Fast feedback for linear colliders Page: 4 of 6
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figure 3. indicate that when corrector response is slow
compared to the design feedback control of 6 pulses, there
is performance degradation. Furthermore, the response
becomes more sensitive to othe . actors such as imperfect
modeling. Near the end of the last SLC run, attempts were
made to design matrices with a better model of the slow
corrector response. Tests of the new design showed
improved feedback response, hut other problems made it
operationally unacceptable Additional work is needed.
0 5 10 15 20 25 30
Figure 3: Simulations of feedback response with slow
corrector speeds and imperfect calibrations. Plots shown
are for the ideal case (o), slow correctors (*). poor
modeling (+). and the combination of slow correctors with
poor modeling (-).
Figure 4 shows estimates of feedback response for the
series of linac launch loops. The response is measured by
inducing a step function upstream of the Imac, first with the
feedbacks on and then with the feedhacks off. Fitted heam
position data for both cases is acquired for several hundred
consecut e pulses The FFTs for both data sets are
calculated and the ratio is plotted Unfortunately this
measurement is noisy An alternate technique involves
inducing sine sases over a range of known frequencies and
measuring the resulting amplitudes with feedback on and
off The sine wave technique produces cleaner results less
invasively, but it is more tine-consuming. Alsi shown in
figure 4 are simulations for feedback performance. Note
that the "ideal' simulation assumes that the accelerator
model is perfeci, correciors are as fast as modeled, that all
of the loops are operating with gain factors of 1.0 and that
the cascade system is working perfectly This is identical to
the ideal simulaion lor a single loop. An initial attempt at a
more realistic simulation includes effects of imperfect
modeling, low gain factors and imperfect cascade
performance. More work needs to be done to measure.
simulate and hopefully to optimize the performance of the
linac loops as a system.
E10 e .
E 01 -
Figure 4. Measurement and simulations of feedback
response (on/off) for the system of linac loops. Plots shown
are for the ideal case (-). measured data taken from a ratio
of FFTs (o), and an attempt at a realistic simulation (+)
"CASCADED" FAST FEEDBACK
As shown in figure 1. steering in the SLC linac is
controlled by a series of feedback loops. In the original
system, these loops were all controlling the same
parameters: this resulted in problems with overcorrection
of upstream perturbations and amplification of heam noise.
This effect was predicted in the initial feedback design
simulations and the cascade system was designed to correct
this problem. Now, after receiving new measurements on
each heam pulse. each linac loop sends its calculated states
to the nent downstream loop, and receives the current states
from its upstream neighbor The downstream loop
performs corrections based on the differences between the
states of the upstream and downstream loops Therefore
each loop should correct only the perturbations initiated
immediately upstream of it These corrections depend upon
a reliable method for mathematically transporting the
positions and angles at one point to the downstream
location The model is not good enough over these
distances, so adaptive methods are used to dynamically
update the transport matrices. The adaption calculations are
based upon the SEquential Regression (SER) algonrhml7l.
adapted for use in the SLC feedback sysiemll.
Cascade performance can he characiered hy rejection
ratios. This is the fraction of an incoming zrturbation
which is seen and corrected by each feedback loop.
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Hendrickson, L.; Adolphsen, C.; Allison, S.; Gromme, T.; Grossberg, P.; Himel, T. et al. Fast feedback for linear colliders, article, May 1, 1995; Menlo Park, California. (digital.library.unt.edu/ark:/67531/metadc691680/m1/4/: accessed January 23, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.