76 Beam-based Correction and Optimization for Accelerators
y (mm)
-0.1
-0.05
0
0.05
0.1
∆y (mm)
-0.2
-0.1
0
0.1
0.2
Quadrupole center
Figure 3.3 Example of a bow-tie plot in beam-based alignment. The horizontal axis
is the orbit reading on the nearest BPM to the quadrupole. The vertical axis is
the orbit change at other BPMs corresponding to a step change of the quadrupole
strength. Each line represents data for one BPM.
corresponding to a step change of the quadrupole current can be derived with
∆θ =
∆x i
R iq
,
(3.6)
where ∆x i is the orbit shift at BPM i and R iq is the orbit response for a kick at
the quadrupole location to the BPM. BPMs close to the quadrupole yet with
a sufficiently long lever arm are preferred to avoid effects of lattice errors.
Multiple BPMs can be used to derive the kick angle ∆θ for a quadrupole
current change ∆I. If the current to gradient conversion rate, r =
∆K
∆I , and
the effective length of the quadrupole, L q , are known, the orbit offset, x q , at
the quadrupole can be calculated from
∆θ
∆I
= rL q x q .
(3.7)
This approach can also be applied to storage rings, although in this case
the accuracy may be impacted by the linear optics errors introduced by the
quadrupole strength modulation.
3.3 ORBIT CORRECTION
The goal of orbit correction is to steer the beam orbit with correctors toward
the target orbit. The target orbit may be specified only at one or a few selected
locations, or throughout the beam path. The former case is referred to as local
orbit correction and the latter global orbit correction.