1
Plan for the next three months
Shinji Machida
ASTeC/STFC/RAL
16 December 2010
2
Main tasks
•
Acceleration/deceleration needs the following
tasks
–
Phase adjustment of individual cavity (longitudinal).
–
Orbit correction (transverse).
–
Attempt at extraction (if possible).
•
Hopefully all the BPM (42 between QD and QF)
will be ready by January 2011.
3
Phase adjustment of individual cavity
4
Possible methods
•
Without beam
–
Relative phase between LLRF and monitor port.
•
With beam
–
Beam loading signal at monitor port.
–
Horizontal displacement at BPM.
–
Synchrotron oscillation amplitude and frequency.
–
With and without cavity detuning
5
Request and assumption
•
An issue of “random new angle after a sweep”
must be resolved before any beam based
measurements.
6
Beam loading signal at monitor port (1)
•
This is done with multiple turns only.
•
No need to detune other cavities.
•
Phase slippage (questioned by Jamison) may
not be a problem because cavity is tuned to
revolution frequency (and self bunching).
•
Accuracy is not clear.
7
Beam loading signal at monitor port (2)
•
Can be improved if we can choose a shot
with similar number of turns.
•
Is it possible to take beam loading signal and
BPM signal of the same shot through EPICS?
8
Horizontal displacement at BPM (1)
•
A beam is deflected by different angle with
different momentum.
•
Dispersion function tells a rough estimate.
e.g. 120 kV energy gain at a cavity
dispersion function of 60 mm
•
All the cavity except one has to be detuned.
9
Horizontal displacement at BPM (2)
•
Betatron oscillation is excited at cavity #4
because of a sudden jump of equilibrium orbit.
•
Osc. amplitude is ~0.7 mm (full) with 120 kV.
Red:
+120 kV
Green:
0 V
Blue:

120 kV
cavity #4
10
Horizontal displacement at BPM (3)
•
In reality, injection error excites another betatron
oscillation at the beginning.
•
Have to measure small difference.
Red:
+120 kV
Green:
0 V
Blue:

120 kV
11
Horizontal displacement at BPM (4)
•
Multiple passage gives more energy gain and
larger displacement.
•
This is nothing but synchrotron oscillation
observed through dispersion function.
Red:
+120 kV
Green:
0 V
Blue:

120 kV
100 turns
0 turns
12
Synchrotron oscillation (1)
•
Assume that all the cavity except one is
detuned.
•
Synchrotron oscillation
amplitude
depends on
the initial phase.
Initial phase
Red:
270 deg.
Green: 340 deg.
Blue:
350 deg.
13
Synchrotron oscillation (2)
•
When vector sum becomes the maximum, it
gives the maximum synchrotron oscillation
frequency
.
•
No need to detune cavities.
•
Maximize synchrotron frequency by sweeping
individual cavity phase.
•
Simulation is in progress.
14
Plan for phase adjustment
•
My preference of “with beam” measurement is
the following order.
–
Beam loading measurement synchronized with BPM
signal.
–
Synchrotron
frequency
measurement.
both do not need detuning
–
Synchrotron
amplitude
measurement.
–
Measurement of displacement at BPM.
need detuning
15
Orbit correction
16
horizontal
vertical
Source of COD (1)
•
Assume the observed COD comes only from
misalignment of QD (red) and QF (green).
•
It needs rather large misalignment.
17
Source of COD (2)
•
Vertical corrector is suspicious although a
simple model with different integrated
gradient was not enough to explain the COD.
•
Field calculation has been done (Shepherd.)
•
More detailed simulation including field
distribution has not finished yet.
18
Source of COD (3)
•
QF41 shifted longitudinally by 6.5 mm.
•
This could be a source although simple hard edge
model was not enough to explain the COD.
•
Field calculation has been done (Giboudot.)
•
More detailed simulation including field
distribution has not been done yet.
19
Correction (1)
•
Setup a model lattice which has a similar
COD in vertical direction.
•
Use vertical misalignment of 84 quadrupoles.
Red cross: observed COD
Green: COD reconstructed
20
Correction (2)
•
Correct COD by SVD using 16 V

corrector.
•
Decelerate in serpentine channel.
Green: before correction
Red: after correction
COD
Tracking results
21
Correction (3)
•
Identify tune where beam amplitude grows.
Green: before correction
Red: after correction
Red:
horizontal tune
Greed: vertical tune
Tracking results
deceleration
Qz=8
7 6 5
22
Correction (4)
•
Harmonic analysis before and after COD
correction with SVD.
Green: before correction
Red: after correction
COD
23
Correction (5)
•
COD after removing harmonic of 8.
Green: all harmonics
Red: after removing h=8
COD
24
Correction (6)
•
Amplitude growth is suppressed after
removing h=8.
Green: all harmonics
Red: after removing h=8
COD
Tracking results
25
Correction (7)
•
Tracking simulation shows eliminating one
harmonic component is more effective than
reducing orbit deviation on average by SVD.
•
Eliminating harmonic component of integer
part of tune (4 to 11 for vertical) seems to be
a way of orbit correction in a linear nonscaling
FFAG.
26
Possible explanation
•
If a lattice has harmonic of
n
, integer tune of
n
becomes systematic resonance.
•
Tune change per periodic unit decreases by a
factor of 42/
n
. For example, with harmonic of
n
=8, crossing speed becomes one order
lower.
•
With harmonic of
n
, it is equivalent to have
n
times smaller ring with
n
times more turns.
•
…
27
Plan for orbit correction
•
Measure COD at several different momenta
to identify error source or harmonics of errors
at least.
•
Apply harmonic correction.
•
If necessary, move some of quadrupole
magnets vertically.
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