Feedback damper system for quadrupole oscillations after transition at RHIC. Page: 4 of 5
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sFigure 2: Modulation introduced in the the RF voltage by
the feedback system.
In order to reduce the longituginal quadrupole oscilla-
tions after transition, the following scheme was applied:
detect the average bunch length using a longitudinal pick-
up, rotate the signal by 90 degrees by mean of an appro-
priate filter, amplify and finally give an energy kick with
a longitudinal kicker. To detect the bunch oscillations we
monitored the amplitude of the signal of a Wall Current
Monitor (WCM) at the 4*h harmonic of the RF frequency
which is proportional to the inverse of the bunch length, if
we consider a Gaussian beam [4]. We then digitized the
signal at 96 kHz sampling rate and performed a 90 degree
phase shift. A schematic of the system is in Figure 1. The
shifted signal is transformed back from digital to analog
and is sent back to the RF drive which will modulate the
cavity voltage at the desired frequency. It is worth not-
ing that, in order to maintain the optimum phase-shift, the
filter used must be tunable in the range of the allowable
synchrotron frequencies, as show in Table 1.
So as not to disturb the bunch motion, the filter gain has
to increase smoothly when the bunch oscillation starts and
be able to fade away once the motion is damped, as show in
Figure 2. As feedback system is active only in the early part
of the energy ramp a set of triggers was configured which
automatically turns on the DSP board, responsible for the
phase shift, for 4 seconds starting at transition.
RESULTS
The loop for the feedback system was first closed dur-
ing an Accelerator Physics Experiment (APEX) in 16 Jan-
uary and was left operational for the rest of the d-Au run in
the Yellow ring only. Figure 3 shows the amplitude of the
41h RF harmonic line of the beam spectrum as a function
of time before and after the loop was closed. This signal
shows the mode n=0 and m=2 only, where all bunches os-
cillate in phase, and is proportional to the average bunch
length from all the 95 bunches stored. The longitudinal
feedback is able to damp the phase oscillation in less than a
second-after transition that is equivalent to a damping fac-
tor of 1.7 s- which is half of the damping calculated by2A,
Ts/ ia,
2.2
1.4
1.2 ? I
1 1S5 2 25 3 2.5 4Figure 3: Amplitude of the WCM signal filtered at the
fourth RF harmonic. This signal is proportional to the in-
verse of the bunch length, and is the averaged quadrupole
motion of all 95 bunches stored in the machine. Without the
feedback loop these oscillations persist for a period on the
order of 10 seconds, while with the feedback loop closed
they are damped in less than I second after transition.
equation 1 and is equivalent to a damping time of 0.6s.
In Figure 2 is the RF voltage with the modulation from
the quadrupole damper, notice that the required modulation
amplitude necessary to damp the oscillation is less than 2
kV peak-to-peak, i.e., less than 3% of the total storage volt-
age. Figure 4 shows an average of 20 energy ramps before
and after the feedback loop was closed. The emittance af-
ter transition when the feedback is working is on average
10% smaller than in previous ramps, when there was noI
SFigure 4: Average of the longitudinal emittance for 20
ramps, before and after the use of the feedback damper for
longitudinal quadrupole oscillations. There is a clear dif-
ference in trend with the use of the feedback; on average
the longitudinal emittance is 10% smaller after transition
and this improvement is kept until store. It is also possible
to notice that there are other effects which cause emittance
growth during the energy ramp that were not damped with
the feedback system. The gap in the data around transi-
tion is due to the lack of data for the average bunch length
during this period.Yel,4OhC3If-
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*1 -5.5 0 0.s 1 1.5 2a. -
ass
0.35 r
a3 -- - fr
0.25ti110 20 30 +0 50 00 70 80 90 100
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Abreu, N.; Blaskiewicz, M.; Brennan, J. M. & Schultheiss, C. Feedback damper system for quadrupole oscillations after transition at RHIC., article, June 23, 2008; United States. (https://digital.library.unt.edu/ark:/67531/metadc894578/m1/4/: accessed March 19, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.