Simultaneous beam-based alignment measurement for multiple magnets by correcting induced orbit shift

We propose a method to simultaneously determine the magnetic centers of multiple quadrupoles in a transport line or a storage ring. The method finds the magnet centers by correcting the induced orbit shift due to a change of the quadrupole gradient strengths, with the goal of eliminating or minimizing such orbit shifts. The correction of the induced orbit shift is done by steering the orbit toward the quadrupole centers with correctors, using the response matrix of the induced orbit shift with respect to the correctors. The quadrupoles are selected with orbit corrector magnets and beam position monitors in between to ensure that orbit correction at the quadrupole locations can be achieved. The response matrix can be measured or calculated. Simulations with a section of the Linac Coherent Light Source II and the Stanford Positron Electron Asymmetric Ring (SPEAR3) storage ring are done to demonstrate the feasibility and performance of the method. It is also experimentally tested on SPEAR3. The method can be extended for beam-based alignment measurement of nonlinear magnets.

Figure 1

Schematic of an accelerator section for parallel BBA.

Figure 2

The induced trajectory shift by a 5% increase of the strengths of group 1 quadrupoles. Solid lines show actual values obtained by tracking. The dashed lines (“linear”) show the values scaled up from a 0.1% gradient change by a factor of 50.

Figure 3

Singular values of the horizontal and vertical response matrices of the induced trajectory shift by a 5% increase of the strengths of group 1 quadrupoles with respect to the corrector magnets.

Figure 4

Top: the beam trajectory after correction of the induced trajectory shift. Quadrupole locations in the group are marked with vertical lines. Bottom: the required kick angle changes on the correctors for the correction.

Figure 5

The quadrupole offsets found with the PBBA method, with BPM error sigma at $5\mu \mathrm{m}$.

Figure 6

The quadrupole center offsets registered by BPMs through the PBBA method are compared to the target values at the quadrupole locations, for all quadrupoles in the LTU section.

Figure 7

The IOS in the SPEAR3 ring when the gradients of the selected 14 QF quadrupoles are varied by $+2\%$ or $-2\%$. The dashed lines are obtained by varying the gradients by only $+0.02\%$ or $-0.02\%$ and scaling up the orbit shift linearly.

Figure 8

The singular values of the horizontal and vertical response matrices of the IOS by the 14 QF magnets (with a scale change of $+2\%$ or $-2\%$ of alternating signs) with respect to the correctors.

Figure 9

Top: the beam orbit after correction of the IOS for the SPEAR3 example. The locations of the quadrupoles in the BBA group are marked with vertical lines. Bottom: the corresponding corrector kick angles.

Figure 10

The quadrupole center offsets found by the PBBA method are compared to the target values for the SPEAR example. Error bars are by standard deviations of 10 random seeds, with BPM noise sigma of $1\mu \mathrm{m}$.

Figure 11

The measured IOS by 14 QF magnets in a SPEAR3 experiment during three iterations of correction. The quadrupole gradient changes are $\pm 2\%$ alternately.

Figure 12

The quadrupole center offsets from the initial beam orbit as measured by PBBA in experiment are compared to the QMS offsets.