220 Beam-based Correction and Optimization for Accelerators
One way to optimize DA and LMA simultaneously is to inject into a single
bunch to a fixed amount of current at which the Touschek lifetime is dominant.
The lifetime can be measured and after that the DA is measured by kicking the
beam with an increasing kick angle, until the beam is lost. Each data point may
take 15-30 seconds, but it would still be acceptable. In an experiment at the
MAX-IV storage ring, the DA optimization was done by minimizing the beam
loss for a beam under a fixed kick [91]. In this approach, the measurement for
each data point will be faster since not all beam is lost.
In the next we will discuss the DA and LMA optimization separately.
8.4.1 Dynamic aperture optimization
General considerations: As mentioned in the above, the DA can be measured by kicking a low charge beam with an increasing kick strength and
recording the kick strength when the beam loss occurs. The measured DA
can then be used as the objective function. The beam charge can be as low as
∼ 10 µA, which helps limit the accumulated beam loss during the experiment.
This approach would be particularly useful for the commissioning of a new
ring before high current beams can be stored.
An alternative approach is to optimize the injection efficiency directly. If
the tuning knobs change only the DA and not the other factors in the injection
process that affect the injection efficiency, optimizing the injection efficiency
is equivalent to optimizing the DA. Since the injection efficiency cannot go
above 100% or below 0%, if the DA is so small such that no beam is captured,
or if the DA is so large such that the injection efficiency is already 100%,
the optimization algorithms could fail since the objective function may not
respond to the tuning knob changes. In such cases, changes may be made to
bring the injection efficiency to the medium range. If the DA is initially too
small, random settings of the tuning knobs may be tried until one solution is
found to allow some injected beam to be captured. If the DA is large enough to
have a high initial injection efficiency, yet it is still desired to further increase
the DA, the injected beam can be mis-steered from the ideal trajectory to lower
the injection efficiency. In the case of off-axis injection, which is the injection
scheme adopted for the existing storage rings, the injection efficiency can be
lowered by reducing the kicker bump.
Figure 8.11 illustrates the horizontal off-axis injection of a storage ring. The
centers of the stored beam and the injected beam are normally separated by
a distance D. During injection, the stored beam is kicked toward the septum
wall. To fully capture the injected beam, the DA needs to be larger than the
distance between the injected beam and the kicked stored beam plus half of
the size of the injected beam. If the DA is smaller, the part of the injected
beam beyond the DA will be lost. If the kicker bump is reduced, the DA
boundary will shift with the stored beam and the loss of the injected beam
will occur if the boundary moves into the injected beam. For the injection
One way to optimize DA and LMA simultaneously is to inject into a single
bunch to a fixed amount of current at which the Touschek lifetime is dominant.
The lifetime can be measured and after that the DA is measured by kicking the
beam with an increasing kick angle, until the beam is lost. Each data point may
take 15-30 seconds, but it would still be acceptable. In an experiment at the
MAX-IV storage ring, the DA optimization was done by minimizing the beam
loss for a beam under a fixed kick [91]. In this approach, the measurement for
each data point will be faster since not all beam is lost.
In the next we will discuss the DA and LMA optimization separately.
8.4.1 Dynamic aperture optimization
General considerations: As mentioned in the above, the DA can be measured by kicking a low charge beam with an increasing kick strength and
recording the kick strength when the beam loss occurs. The measured DA
can then be used as the objective function. The beam charge can be as low as
∼ 10 µA, which helps limit the accumulated beam loss during the experiment.
This approach would be particularly useful for the commissioning of a new
ring before high current beams can be stored.
An alternative approach is to optimize the injection efficiency directly. If
the tuning knobs change only the DA and not the other factors in the injection
process that affect the injection efficiency, optimizing the injection efficiency
is equivalent to optimizing the DA. Since the injection efficiency cannot go
above 100% or below 0%, if the DA is so small such that no beam is captured,
or if the DA is so large such that the injection efficiency is already 100%,
the optimization algorithms could fail since the objective function may not
respond to the tuning knob changes. In such cases, changes may be made to
bring the injection efficiency to the medium range. If the DA is initially too
small, random settings of the tuning knobs may be tried until one solution is
found to allow some injected beam to be captured. If the DA is large enough to
have a high initial injection efficiency, yet it is still desired to further increase
the DA, the injected beam can be mis-steered from the ideal trajectory to lower
the injection efficiency. In the case of off-axis injection, which is the injection
scheme adopted for the existing storage rings, the injection efficiency can be
lowered by reducing the kicker bump.
Figure 8.11 illustrates the horizontal off-axis injection of a storage ring. The
centers of the stored beam and the injected beam are normally separated by
a distance D. During injection, the stored beam is kicked toward the septum
wall. To fully capture the injected beam, the DA needs to be larger than the
distance between the injected beam and the kicked stored beam plus half of
the size of the injected beam. If the DA is smaller, the part of the injected
beam beyond the DA will be lost. If the kicker bump is reduced, the DA
boundary will shift with the stored beam and the loss of the injected beam
will occur if the boundary moves into the injected beam. For the injection