Brief discussions with JPS, DHR, MGB, MJF, GWC and ST provided
input to the following analysis and planning.
Analysis of Machine Studies Measurements of 12 August 2005
==========================================================
JPS and I measured electron orbit differences in BPMs 12W-2E with
and without 2 mA of positrons in trains 2-6 bunch 1-5
<a href=
"http://cesrelog.lns.cornell.edu/MSLOG/cesrc/2005/cesrc_050812.html"> last Friday</a>.
We found orbits remarkably similar to those calculated with the
BMAD simulation of lattice 3970_0809.0800v2. You can see examples
of the measured orbit differences and their reproducibility here:
<a href=
"http://cesrelog.lns.cornell.edu/MSLOG/cesrc/2005/gif/mode00072159.gif"> 107685</a> and
<a href=
"http://cesrelog.lns.cornell.edu/MSLOG/cesrc/2005/gif/mode00072161.gif"> 107682</a>.
Two of the BPM's in this region gave anomalous data and were vetoed.
The corresponding BMAD calculations for the horizontal orbits can be found here:
<a href=
"http://www.lns.cornell.edu/~critten/cesr/injection/notes/16aug05/all/P001.html">0W-12W</a>.
<a href=
"http://www.lns.cornell.edu/~critten/cesr/injection/notes/16aug05/all/P002.html">0E-2E</a>.
The blue lines indicate the positions of the BPM's. Crossing positions are marked by yellow lines.
(The IP is marked here, but there was no current in e+ t1.b1.)
The agreement at each of the BPMs is better than 10% (!) for orbit distortions up to 0.65 mm.
The BMAD calculations for the vertical orbits are shown here:
<a href=
"http://www.lns.cornell.edu/~critten/cesr/injection/notes/16aug05/all/P003.html">0W-12W</a>.
<a href=
"http://www.lns.cornell.edu/~critten/cesr/injection/notes/16aug05/all/P004.html">0E-2E</a>.
The measurement shows a deviation of up to 0.08 mm in 1W. The calculation shows a distortion
of similar magnitude and shape, but not at the BPM positions. Also, the measurements show
a positive deviation of up to 0.05 mm in the region 7W-12W which is not found in the calculation.
The agreement is better at 1E (0.05 mm) and 2E (0.0 mm), but the measurements show a 0.05 mm
deviation at 0E which does not appear in the BMAD calculation. Note that these are quite small
orbit deviations, likely caused by coupling effects, and the BMAD simulation is not expected
to accurately reproduce the coupling in this electron injection set.
Plan for Future Machine Studies
===============================
The measurements described above were done in the context of a feasibility study which
took about 20 minutes of beam time. The results encourage a more substantial follow-up
program, a plan for which I present here after discussions with the experts.
I. Colliding pretzel
--------------------
The measurement was done in electron injection conditions, whereas the calculation
is done in colliding conditions. We should check that setting PRZ13 to zero does
not affect our orbit measurements.
II. Linearity test
-----------------
This measurement was done with 2 mA e- t1.b1 on 25 e+ bunches of 2 mA each.
A simple test of the linearity of the effect should be done. Lowering the electron
bunch current is a test of the weak-strong approximation. If the approximation is good,
there should not be a dependence on the electron bunch current. We can easily measure
orbits at 1 mA e- bunch current. Testing the limits in both directions would be interesting.
Also easy is changing the positron bunch current. Presumably there is some upper limit
where we could not inject electrons. With 2 mA per bunch, electron injection stopped at
1.4 mA, but changing the horizontal tune by less than 1 kHz permitted injection to 2 mA.
The orbit measurement accuracy is sufficient to measure the half-deflection at a positron
current of 1 mA/bunch. Exploring the range of linearity would be a useful exercise.
A calculation with 4 mA/bunch showed the orbit deviation to scale with the factor of two.
III. Bunch configuration
-----------------------
Does the simulation work as well for various bunch configurations causing different types
of orbit distortions? I had some trouble finding configurations which result in a different
shape of the orbit distortion. I tried the following:
1) 5x5, omit train 1
2) omit train 2 as well as train 1 in the e+ 6x5 configuration,
3) populate train 2 only,
4) 8x5, omitting t1.b1 only (this has crossings in 0E-2E and between hseps 45E/W),
5) 9x5, omitting t1.b1 only (crossings in 0E-2E, near 6W and 7W and between hseps 45E/W),
6) use the 3770 MeV lattice 12wig_20050626 instead of 3970_0809.0800v2.
In each of these cases, the shape of the orbit distortion was very similar to the one
already measured. To a good approximation, the p.c. kicks are in phase and add coherently.
I was finally able to change the distortion with two configurations.
1) 1x1, omit t1.b1 only. This gives crossings between the horizontal separators in
the north and also in the 0E-2E region, so we may not get orbit info from here.
Also, the orbit distortion in 0W-12W is only 0.15 mm, as can be seen here:
<a href=
"http://www.lns.cornell.edu/~critten/cesr/injection/notes/16aug05/all/P005.html">0W-12W</a>.
Nonetheless, this is a qualitatively different orbit change which can likely
be measured. Its magnitude can be increased over the range studied in part II, and
perhaps by lowering the pretzel as well (see below).
2) train 9 only. One of these crossings is located inside HSEP45E. There are also crossings
near BPM's 6W and 7W, as can be seen here:
<a href=
"http://www.lns.cornell.edu/~critten/cesr/injection/notes/16aug05/all/P006.html">0W-12W</a>.
The orbit distortion reaches 0.25 mm for 2 mA and can likely be measured.
III. Pretzel Amplitude
----------------------
Lowering the pretzel amplitude from a crossing angle of 3.0 mrad (design) to 2.0 mrad
in the BMAD simulation results in doubling the magnitude of the orbit distortion in the
conditions of the machine studies measurements. Corresponding measurements would be an
interesting test of the model and may provide a way of increasing the sensitivity to
weaker orbit distortions in other bunch configurations. However, electron injection
may become more difficult, and there may be consequences for the betatron phase as well.
IV. Measurements of Tune and Phase
----------------------------------
The orbit changes can be used to estimate the magnitudes of the dipole kicks of the BBI,
but the defocusing effects can be verified only by measurements of tunes and phase.
ST says tune measurements are easy, but MGB has a thousand reasons why they can be
misleading when two beams are present. GWC is working on speeding up his single-bunch
tune measurements.
The BMAD simulation shows the e- t1.b1 tune change associated with 2 mA of positron bunch
current to be 3 kHz in the conditions of the machine studies, as can be seen here:
<a href=
"http://www.lns.cornell.edu/~critten/cesr/injection/notes/16aug05/all/P007.html">horizontal
tune</a>.
However, we did not measure the tune change. We should include such measurements in the
future and include phase measurements as well. The simulation showed a phase wave of
1-degree amplitude for the conditions of the machine studies, increasing to 8 degrees when
the pretzel was lowered from 3 mrad to 2 mrad crossing angle.
========================================================
James Crittenden Tel. (607) 255-9424
Wilson Synchrotron Laboratory Fax (607) 255-8062
Cornell University
Ithaca, New York 14853-8001
========================================================
