9 Accelerator Operations
529
• facilities for dispersion measurement, harmonic analysis, energy offset analysis;
• facilities for threading, averaging and correction of the first N turns, injection
point correction;
• multi-turn capture and analysis facilities.
9.4 Beam Feedback Systems
R. Steinhagen
The domain of control system design is too vast to be comprehensively and
briefly covered and thus this section focuses only on the key aspects that are
applicable to accelerator control. The inclined reader is referred for a more detailed
introduction to [6]. One distinguishes two paradigms that are used to drive and
stabilise any given beam parameter:
• Feed-Forward which relies on the knowledge of the transfer function between
beam parameter, required current and corresponding effective magnetic field,
and essentially consists of inverting the scalar or matrix relations discussed
in Sect. 9.3, and for matrices most commonly done using a Singular-ValueDecomposition based approach[7]. While this scheme is often sufficient, its
intrinsic weakness of being limited by inaccuracies of the magnet’s transfer
function, dynamic field effects such as e.g. the decay- and snapback phenomenon
in superconducting magnets and random external perturbations may lead to a
potentially out-of-tolerance systematic error = 1 − , which is illustrated as
a difference between the reference and actual beam process variable in Fig. 9.2a.
Still, this type of control is suitable for many beam parameters such as the beam
momentum where the magnet and RF transfer functions involved are typically
known on the 0.1% level.
• Feedback may be used in case the beam parameter model is insufficient (due
to, for example, multiple dependencies or random perturbations) and at the
same time the parameter deviations being accessible by beam instrumentation
or diagnostics methods. In this case, the corresponding measurements can either
be used to: (a) improve the knowledge of the beam parameter to magnetic
field to current transfer function (feed-forward scheme), or (b) to ‘feed back’
part of the measured value into the reference that is send to the magnets or
RF systems. In this case the difference = 1 − drives a controller that
iteratively optimises the actuator signal by minimising till the actual beam
process variable matches the desired reference value as shown in Fig. 9.2b. Due
to intrinsic limitations such as the bandwidth of the magnetic circuits and nonlinear effects such as delays and rate-limits, the stabilisation is typically not
instantaneous. To cope with these effects requires a more complex form of
controller to optimise temporal convergence.
529
• facilities for dispersion measurement, harmonic analysis, energy offset analysis;
• facilities for threading, averaging and correction of the first N turns, injection
point correction;
• multi-turn capture and analysis facilities.
9.4 Beam Feedback Systems
R. Steinhagen
The domain of control system design is too vast to be comprehensively and
briefly covered and thus this section focuses only on the key aspects that are
applicable to accelerator control. The inclined reader is referred for a more detailed
introduction to [6]. One distinguishes two paradigms that are used to drive and
stabilise any given beam parameter:
• Feed-Forward which relies on the knowledge of the transfer function between
beam parameter, required current and corresponding effective magnetic field,
and essentially consists of inverting the scalar or matrix relations discussed
in Sect. 9.3, and for matrices most commonly done using a Singular-ValueDecomposition based approach[7]. While this scheme is often sufficient, its
intrinsic weakness of being limited by inaccuracies of the magnet’s transfer
function, dynamic field effects such as e.g. the decay- and snapback phenomenon
in superconducting magnets and random external perturbations may lead to a
potentially out-of-tolerance systematic error = 1 − , which is illustrated as
a difference between the reference and actual beam process variable in Fig. 9.2a.
Still, this type of control is suitable for many beam parameters such as the beam
momentum where the magnet and RF transfer functions involved are typically
known on the 0.1% level.
• Feedback may be used in case the beam parameter model is insufficient (due
to, for example, multiple dependencies or random perturbations) and at the
same time the parameter deviations being accessible by beam instrumentation
or diagnostics methods. In this case, the corresponding measurements can either
be used to: (a) improve the knowledge of the beam parameter to magnetic
field to current transfer function (feed-forward scheme), or (b) to ‘feed back’
part of the measured value into the reference that is send to the magnets or
RF systems. In this case the difference = 1 − drives a controller that
iteratively optimises the actuator signal by minimising till the actual beam
process variable matches the desired reference value as shown in Fig. 9.2b. Due
to intrinsic limitations such as the bandwidth of the magnetic circuits and nonlinear effects such as delays and rate-limits, the stabilisation is typically not
instantaneous. To cope with these effects requires a more complex form of
controller to optimise temporal convergence.