Author: Henry Glass; Andreas Jansson
Date: 2003-04-02

BETA FUNCTION MEASUREMENT IN THE TEVATRON USING QUADRUPOLE GRADIENT MODULATION

A. Jansson, P. Lebrun, J. T. Volk, Fermilab, Batavia, IL, USA

f

ion

Proton beam

Pbar beam

Micro chan nel plate

e-

E=100kV/m

B=0.2T

Early in Run2, there was an effort to compare the different emittance measurements in the Tevatron (flying wires and synchrotron light) and understand the origin of the observed differences. To measure the beta function at a few key locations near the instruments, air-core quadrupoles were installed. By modulating the gradient of these magnets and measuring the effect on the tune, the lattice parameters can be extracted. Initially, the results seem to disagree with with other methods. At the time, the lattice was strongly coupled due to a skew component in the main dipoles, caused by sagging of the cryostat. After a large fraction of the superconducting magnets were shimmed to remove a strong skew quadrupole component, the results now agree with the theoretical values to within 20%.

Abstract

Air-core quadrupole magnets

RPAT033

Magnet
E0QT
E1QT
C0QT
Distance from B0
3153.65m
3357.68m
1168m
Close to
E11 flying wires
E17 flying wire
Sync lite
Hor beta
89 m
77 m
100m
Ver beta
65m
32m
60m

E0QT
E1QT
C0QT
Horizontal tune modulation
0.00284
0.00252
0.00395
Measured horizontal beta
71.1 m
62.4 m
98.6 m
Horizontal discrepancy
-22%
-21%
-5%
Vertical tune modulation
0.00172
0.00072
0.00163
Measured vertical beta
43.0 m
17.9 m
40.6 m
Vertical discrepancy
-37%
-47%
-35%

E0QT
E1QT
C0QT
Horizontal tune modulation
0.00294
0.00298
0.00383
Measured horizontal beta
73.3 m
74.4 m
95.4 m
Horizontal discrepancy
-18%
-4%
-10%
Vertical tune modulation
0.00265
0.00126
0.00216
Measured vertical beta
66.1 m
31.5 m
53.8 m
Vertical discrepancy
+1%
0%
-5%

E1QT
C0QT
Horizontal tune modulation
0.00324
0.00374
Measured horizontal beta
80.7 m
93.3 m
Horizontal discrepancy
+5
-7%
Vertical tune modulation
0.00111
0.00193
Measured vertical beta
27.6 m
48.1 m
Vertical discrepancy
-14%
-20%

Measurements in 2003

Measurements in 2004

Measurements in 2005

Tevatron slow extraction (QXR) quadrupole before modification

The air-core quadrupole was modified to fit on a 4” beam pipe. Above it is being measured in the Magnet Test Facility (MTF) using a rotating coil.

Measured transfer function (integrated gradient per unit current).

Air-core quadrupole being installed at E0. The magnets clamp onto the existing beam pipe without any need for breaking vacuum.

Gradient modulation method

The local beta function at a quadrupole can be measured by varying its gradient, using the linearized formula

Air core quadrupole
Flying wires
Sync lite

or, if the tune is close to a half-integer resonance, the more appropriate formula to use is

although, in the Tevatron, this is a small (few percent) effect. Both formulas only account for the direct change in tune, and not any indirect effects due to changing orbits. So it is important to center the beam in the quadrupole and monitor the orbit motion during the experiment.

In 2003, a rather large disagreement was observed between measured and design beta functions. The results also disagreed with lattice measurements using differential orbits. All values were significantly smaller than expected

In 2004, the measured values were found to agree with design to within 20%. Moreover, the systematic shift toward lower values seemed to be gone, or at least less pronounced. Between 2003 and 2004, 14% of the Tevatron main dipoles were re-shimmed, reducing the coupling in the machine significantly.

Betas at Flying Wires

Effects of coupling

In 2005, the measured values still agree with design to within 20%. Between 2004 and 2005, another 53% of the Tevatron main dipoles were re-shimmed.
In 2005, the measurements were taken using the new tune tracker.

The quadrupoles were installed to get a handle on the local beta function error at the instruments measuring beam size, in order to understand (and correct) the error in the emittance calculation. However, due to space restriction, the magnets had to be installed some distance away from the instruments
Since there are two data points in the E-sector, the phase an amplitude of the beta beat wave can be calculated, assuming that there are no error sources between the two locations. From this, the beta functions at the exact flying wire locations can be calculated from the 2004 data.

E11 Horizontal
E11 Vertical
E17 Horizontal
This measurement
66.0 m
81.4 m
60.2 m
MAD design lattice
82.1 m
83.1 m
59.8 m
Values used in Flying Wires
83.5 m
80.9 m
62.5 m
Differential orbits*
86.9 m
101.3 m
67.6 m

* measured in 2004 by V.Lebedev, results in BeamDoc #1465

E0

E17

C0

C0

E17

E0

C0

E17

If there are sources of coupling in the machine, the measured tune separation is

so that close to the diagonal, the observed tune change for a given change in set (lattice) tune is less than expected, as was observed in 2004. However, the effect is small is the tune separation is much larger than the global coupling parameter C (minimum tune split). Therefore, the effect should only have been a few percent in the 2003 data.
A more likely suspect is local coupling. If the normal modes are significantly inclined at the location of the trim quadrupole, the beam will see it as a skew quadrupole instead on a normal one, yielding less effect on the tune.

Measurements at 980GeV

At 980 GeV, the tune modulation is only barely above the noise level of the tune fitter, and smaller than the synchrotron frequency. Occasionally, the tune fitter picks the wrong synchrotron line, but this component of the noise can be removed with post-processing of the data.

The new tune tracker may provide more accurate data, making the air-core quadrupoles useful at 980 GeV as well.
So far, little time and effort have been spent on measurements at flattop.