To: Uli Wienands Oct 11, 1999
From: Howard Smith
cc: http://www.stac.stanford.edu/grp/ad/op/
Topic: Ideas for steering feedback control of HER Sextupole
SD2A/SD4A trajectory.
Overview:
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Importance of the trajectory in HER ARC1B/3A large beta defocusing
sextupoles (SD4A sext 6052/6112 and SD2A 9072/9132) is self evident.
It should be recognized that trajectory control in these magnets could
be implemented via a fast steering feedback mechanism. Below I discuss
a manner in which this could be implemented, with ramifaction for
existing IR2 orbit control (HER0, dither loops) quite negligible.
Further I elude to manner in which orbit manipulation in these sextupoles
could be utilized as an optimization and diagnostic tool.
New Task/Technique:
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Each of these magnets has an associated vertical position monitor.
Magnet "bump knobs" currently exist which are routinely used to manually
maintain sextupole trajectories, as determined by each sextupole's
associated position monitor. This task is a good candidate for steering
feedback, however the formalism required would differ from most
steering feedback techniques currently used, and would require (modest)
software effort in order to be implemented.
I propose a steering feedback described as follows. The "loop" would
have four measurements; the vertical position at each of the four
sextupole magnets. The feedback "states" could be merely these four
measurements, or appropriate linear combinations of them (more on this part
later). The "actuator" part of the loop is where the deviations from
standard feedback surface. One version would implement a set of "pseudo
actuators" each of which is essentially the bump knobs which we routinely
use. Each "pseudo actuator" would map to the (real) actuators by the
coefficients of the bump knob. This "pseudo actuator" formalism already
exists in feedback. Loop closure would result from feedback
state<->actuator matricies which have each state map to it's associated
pseudo actuator only. One could conceptualize this as four separate
feedbacks, whose actuators and states are all exclusive of one another.
The exclusivity among these states/actuators relies upon the closure
of the pseudo actuator bump knob coefficients, and such closure has been
demonstrated.
Ramifications for HERO:
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The existing HERO steering loop uses BPMs in ARC1B/3A to fit for
kicks coming from the IP. Changes to the ARC1B/3A trajectory will effect
the kick calculated by HER0. However HERO currently does not use all of the
ARC1B/3A BPMs to determine this kick. In the vertical plane, only four of the
eight BPMs in each half arc are used. Currently HERO's BPM list includes
one of the SD2A/SD4A BPMs per side. I would propose changing HERO's BPM
list to exclude the SD2A/SD4A BPMs, and include all others (six per half
arc). Since the actuation mechanism of the proposed sextupole bump feedback
would (to the extent that the pseudo-actuators are truly closed bumps)
effect only SD2A/SD4A BPMs, changes to the trajectory implemented by the
new sextupole orbit loop would be transparent to HERO...if the SD2A/SD4A
BPMs are excluded from HERO. This change to HERO would be simple,
straightforward, and viable.
Now for something REALLY controversial:
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Up to this point I discuss a loop whose states are merely the
individual BPM readouts. From the standpoint of orbit control, this would
be sufficient. However a linear transformation of these measurements could
be made in which the loop's states are expressed in terms of average orbit
offset, symetric and antisymetric sextupole offset, and arc left/right orbit
difference.
Here's the idea (See ref. #1). The location of these sextupole
magnets is such that symetric/antisymetric orbit bumps generate
coupling/vertical dispersion at the IP. If such symetric/antisymetric bumps
are introduced in a fashion which is antisymetric across the IP (i.e. what
gets introduced in ARC1B gets un-introduced in ARC3A), then the coupling or
dispersion introduced would be localized to the IR2 area. Such controlled
bumps can offer IR2 local coupling/vertical dispersion compensation.
By expressing the Feedback Loop's states in terms of
symetric/antisymetric (or equivalently dispersion-like and coupling-like,
or even sine-like and cosine-like...all depending on one's culture) bumps,
such a feedback could prove very useful in routine tuning. I envision
a version of our "scheduler" which would dither the sextupole orbits via
such a feedback's setpoints, to periodically optimize the IR local vertical
dispersion and coupling.
I believe that such a tool could be very useful towards understanding
the distinctions between IR2 local and ring global dispersion and coupling
issues.
What about the LER?
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Everything stated above directly referenced the HER. However the
same discussion could easily be transposed into the language of the LER.
The only complication I have uncovered in applying this treatment to the
LER is that the sextupole bump knobs "share" a corrector (i.e. bump knobs for
sextupoles SCYR3 4112 and 4072 each use YCOR 4092). I have confirmed with
Linda Hendrickson that this complication could be easily handled by the
pseudo actuator formalism.
Ref #1 Beam Based Alignment of the SLC Final Focus Sextupoles.
P. Emma, et.al SLAC Pub 6209 5/93