β-beat Correction

The β-beat correction is carried out after the Golden orbit is set using a few selected quadrupole PSs. The β-beat response matrix due to the gradient errors Dkl at the m^th quadrupole is:

Beta beat correction: Example -1: The unperturbed optics is distorted with random gradient errors at DK/K=0.004 truncated at 2s given to all the quadrupoles only without any sorts of other errors. The beta beat so obtained is corrected by use of 144 thin lenses placed at the new DBA octant, two damping wiggler sections and in the short straight sections. The simulation results for the Random Number 62345600 are shown below.

Beta beat correction: Example -2: The unperturbed optics is distorted with random gradient errors at DK/K=0.001 and all other field and alignment errors truncated at 2s given to all the magnets as usual. Then the Golden orbit is obtained with orbit correction procedure. The resulted beta beat so obtained after orbit correction is corrected by use of 144 thin lenses placed at the new DBA octant, two damping wiggler sections and in the short straight sections. The simulation results for the Random Number 72345600 are shown below.

Beta beat correction: Example -3: The unperturbed optics is distorted with random gradient errors at DK/K=0.001 and all other field and alignment errors truncated at 2s given to all the magnets as usual. Then the Golden orbit is obtained with orbit correction procedure. The resulted beta beat so obtained after orbit correction is corrected by use of 144 thin lenses placed at the new DBA octant, two damping wiggler sections and in the short straight sections. The simulation results for the Random Number 88765432 are shown below.

β-beat correction using the monitor to quadrupole corrector sensitive matrix.

The horizontal and vertical β-beat dβ_i at the position of the i^th monitor caused by a strength perturbation dK_j of the j^th quadrupole is contained in the (2*220)x77 sensitive matrix S;

Which can be derived from a model. A SVD technique is then used to invert S and determine dK_j as a function of dβ_i. Feeding -dK_j into the β-function corrector magnets restores the ideal optics.