Summary of Tevatron Lattice/Dispersion Studies

David Johnson and Ming-Jen Yang

July 10, 2003

# This is a summary of the matching measurements, conclusions, and recommendations made for the P1 and A1 beamlines. Slides from a more detailed presentation can be found in the document database as document number 725. 

# Motivation

The flying wires in the Main Injector and Tevatron (as reported by the
SDA) show an emittance dilution of about 10 π-mm-mr in the vertical
plane and none in the horizontal plane for proton injection. For pbar
injection both the horizontal and vertical wires indicate on the order
of 8-10 π-mm-mr growth. We wanted to determine if the source of this
growth was due to lattice or dispersion mismatch.

Previous studies (Syphers and Annala) with the Tevatron skew quads
showed that the vertical dispersion in the Tevatron could be reduced at
F0 with different skew quad settings. They showed this lead to a
reduction in the round trip emittance dilution.

In addition, the P1 line design incorporated a set of 4 quad rolls to
de-couple the x-y motion at the Tevatron injection point.

Due to installation issues, these quads were not rolled during
installation. We propose to rectify this situation

Conditions and Measurements for P1

Prior to the study operations tuned up forward and reverse injection
into the Tevatron using the standard 30 bunches. The program I91 was
used to collect BPM flash data, BLM readings, magnet current readbacks
(at extraction time), beamline multiwire profiles, intensities (DCCT and
toroid) , and RF frequency reading from the beamline as well as both MI
and Tevatron. Data for at least 4 settings were taken from one bump
measurements from dipoles in the MI and beamline. The frequency range of
+/- 200 Hz (in steps of 50 Hz) was used for dispersion measurements on
both first turn and Tevatron circulating beam on central orbit. We kept
track of losses in the Tevatron and beamline and do not include data
were the beam is significantly scrapped. In addition, we measured the
beam profiles in the beamline. The input emittance and momentum spread
were adjusted in the model to match the measured beam sigmas. The
resultant values are consistent with expected parameters. The predicted
beam size was propagated from the MI thru F-sector. These were compared
with expected beam size as predicted from the Tevatron injection lattice
MAD model.

P1 Measurement Results

Both horizontal and vertical differential orbits from bumps in the MI
and start of the P1 line beamline agree with the model (using measured
currents) for the P1 multiwires and Tevatron BPM's. The response of each
detector over the range of the bump amplitude was measured to find
scaling error or noisy signals. The beamline BPM were not stable enough
to use for data analysis (thank goodness for multiwires). The horizontal
differential orbit from the MI extraction Lambertsons (rolled) agreed
well with the multiwires and Tevatron BPM's (in both planes).

We compared the measured first turn lattice with the model of the
Tevatron injection lattice. The comparison was quite good and does not
appear to lead to any emittance growth.

The comparison of the circulating and first turn dispersion showed a
mismatch in amplitude and phase.

Roll angles were determined for Q707 (-1.7 deg) and Q709 (-2.0 deg) to
match the first turn dispersion with the current Tevatron circulating
dispersion. In addition, the roll angles for Q706 (-0.65 deg), Q707
(-2.6 deg), Q708 (-0.05 deg), and Q709 (-1.25 deg) were determined to
completely cancel the first turn vertical dispersion into the Tevatron.
Both solutions did not alter either the lattice match or the horizontal
dispersion match into the Tevatron. The coupling terms from the beamline
at the Tevatron injection point were cancelled.

Conclusions from P1 Measurements

The lattice functions between the MI and Tevatron appear to be matched.
There does not appear to be any dilution from steering errors
(Operations tuned up closure to shot standards prior to study). There
does not appear to be any horizontal dispersion mismatch. For the
settings of the Tevatron skew quads used in the study (nominal operating
values) there is a vertical dispersion mismatch of ∆Deq = 1.25 m. For a
momentum distribution of

σp/p \~ 0.5 X10-3 we get a calculated emittance growth of ∆εN \~1.5 to
1.9 π−mm-mr. [This does not explain the observed growth from the flying
wires.]{.underline}

Measurements for A1

Operations tuned up reverse injection on the pbar helix prior to the
study. The same type of data was taken for this transfer.

A1 Measurement Results

From comparison of "nominal" conditions taken at various points during
the study, we found the A1 BPM's to be unreliable for any serious data
analysis and the Tevatron BPMs show a, yet to be explained, systematic
offset as compared with one of the "nominal orbits". The comparison of
the multiwire centroids was very good. The measured Tevatron and MI BPM
response and beamline multiwires to both horizontal and vertical
differential orbits started in the Tevatron (E2) agreed well with the
model. For the orbit distortions started at the Tevatron end of the A1
line, the beamline multiwires agree well with the model, but there were
some discrepancies in the MI response to horizontal kicks. The
horizontal data could be made to agree better by adjusting Q902 by about
25%. This is not understood and only affects the MI BPM data.

The measured lattice parameters show about a 20% beta wave in the
vertical plane. The agreement in the horizontal is on the order of 10%.

Circulating dispersion on the helix was measured using VFKNOB. A
vertical dispersion wave of about ½ meter was seen. The horizontal
dispersion matched the model prediction. The dispersion measurement for
reverse injection was measured for the Tevatron, beamline and MI. A
residual vertical dispersion of about ¼ meter was seen in the MI.
Propagating this dispersion in the pbar direction (starting with zero
vertical dispersion in the MI) showed a mismatch between the vertical
dispersion generated in the A1 line and the Tevatron circulating
dispersion. Again, the horizontal dispersion was matched.

Roll angles were determined for Q906 (-0.8 deg), Q907 (-1.1 deg), Q908
(0.0 deg),and Q909 (-0.3 deg) to match the first turn dispersion with
the current Tevatron circulating dispersion on pbar helix. In addition,
the roll angles for Q906 (-0.08 deg), Q907 (0.67 deg), Q908 (0.03 deg),
and Q909 (-0.05 deg) were determined to completely cancel the first turn
vertical dispersion into the Tevatron. Both solutions did not alter
either the lattice match or the horizontal dispersion match between the
MI and Tevatron. The coupling terms from the beamline at the Tevatron
injection point were cancelled.

Conclusions from A1 measurements

The lattice functions between the Tevatron and MI appear to be
sufficiently matched as not to contribute significantly to any emittance
growth. Since the closure was performed in the tune up, any residual
steering error was small enough as not to contribute to emittance
growth. The horizontal dispersion between the two machined appear to be
well matched. But, the vertical dispersion did show a smaller mismatch
than for proton injection. We see a ∆Deq of about ½ m and with a
momentum spread of σp/p \~ 0.5E-3 the emittance growth is ∆εN \~ 0.5
π−mm-mr. [This is not significant and does not explain the observed
emittance growth.]{.underline}

Recommendations

The roll angles for Q707, and Q709 should be installed before the
shutdown to further reduce emittance growth and verify the procedure.
When the vertical dispersion in the Tevatron is fixed during the
shutdown, the roll angles should be modified as described (and as
initially designed).

An additional systematic study of proton injection looking at the
Tevatron flying wire response to known injection steering errors,
initial emittance, initial momentum, and helix size, VFKNOB settings,
should be performed (either before or after rolling quads).

An additional detailed and systematic measurements of round trip
emittance growth from both the central orbit and pbar helix should be
performed to understand the measured emittance growth. These would
entail dependence on initial emittance, helix amplitude, extraction on
central orbit, steering errors into and out of the Tevatron, momentum
dependence on central orbit, flying wire response to momentum spread
(using VFKNOB to fuzz the beam after injection), etc.

The quads in the A1 beamline should be rolled to decouple the x-y motion
and cancel the vertical dispersion into the Tevatron. The timing of this
modification needs further consideration but should not be done before
the additional round trip emittance study.