11

Luminosity Optimization Feedback in the SLC
L. Hendrickson, S. Bes, P. Grossberg, D. McCormick, N. Phinney, P. Raimondi, M. Ross
Stanford Linear Accelerator Center, Stanford University
Stanford, California 94309

The luminosity optimization at the SLC has been limitedby the precision with which one can measure the micron size
beams at the Interaction Point. Ten independent tuning parameters must be adjusted. An automated application has
been used to scan each parameter over a significant range
and set the minimum beam size as measured with a beambeam deflection scan. Measurement errors limited the accuracy of this procedure and degraded the resulting luminosity.
A new luminosity optimization feedback system has beendeveloped using novel dithering techniques to maximize theluminosity with respect to the 10 parameters, which are adjusted one at a time. Control devices are perturbed aroundnominal setpoints, while the averaged readout of a digitizedluminosity monitor measurement is accumulated for eachsetting. Results are averaged over many pulses to achieve
high precision and then fitted to determine the optimal setting. The dithering itself causes a small loss in luminosity,
but the improved optimization is expected to significantly
enhance the performance of the SLC. Commissioning results
are reported.

the scans are relatively slow, the results may also be adversely affected in unrelated beam changes during the scan.
Inaccuracies of the IP tuning are estimated to have been responsible for about 20-40% average luminosity loss over the1995 and 1996 SLC runs [1]. An automated feedback was
designed to improve the resolution of the measurements, andto maintain maximum luminosity.
Y = A * (X–B) **2 + C
A = 0.9062
B = 0.6133
C = 9.597
RMS FIT ERROR
Chi–square/DOF

STD DEV = 0.2662
STD DEV = 0.2863
STD DEV = 0.7266=2.704+2.1732018
BSCN E+X_WIDSQ

Abstract

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1 Introduction
6

As the SLC beams approach the collision point, they are focused through a series of quadrupole and sextupole magnets.
For each beam, five orthogonal combinations of magnets areadjusted to optimize beam size at the interaction point. Priorto 1997, optimization was performed periodically at operator request by a semi-automated procedure which scans thedevices through a series of values while measuring the resulting beam size. A parabolic fit to beam size squared asa function of setting determines the optimal device values
but operator judgement is required to decide whether to implement the proposed correction. Figure 1 shows a typicalscan. This procedure has several shortcomings which havebecome more evident as upgrades to the SLC optics reduced
the minimum beam size achievable. One problem is that on
the extreme ends of the scan, the error in the beam size measurement is large, degrading the scan resolution. Because theoptimization is dependent on human intervention, the machine was not always kept in a fully optimized state; typically corrections were applied only every 8 hours. The fullset of scans could take up to an hour to complete with the machine necessarily mistuned during much of that time. Since
 Work supported by the Department of Energy, contract DE-AC03-76SF00515–3–2–10

1

23

KNOB (NXD_CCS)KNOB (NXD_CCS) STRT=–3.000 STEPS = 7 SIZE = 1.000
21 – OCT – 97 10:14:35

Figure. 1. Optimization scan method. A linear combinationof magnets is scanned. At each point in the plot, the beamwidth is measured by steering one beam across the other andfitting the resulting deflection angles.

2 Dithering feedback
Dithering techniques were developed as an alternative to thescan method. They are useful where measurements respondparabolically with actuator movement. In these cases, givena single raw measurement, there is not enough information
for a feedback to tell which way to move the actuator, because it may be on either side of the curve. One way to obtain this information is to move the actuator and observe themeasurement change. Dithering involves perturbing the actuator by a small amount above and below its nominal setting
while taking synchronous beam measurements. A digitizedanalog readout which is proportional to luminosity is readon each accelerator pulse, at 120 Hz. As the feedback software moves the devices, it accumulates average luminosity
readouts for each of the three settings (nominal, above andbelow). After averaging many pulses, the software calculates
the offset of the parabola, and moves to the newly calculated
optimal setting.
The dithering method was first proposed and developedin 1993 [2]. A system was designed to optimize the energy
spread of the SLC beams, but was discontinued due to operational complications. The design for the current luminosity optimization feedback is built upon the previous implementation, but upgraded to handle slower devices. The
earlier system used only two dithering steps (up and down)
and required the use of quickly responding devices; it included assumptions about the slope of the parabola being
optimized. The current system, with three dither settings,
makes no modeling assumptions.
Dither knob, mm0.50Bhabha−0.5−7−6−5−4−3−2−10−8−7−6−5−4−3−2−10−8−7−6−5−4TIME−3−2−10600
400
2000Beamstrahlung−8600
4002000Figure. 2. Response of digitized luminosity monitors during dithering. The dither pattern is CENTER, UP, CENTER, DOWN. Originally a radiated bhabha counter was usedas the monitor, but at higher luminosity, the beamstrahlung
monitor provides a more stable result.

3 Software design
The software design for the optimization system is built upon
existing feedback systems. The SLC fast feedback is capableof measuring and controlling the beam at the full beam rateof 120 Hz [3]; it was upgraded to perform the dithering functions described above. To keep the design simple, the fast
feedback system is not required to handle the interaction between multiple tuning parameters. Ten feedback loops werecreated and commissioned, turning on only one at a time.
The system is database-driven, so that only database work isrequired to support new loops of an existing type.
In order to eliminate interaction between the optimization
parameters, a scheduler is used. The user configures thefrequency for performing each optimization, and only one
is on at a time. The user may enable or disable individualloops. By turning off the automatic scheduling, the user regains manual control over the optimization. At present, thescheduler runs at a 15 second interval, turning on or off theindividual feedback loops according to user determined criteria.

4 Timing and luminosity losses
The dithering technique inherently requires a luminosity loss
in order to perform the measurement. Therefore the systemparameters are tuned to provide the most optimal tuning withthe least disruption and luminosity loss. Several parameters
are provided for user control, and the goal of maximum total luminosity does not necessarily result in the most precise
optimization. For example, by increasing the dither size, themeasurement becomes more accurate but also more invasive.
Increasing the number of averaged pulses for each measurement also improves the resolution; but the tradeoff is a longer
dithering time and sensitivity to unrelated beam movements.
The optimization devices are slow to repond, and take about
a quarter of a second to achieve a requested change. On eachnew dither setting, the feedback rejects a specified numberof pulses while the magnets settle. The user can also control
the number of good pulses on which the feedback stays ateach dither value before moving to the next setting. In addition, filtering parameters allow the user to reject data on
anomalous pulses. Tolerances for each optimization parameter enable the scheduler to determine whether to iterate or
to move on to the next loop. Finally, a timer for each parameter is provided, so that slowly changing parameters may beoptimized less frequently if desired.
As presently configured, each optimization parameter iscontrolled on a 40 minute timer. For each dither step, thedevices settle for 30 pulses before the feedback collects 200
good pulses of data. The number of good pulses averaged
for an optimization measurement is 3200, which takes about
38 seconds. While the dithering is on, 70% of the pulses areused for results, 11% are for magnet settle time and 19% arefiltered or rejected. When a measurement is within the user
specified tolerance, the scheduler turns it off and moves on tothe next loop. If necessary, the feedback loop is left on for up
to 5 minutes in order to converge. Each feedback loop executes for 105 seconds on average and typically, some dithering is active 44% of the time.
The luminosity loss due to dithering is calculated using
the configured dither size and the parabolic parameters fromthe scan method. The average dither size results in 16% luminosity loss, but the nominal dither value is used half of thetime, and the dithering is running 44% of the time. This results in a luminosity loss due to dithering of just over 3% asof October, 1997. Earlier in the commissioning, more conservative system parameters were used, resulting in a larger
luminosity loss of about 6%.

5 Commissioning experience

0Positron Y Waist offset, cm

Several weeks were required to complete commissioning of
the optimization system, as various operational challenges
were encountered and overcome. An essential element of
the optimization system is a monitor which reliably reads amaximum value where the luminosity is a maximum. Originally, counters which detect radiated bhabha events wereused for optimization; one of these monitors seemed to havea good response, but may have had acceptance problems
which caused the peak signal to occur at other than the optimal point. This would have resulted in the feedback maintaining a suboptimal luminosity! Furthermore, at higher luminosities, backgrounds and other systematics in these monitors made them unreliable. Finally the beamstrahlung monitors, which measure the energy of photons radiated during
the beam-beam interaction were found to provide a stable
response with minimal noise. Figure 2 shows the dithering
response for both types of monitors. This only emphasizes
the importance of finding a reliable luminosity signal free ofcontamination.
During testing, each of the ten optimization variables wasdeliberately mistuned to study the correctness and convergence of the feedback response. For small changes, the feedback converges quickly with few iterations. For mistuning
larger than the dither size, the parabolic fit is poorly constrained and the feedback typically overestimates the correction needed. To prevent overshooting, the maximum allowed
movement after a single measurement is required to be lessthan dither size.
By averaging a large number of pulses, the optimization
feedback is able to achieve much better resolution on eachparameters than with the previous scan technique. Figure 3
shows the improved resolution of the feedback optimization
measurements, compared with results from the scans. The
measurement resolution is improved by about a factor of 5.

0.1
0.05

−0.05
−0.1
−0.15
−0.2
−0.25
−0.3
−0.35
−0.4
12345678910TIMEFigure. 3. Resolution of optimization measurements forscan results (o) compared to feedback measurements (+).
With the feedback off, ten optimization scans were performed (o) and corrections were not implemented. Then thefeedback system was used to take ten comparable measurements (+).

commissioning phase was completed, the luminosity feedbacks have remained on, with few complaints. Since theintroduction of the system, the SLC has been able to achieve
and maintain record-high luminosity, and the feedback system is credited with contributing to this success.
In the future, the optimization system may be extended tocontrol beam orbit bumps in the SLC linac, which are currently controlled via operator scans. Additionally, the system may be used to maximize luminosity in the PEPII BFactory.
Acknowledgements

6 Conclusions and future plans
A novel dithering feedback has been implemented to optimize the beams at the SLC interaction point. Ten parameters
are tuned including horizontal and vertical focus, dispersion,and coupling. With the new feedback the measurement resolution is improved by about a factor of 5. Over long periods,
the feedbacks are able to maintain the optimization parameters within much tighter tolerances than previously.
The new optimization feedback has many other operational benefits. Because it is completely automatic, recovery
from interruptions is faster and more reliable. The feedback
also keeps these final parameters tuned for peak performance
without relying on the skill or judgement of particular operators or physicists. In addition, previous techniques absorbed
a large fraction of the efforts of an operator who is now freed
to concentrate on analysis and tuning of other parts of themachine.
One measure of the success or failure of a feedback system is whether the operators choose to turn it off: after theThe optimization system has benefitted from the contributions of many operators and physicists as well as hardware
and software engineers. In particular, Paul Emma and Frank
Zimmerman were instrumental in analyzing the potentional
luminosity improvements and initiating development of thesystem.
References[1] P. Emma et al., Limitations of Interaction-Point SpotSize Tuning at the SLC, In Proc. of the IEEE Part. Acce.
Conf., SLAC, May 1997. SLAC-PUB-7509.
[2] M.C.Ross, L. Hendrickson, T. Himel and E. Miller, Precise System Stabilization at SLC using Dither Techniques, Proc. of the IEEE Part. Acce. Conf., SLAC, May
1993. SLAC-PUB-6102.
[3] L. Hendrickson et al., Generalized Fast Feedback System in the SLC, in Proc. of ICALEPCS’91, SLAC,November 1991. SLAC-PUB-5683.