IPM measurements in the Tevatron\*
==================================

A. Jansson^\#^, K. Bowie, T. Fitzpatrick, R. Kwarciany, C. Lundberg, D.
Slimmer, L. Valerio, J. Zagel, Fermilab, Batavia, IL 60510, USA

Abstract

Two Ionization Profile Monitors (IPMs) were installed in the Tevatron in 2006. The detectors are capable of resolving single bunches turn-by-turn. This paper presents recent improvements to the system hardware and its use for beam monitoring. In particular, the correction of beam size oscillations observed at injection is discussed.
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 INTRODUCTION
------------

The Tevatron Ionization Profile Monitors\[1\] were developed primarily
to detect mismatch-induced beam size oscillations at injection, but also
to measure emittance evolution during e.g. ramp and squeeze. The
detectors are capable of measuring the profile of single proton and pbar
bunches. This is achieved by continuously integrating the ionization
signal from each anode strip in \~60ns intervals (7/2 times the RF
period), using very sensitive electronics (2.9fC LSB). Since individual
proton bunches are separated by 21 RF buckets and protons and pbars are
separated by \~7 RF buckets at the location of the IPM, individual
bunches may be studied by selecting the appropriate samples. This is
useful e.g. to measure injection matching of bunches injected into a
partially filled machine.

To achieve low noise, the integration is done in the tunnel and signals
are sent to the service building in digital form on optical fibers. Each
front end board handles eight channels, and up to 16 front end boards
(128 channels) may be used per system. The front end boards all receive
a common clock frequency and timing signals generated from the Tevatron
Beam Sync Clock by a PC in the service building.

Each board returns data on a separate high-speed optical link. The data
from the individual boards is then collected, synchronized and buffered
in a Data Buffer Card in the same PC that hosts the timing card. The
Buffer card can handle eight links, and two boards may be daisy-chained
to handle the full 16 links. The total data rate may exceed to 20Gbps,
depending on how many cards are installed, and the Buffer card is
capable of storing 20000 turns of continuous data. Data can also be
reduced on-the-fly to select only interesting samples, raising the total
number of turns to 6 Million for a single bunch. However, when the full
buffer memory is used, analysis time with the LabView software becomes
prohibitive. However, in practice measurement are typically restricted
to less than \~1000 turns, which is sufficient for most applications.

RECENT IMPROVEMENTS
-------------------

For the initial measurements\[2\], a LabView program was used to set up
the measurement parameters. Data was then downloaded from the buffer
card, saved to file and analyzed off-line using Mathematica. This
analysis has now been incorporated into the LabView program, making the
turnaround time for a measurement much shorter and the system more
user-friendly.

![screenshot2](media/image1.png){width="3.25in"
height="2.1145833333333335in"}

Figure 1. Screenshot from the Tevatron IPM Labview program. At low beta,
the vertical system is capable measuring both protons and pbars
simultaneously, without moving the detector.

The initial systems had five prototype front end boards each, for a
total of 40 channels per system. At a channel pitch of ¼ mm, this
corresponds to an active width of 1cm. These prototype systems were used
to debug the firmware before the production run, since the front-end
boards use one-time programmable FPGAs (for radiation hardness). While
1cm is sufficient to cover the vertical beam size, both at injection and
flattop, it is too small to measure the horizontal beam size at
injection. For this reason, the horizontal system was chosen to test the
production front end boards. Recently, 10 boards (80 channels) with new
firmware were installed in the horizontal system. This upgraded system
is currently being tested.

PROTON InJECTIon MATCHING
-------------------------

### Observation of mismatch

The primary purpose for the IPMs is to detect injection mismatch by
measuring the beam size over the first few hundred turns following
injection. Indeed, during proton injection a vertical beam size
oscillation of about ± 20% was detected. The mismatch is clearly visible
and consistent for all 36 proton bunch injections during shot setup. A
beam size oscillation of this magnitude corresponds to an emittance
blow-up of about 10%.

![](media/image2.wmf){width="3.0in" height="1.8333333333333333in"}

Figure 2. Vertical beam size for the first 85 turns following injection
for proton bunches \#5 (black), \#11 (red), \#15 (green) and \#19
(blue), taken during the same collider shot. There is clear and
consistent evidence of mismatch.

### Correction of mismatch

The evolution of the beam size (or rather the square of the beam size)
when the beam is injected with small errors *Δβ* and *Δα* in the
Courant-Snyder parameters, is given by

$$\sigma^{2}\left( n \right) = \varepsilon\ \beta\ \left( \frac{\mathrm{\Delta}\beta}{\beta}\cos{2\omega} + \left( \mathrm{\Delta}\alpha - \alpha\frac{\mathrm{\Delta}\beta}{\beta} \right)\sin{2\omega} \right)$$

where υ is the betatron tune multiplied by 2π, and *n* is the turn
number. A dimensionless mismatch vector *m={Δβ/β, Δα-α Δβ/β}* may
therefore be defined, and its value determined by fitting a sinusoidal
curve with a frequency *2*υ to the beam size data measured by the IPM.
The mismatch vector may be viewed as the analog of a position-angle
error in the case of injection steering. The effect of a transfer line
quadrupole on the mismatch vector can be calculated analytically\[3\],
but due to imperfect knowledge of the optics, it is often better to
measure it. A correction to the observed mismatch may then be found by
solving a system of linear equations. Figures 1-2 show the measured
effect of two proton transfer line quadrupoles on the vertical mismatch
vector. The effects of these quadrupoles are nearly orthogonal in the
vertical plane, which simplifies correction.

Since quadrupoles affect both vertical and horizontal planes, both
planes should be considered simultaneously when correcting the mismatch.
As horizontal matching data is not yet available, the full correction
has not been done. However, since the effect of a quadrupole is
proportional to the local beta function, a partial correction of the
observed vertical mismatch was made using quadrupoles in locations with
small horizontal beta functions. This correction reduced the vertical
mismatch to below the noise level.

![](media/image3.wmf){width="3.0in" height="2.9895833333333335in"}

Figure 3. Vertical mismatch vector for different settings of the Q701
quadrupole. Black is nominal current, red is -22A, green is -42A

![](media/image4.wmf){width="3.0in" height="2.9895833333333335in"}

Figure 4. Vertical mismatch for different settings of the Q711
quadrupole. Black is nominal current, red is +10A, green is +20A.

Measurements oN pbars
---------------------

The intensity of antiprotons is naturally lower than the intensity of
protons, which translates into a smaller signal. However, for matching
measurements this can be compensated to some degree because pbars are
injected in groups of four. With the pbar intensities achieved recently,
adding up the four pbar profiles yields signals almost as strong as for
a single proton bunch. Furthermore, the pbar emittance is significantly
smaller than the proton beam size at injection. This makes it easier to
measure the pbar profile, since the signal is spread over fewer
channels.

Injection matching measurements on pbars using the vertical IPM has
indicated that the vertical plane is quite well matched. This conclusion
is supported by reverse proton injection (protons being sent back into
Main Injector from the Tevatron via the pbar transfer line) measurements
using the Main Injector IPMs. Reverse proton measurements also indicate
that there is a significant horizontal pbar mismatch, although due to
the limited active width of the prototype system it has not yet been
possible to verify this with pbars.

![](media/image5.wmf){width="3.0in" height="1.8333333333333333in"}

Figure 5. Vertical pbar bunch size, averaged over the four bunches in
the transfer batch, for the first 175 turns following injection. No
significant mismatch is apparent.

Future plans
------------

At the moment, the horizontal IPM with the production boards is still
being tested. Some issues with synchronization between multiple boards
have been identified. Once these problems are sorted out, the vertical
system will be retro-fitted with new boards. This will allow the
mismatch of both planes to be measured and corrected simultaneously.

SUMMARY
-------

The Tevatron IPMs are capable of measuring single bunches of protons and
pbars turn-by-turn at injection and high energy. A significant vertical
proton injection mismatch was observed and corrected. For pbars, no
significant vertical injection was observed. Horizontal measurements
should be available soon.

References
----------

\[1\] A. Jansson et al, The Tevatron Ionization Profile Monitors, 12^th^
Beam Instrumentation Workshop, Fermilab, Batavia, IL, 2006.

\[2\] A. Jansson et al, Tevatron Ionization Profile Monitoring, 10^th^
European Particle Accelerator Conference, Edinburgh, UK, 2006.

\[3\] B. Autin et al, "Emittance Preservation in the PS Complex",
PAC'07, Vancouver, CA.