Stabilizing effect of a double-harmonic RF system in the CERN PS Page: 3 of 3
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None of the RF cavities in the the PS have correct fre-
quency and quality factors that would explain the observed
coupled-bunch instability. A similar coupled-bunch insta-
bility was observed for the first time in 2008 during the first
splitting of the nominal 25 ns beam for LHC with new kick-
ers in the PS . Therefore, these kickers are suspected
as a possible source of impedance.
TRANSIENT BEAM LOADING
During the experiment, the relative phase between the
two RF systems has been adjusted such that the arbitrarily
chosen bunch 12 was well flattened. However, the bunches
at head and tail of the batch become noticeably asymmet-
ric as shown in Fig. 5. Obviously, this is due to the relative
First bunch, 1ti Reference, l12 Last bunch, 18
Figure 5: First, reference and last bunch of the batch
(recorded on the same cycle, time span: 21 ms).
phase changes along the batch due to transient beam load-
ing. Since the relative phase of the gap voltages h 21/42
has not been measured, an estimation of the phase error
based on the asymmetry of the bunch profiles has been per-
formed. Starting from a Hofmann-Pedersen distribution
in longitudinal phase space , bunch profiles for vari-
ous longitudinal emittances and relative phase errors have
been calculated. Selecting those profiles with the measured
(tomographic reconstruction for the SH case) longitudinal
emittance results in a set of profiles with the correct el and
various phase errors. Comparing them with the measured
profiles, estimates on phase errors are done that give the
best representation of the data.
Fig. 6 illustrates the estimated phase error along the
batch. A relative phase slippage of h 21/42 RF com-
Figure 6: Estimated phase offset along the batch for five
individual cycles (blue) and averaged (red).
ponents along the batch of the order of 20 can be esti-
mated. It should be mentioned that the measurement does
not allow to disentangle which of the RF systems (10 MHz,
20 MHz or both) is the major contributor. It is thus planned
to measure the RF phases along the batch directly.
Beam experiments in the CERN PS to address the lon-
gitudinal beam stability in the DH RF system with h
21/42 and a voltage ratio of 0.5 have been performed. As
expected, the flat bunches in DH RF buckets are more sta-
ble compared to bunches in SH RF buckets where strong
coupled-bunch oscillations have been observed. The sym-
metry of flat bunches turned out to be very sensitive to
small phase errors of the two RF harmonics applied. A
beam-loading induced phase error of a few degrees is suf-
ficient to produce significantly asymmetric bunches at the
head and tail of the batch. Any effect of electron cloud,
which is normally observed close to extraction of 72 short
bunches spaced by 25 ns, could not be detected with normal
or flat bunches spaced by 100 ns.
The authors would like to thank Elena Shaposhnikova,
Thomas Bohl and Jim MacLachlan for helpful discussions.
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Bhat, C.; /Fermilab; Caspers, F.; Damerau, H.; Hancock, S.; Mahner, E. et al. Stabilizing effect of a double-harmonic RF system in the CERN PS, article, April 1, 2009; Batavia, Illinois. (https://digital.library.unt.edu/ark:/67531/metadc933123/m1/3/: accessed March 20, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.