Accelerator complex of KEK-ATF, consisting of an electron linac, a damping ring, a beam extraction line, and the ATF2 beam line.

Figure 2

Beam optics of the ILC final focus beam line (a) and the ATF2 beam line (b). Both the $1\times 1$ optics and the $10\times 1$ optics are shown.

Figure 3

Tolerances of multipole field errors for the final doublet (QF1 and QD0) of the ILC and ATF2 final focus beam lines. The tolerances are defined as the error of each component required to induce a 2% IP vertical beam size growth. The multipole field errors in the ATF2 magnets are also plotted. Since the bore radius of the ATF2 final doublet magnets are much larger than ILC, the multipole fields of the ATF2 final doublet are measured at $\mathrm{R}=2\mathrm{cm}$ and scaled to $\mathrm{R}=1\mathrm{cm}$.

Figure 4

Tolerances of sextupole field errors for all quadrupole magnets in the ILC and ATF2 final focus beam lines. The tolerances are defined as the error of each magnet required to induce a 2% IP vertical beam size growth. The measured multipole field errors of the ATF2 magnets are also plotted.

Figure 5

Dynamic ranges of the IP-BSM at the ATF2 IP. 3 laser crossing modes are plotted.

Figure 6

Example of IP beam size tuning using linear knobs. The beam size tuning was done with IP-BSM 2-8° mode.

Figure 7

Simulation results showing beam size changes throughout the beam tuning procedure for the $1\times 1$ optics and $10\times 1$ optics. “rms beam size” is the standard deviation of the y distribution of the tracked particles at the IP. “Core beam size” is the width of a Gaussian function fitted to the core of this distribution.

Figure 8

Location of skew sextupole magnets (SK1-SK4). SK3 was installed in January 2011; the other SKs were installed in August 2012.

Figure 9

The observed IP-BSM modulation dependence on the strength of the skew sextupole magnet SK3.

Figure 10

Simulation result showing the orthogonality of the linear and second order knobs. The strength of each knob is normalized so that setting a knob amplitude of 1 contributes 100 nm of vertical beam size at the IP. The simulation was written using the $1\times 1$ optics.

Figure 11

Tolerances of normal sextupole field errors for quadrupole magnets in the $1\times 1$ optics (a) and the $10\times 1$ optics (b). The tolerances are defined by the requirement to induce a 2% IP vertical beam size growth, and the tolerances with and without second order knob corrections are shown. The measured normal sextupole field errors are also shown.

Figure 12

Example use of nonlinear knobs utilizing strength changes of normal sextupole magnets in the final focus beam line. The beam size tuning was done with IP-BSM 30° mode.

Figure 13

Tolerance to skew sextupole field errors in ATF2 magnets for the (a) $1\times 1$ optics and (b) $10\times 1$ optics. The tolerances are defined by the requirement to induce a 2% beam size growth. Tolerances without second order knob correction, with correction by single skew sextupole, and with correction by four skew sextupoles are shown. Measured skew sextupole field errors are also shown.

Figure 14

The simulated results of beam size changes throughout the beam tuning process with and without second order optics knobs for the $1\times 1$ optics. “rms beam size” is the standard deviation of the $y$ distribution of the tracked particles at the IP. “Core beam size” is the width of a Gaussian function fitted to the core of this distribution.

Figure 15

Second order optics knob corrections with skew sextupole magnets in December 2012. Corrections were made to maximize the IP-BSM modulation depth in 30° mode.

Figure 16

Required strengths of the skew sextupole magnets to compensate for the case where each quadrupole magnet has a skew sextupole field $K_{2S}=1{\mathrm{m}}^{-2}$, in the $10\times 1$ optics. (a) Strength of the tuning knobs and (b) strength of each correction magnet.

Figure 17

Second order optics knob corrections with skew sextupole magnets in March 2013 (after magnet swapping). Corrections were made to maximize IP-BSM modulation in 30° mode.