Automated tuning of the advanced photon source booster synchrotron Page: 4 of 5
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where is the response matrix found by the method
given above and A8, is the vector giving the size of varia-
tion of the correctors used. The objective is to reduce
Aum, the error trajectory used for the feedback loop, to
zero, describing the situation in which the first turn trajec-
tory matches the measured closed orbit. Singular value
decomposition is used to invert the matrix 91 . After
AOn = 31- A un ,
which reveals the amount the correctors must be adjusted
(2]. The calculated currents are then multiplied by a gain
factor, and the corrector setpoints are updated by this
amount. This process is repeated in a feedback loop until
the rms of A urn is sufficiently small. A gain of 0.5 was
empirically determined to maximize the system perfor-
mance while avoiding instability.
Because longitudinal and horizontal beam motions
both appear as positional variations at BPMs located in the
non-zero dispersion regions, the longitudinal errors must
be corrected before simple correction of the horizontal can
begin. The longitudinal injection errors result from slight
drifts of the booster dipole magnet ramp or the relative rf
phase between the PAR and booster. Phase and energy
errors appear 90 degrees out of phase. Upon injection, an
energy error, as measured on a turn-to-turn basis at a high
dispersion point, assumes a cosine-like form, while a
phase error has a sine-like signature. Energy errors are
corrected through the adjustment of the start ramp time of
the magnet ramping system. Phase errors are corrected by
changing the relative phase between the PAR and the
In the longitudinal plane, only one reliable beam posi-
tion monitor in a high dispersion region need be used.
The beam position is recorded over a series of 256 turns
and is stored in a beam history module. This number of
turns was chosen such that a sufficient number of synchro-
tron oscillations could be viewed (Qs = 4x10 2). It is
through this data that the energy and phase errors are
The longitudinal corrections can be approached in a
fashion similar to that used for the vertical plane. The
required feedback parameters are again empirically deter-
mined. The start ramp time and relative phase are adjusted
manually to eliminate errors such that only noise
remained. Then, the start ramp time is adjusted in a series
of five steps relative to the original setpoint. and the slope
is determined. Also, the relative phase is adjusted in a
series of five steps relative to the original setpoint, and the
slope is again determined. Figure 1 exemplifies the results
of manual longitudinal tuning in the following order:
energy and phase errors eliminated, phase error only (36
degrees), and energy error only (1.25 MeV). Some signal
processing is first applied in order to extract only the
desired longitudinal motion from the accumulated beam
position history. An example of the processed phase error
is found overlaid in Figure 2.
l o --a 30 20 a
0 50 100 150 200 20
Figure 1: Manual tuning results.
Model and Actual
0 50 100 150 200 250
Figure 2: Model and actual phase error.
Regarding correction of the longitudinal errors, a sim-
ple method is employed. First, the cosine-like component
of the motion is determined. A change in the start ramp
time is then made to zero this energy error. The data is
then processed on the remaining sine-like component, and
a PAR rf system phase change is made to zero the phase
With the longitudinal corrected, it is now simple to per-
form the horizontal correction. This method is quite simi-
lar to that used in the vertical plane; however, the
dispersion in the horizontal plane adds a small complexity.
The revolution freuqency of the booster is adjusted to
accommodate the storage ring. This forces the booster to
run slightly off-energy and creates a constant off-energy
orbit displacement, which must be accounted for and sub-
tracted off the closed orbit measurement to reveal only the
betatron closed orbit. This is measured by calculating the
average offset of the closed orbit in the horizontal plane
and by dividing it by the average dispersion in the booster,
((dp)/p) = (xE)/(Tl) (4)
200 F it'+ j1
20o 1k~ ___
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Biedron, S.G. & Milton, S.V. Automated tuning of the advanced photon source booster synchrotron, article, August 1, 1997; Illinois. (digital.library.unt.edu/ark:/67531/metadc689971/m1/4/: accessed October 18, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.