**Accumulator flying wires status**

I.  **Design and history.**

Flying Wires in accelerator technique is an instrument for direct
measuring the transverse profile of the beam. A thin filament mounted in
a fork passes through the beam at high speed as this fork makes one
revolution. Some beam particles on the way through the wire material
experience interactions with its atoms thus generating a flux of
secondary particles. Secondary particles leave the beam pipe and hit the
loss monitor downstream the location of the FW station. Following the
signal profile in time one can obtain the transverse beam profile in the
direction of wire motion. FWs are extensively used in the Tevatron and
Main Injector. There is an ongoing work to install such a system at the
Recycler too. In the Accumulator FW has been commissioned in early 90-s
but has not been routinely used ever since. Part of the reason for that
is that at 8 GeV wire flies do affect the beam emittance, on the other
hand the task of emittance monitoring is quite successfully being borne
by Shottki detectors. The Pbar FW system has 6 stations to monitor beam
profiles at the extraction, central and stacking orbits at high and low
dispersion regions. It is designed to perform automatic measurements
triggered by the external events and report data to ACNET. A new
interest to Accumulator FW arose in 2002 in view of having an
alternative instrument to the Shottki monitor, mostly for the
calibration purposes.

II. **Activity in 2002**

The Front End of the FW is located in quite aggressive humidity
environment right under the heat exchange unit and in front of the cargo
gates in AP30. During more than 10 years of existence the racks have
suffered few floods, most of panel and cable connections corroded badly,
so no surprise FW stopped functioning long before March 2002. It turned
out that the most damage happened in the VME crate, while motion control
remained in relatively usable state. Unfortunately most of the modules
used for position and analog readout became very rare and ceased their
support at Fermilab. Also most of the failures had an intermittent
nature which was hard to track down and fix. To study the system, FW
performance and help recommissioning, the hybrid stand was set up: the
existing application program would control to wire motion, while the
loss monitor signal would be recorded with both ADC and a digital scope.
Position signal was obtained from the encoder phase A and B readout and
other internal signals were also used to monitor timing and global
positioning of the wires.

A typical scope waveform is shown in Figure 1. Encoder phase signals
represent optical readings of the marker pattern painted on the disk
that rotates along with the main FW shaft. There are 4096 marks on the
disk perimeter, so marker count gives direct and precise wire position
information.

Several issues coming from these measurements are discussed below.

![](media/image1.jpeg){width="3.3756944444444446in"
height="2.542361111111111in"}

Figure 1. Digital waveforms of the loss monitor signal at wire fly
(hollow circles). Red line shows the Gaussian fit to data, blue and
green waveforms- encoder phases A and B. Vertical markers show the 2σ
limits.

**II-1. Unstable measurements**

The biggest concern coming out of these studies was that the beam
profile measured with the same beam is every time different. If the beam
width is the same but reported numbers are different then the whole
instrument becomes not credible. Figure 2 shows beam profile sigmas
measured both by the program and using the scope.

![](media/image2.jpeg){width="2.75in" height="2.75in"}

Figure 2. Beam width measured with standard DAQ (red circles) and with
the scope (blue rectangles), first three measurements done with Core
Vertical wire, last 3 points- Low Dispersion horizontal wire.

The readings are not stable but DAQ and scope measurements agree with
each other well. Hollow rectangles correspond to measured wire velocity
at the moment of beam crossing. Some change in beam width indeed may
occur after a subsequent wire fly, because of emittance growth due to
beam particles scattering on wire. Moreover, sometimes emittance may
experience significant excursions, for example, if beam tuning or
changes in cooling set up take place. Figure 3 shows emittance changing
during one of the studies with FW.

![](media/image3.png){width="3.286111111111111in"
height="2.623611111111111in"}

Figure 3. Vertical (red) and horizontal emittance (blue) stability curve
as logged during one of the FW studies.

Large excursion in the middle of time range has an external cause.
Smaller jumps correspond to wire flies. Also it can be seen that at each
fly beam current makes a little step down (purple).

To make sure that emittance blow ups do not affect measurement, one can
either wait until emittance cools down to its base level after previous
fly, and then perform a next one, or on each fly calculate the expected
width corrected for the emittance change. This is done in Figure 4.

![](media/image4.jpeg){width="3.6222222222222222in"
height="3.6222222222222222in"}

Figure 4. Beam width measured with scope (red markers) and standard DAQ
(blue markers), two points for each fly correspond to first and second
beam crossings on one fly. Solid line shows expectation from emittance
monitor before the fly (lower curve) and right after the fly (upper
curve).

Correlation between two methods suggests that these measurements
correspond to real time wire spends inside the beam on each crossing.
There is a little uncertainty in scaling of the curves due to inaccurate
knowledge of beta functions, but no scaling factor can explain changing
in measured width from fly to fly and from crossing to crossing. Jump at
fly 8 is close to 100% above the expected value.

Figure 5 shows the measured wire speed according to the rotation speed
of the outside encoder disk. No significant variations of speed show up
there.

![](media/image5.jpeg){width="3.127083333333333in"
height="3.127083333333333in"}

Figure 5. Measured speed uniformity during wire fly.

Another possible reason could be that wire is every time parked at
random location, so it may cross the beam at the moment of acceleration
rather than at constant speed. It was proved with the index signal from
encoder that at least this index mark is forced every time to return to
its nominal position, so the only possible way for the fork to park at
random location would be to be really loosely connected to the outside
axis.

There is no obvious indication of the cause of measurement instability.
Among possible theories are loose fork feed through connection and loose
wire in the fork. Both these situations would be immediately confirmed
or rejected at the wire visual inspection.

**II-2. Position offset**

After every fly and upon initialization the fork is moved to its parking
position. Parking position is chosen as the most remote point from the
beam. There is a precision mark on the driving shaft that shows when the
fork is parked. This mark had been aligned at the installation and ever
since it is used for a visual check that parking procedure works as
designed. To find the parking position control program uses a special
mark on the encoder disk (index mark) that is also read out optically by
the encoder. If for some reason an offset occurred inside the vacuum
can, fork and wire would always be parked at wrong spot.

The program defines the current position of the wire based on the
encoder count and parking position.

It calculates the proper time of generating the gate signal based on the
expected beam position and requested gate width. Figure 6 shows the
scope shot of the gate signals and the loss monitor signal at horizontal
Low Dispersion fly. There is a very large shift of the LM signal with
respect to the center of the gates. This shift may happen either because
of some confusion in the program about expected beam position or due to
the physical offset of the wire parking position. In this case the
actual offset would be close to 40^o^. If the gates are not open wide
enough, one of the signal is not digitized in ADC.

![](media/image6.png){width="2.122916666666667in"
height="1.5958333333333334in"}
![](media/image7.png){width="2.122916666666667in"
height="1.5958333333333334in"}

Figure 6. Loss monitor signal and ADC gates for a) clockwise, b)
counterclockwise fly of horizontal LD wire.

In this case gates have almost maximum allowed widths, and for clockwise
fly signal is normally digitized and recorded in ADC. For CCW fly,
however the Pass2 signal is lost because of insufficient depth of FIFO
buffer. Whether the reason of the offset, information on CCW flies is
always lost. As it's been discussed above, parking position random
offset could be a reason of measurement instability. Even more
dangerous, random free motion of the fork may result in stopping within
the beam aperture and destroying the stack.

**II-3. Emittance blow up and beam losses.**

When passing through the wire beam particles experience collisions with
its atoms. These result in Coulomb and nuclear scattering. That may
deflect a particle strong enough to make it leave the beam. Scattering
at smaller angles results in widening the angle spread of the beam and
thus emittance growth.

The cross section of electromagnetic single scattering is given by
formula

$$$\frac{d\sigma}{d\Omega} = \frac{4z^{2}e^{4}}{p^{2}c^{2}\beta^{2}}\frac{d\theta}{\theta^{4}}$,

or
$\frac{d\sigma}{{d\theta}_{k}} = \frac{4{\pi Z}^{2}r_{p}^{2}}{\gamma^{2}\beta^{2}}\frac{{d\theta}_{k}}{\theta_{k}^{3}}$,

and probability of scattering at angles $\theta_{k}$ (k=x,y) can be
conveniently represented as:

$\text{dP}(\theta_{k}) = \theta_{\text{min}}^{2}d(\frac{1}{\theta_{k}^{2}})$
(1)

where
$\theta_{\text{min}}^{2} = \frac{2\pi\text{naZ}^{2}r_{p}^{2}}{\gamma^{2}\beta^{2}}$,
in a sample with thickness *a*. $\theta_{\text{min}}$ for carbon is
about 4\*10^-6^ and close to the angle of atomic screening. Most of the
scattering occurs at very small angles that are negligible in terms of
beam angle spread, but multiple scattering yields noticeable angles. The
distribution of multiple scattering is roughly Gaussian with rms

$\left\langle \theta_{\text{ms}}^{2} \right\rangle = \frac{\text{14}\text{MeV}}{p\beta c}\sqrt{\frac{a}{X_{0}}}\left( 1 + 0\text{.}\text{038}\text{ln}\left( \frac{a}{X_{0}} \right) \right)$
(2)

where $X_{0}$- radiation length of wire material. Emittance growth for a
single beam pass through a sample will be

$\Delta\varepsilon = 3\beta_{x}\left\langle \theta_{\text{ms}}^{2} \right\rangle$
(3)

Adding real wire parameters and number of a single particle passes
through the wire during its fly, one gets

$$\Delta\varepsilon = 5\text{.}5 \ast \text{10}^{- 6}\frac{f_{0}d^{2}\beta_{x}}{X_{0}v_{w}\text{sin}(\theta)}$$

Here *d* is wire diameter, $\theta$ - angle between the wire trajectory
and the beam, $v_{w}$ **-** linear wire velocity,$f_{0}$- Accumulator
revolution frequency. Plugging numbers in, we get
$\Delta\varepsilon$=0.04 $\pi \cdot \text{mm} \cdot \text{mrad}$. This
is close to that observed in Figure 3, but still smaller. It is because
expression (2) underestimates contribution of scattering, as it assumes
Gaussian distribution. However, real distribution has tails that fall
slower than Gaussian due to single scattering at large angles. Although
these tails are low, they still contribute noticeably to the rms value.
In order to get the sense of that contribution one can calculate rms
according to (1) and obtain

$$\left\langle \theta_{\text{ss}}^{2} \right\rangle = \theta_{\text{min}}^{2}\text{ln}\left( \frac{\theta_{\text{max}}^{2}}{\theta_{\text{min}}^{2}} \right) = \theta_{\text{min}}^{2}\text{ln}\left( \frac{\varepsilon_{\text{admit}}}{\text{βθ}_{\text{min}}^{2}} \right)$$

that yields
$\sqrt{\left\langle \theta_{\text{ss}}^{2} \right\rangle} = 1\text{.}\text{36} \cdot \text{10}^{- 5}$
versus
$\sqrt{\left\langle \theta_{\text{ms}}^{2} \right\rangle} = 1\text{.}\text{26} \cdot \text{10}^{- 5}$.

Single scattering also leads to beam losses. We estimate losses
integrating (1) over angles beyond Accumulator aperture:

$P = \frac{\theta_{\text{min}}^{2}}{\theta_{x,\text{admit}}^{2}} + \frac{\theta_{\text{min}}^{2}}{\theta_{y,\text{admit}}^{2}} = \theta_{\text{min}}^{2}\left( \frac{\beta_{x}}{\varepsilon_{x}} + \frac{\beta_{y}}{\varepsilon_{y}} \right)$,

and therefore fraction of beam lost in result of a wire fly is

$P_{s} = \frac{\pi^{2}\text{nZ}^{2}r_{p}^{2}}{\gamma^{2}\beta^{2}}\frac{d^{2}f_{0}}{v_{w}\text{sin}(\theta)}\left( \frac{\beta_{x}}{\varepsilon_{x}} + \frac{\beta_{y}}{\varepsilon_{y}} \right)$,

where $\varepsilon_{x,y}$ - horizontal and vertical Accumulator
admittances. Formula takes into account the fact that wire actually
passes the beam twice during its fly. Using admittance
$\varepsilon_{x,y} = 8\pi \cdot \text{mm} \cdot \text{mrad}$, βx=12.5m
and βy=16.8 m, one obtains from this formula losses of
$4\text{.}5 \cdot \text{10}^{- 4}$per a fly due to single scattering.

Assuming that every act of nuclear scattering effectively kicks out a
particle from the beam, beam losses due to this process per wire fly
would be

$$P_{\text{nucl}} = \frac{{\pi d}^{2}f_{0}}{2\lambda_{\text{nucl}}v_{w}\text{sin}(\theta)} = 7 \cdot \text{10}^{- 4}$$

Together with single Coulomb scattering this makes 11.5\*10^-4^.

In measurements of 02-Jul-02 after 10 flies of low dispersion wire stack
dropped from 35.28 to 34.92 mA. Normalized to a single fly this makes
0.1% of total beam loss, which is pretty close to estimations made
above.

In order to test details of scattering a simple simulation was made in
Mathcad. Simulation took into account wire traveling through the beam
and betatron displacements of each particle at every turn. Simulation
yielded the same numbers for emittance growth and beam losses. Beam
profiles for multiple and single scattering alone are shown in Figure
7,8. No substantial change in shape appeared, Figure 8 features longer
low tails.

![](media/image8.wmf)

Fig. 7. Beam transverse profiles in logarithmic and linear scales before
and after wire fly when only multiple Coulomb scattering applied. Red
trace shows profile before fly, blue trace -- after.

![](media/image9.wmf)

Fig. 8. Beam transverse profiles in logarithmic and linear scales before
and after wire fly when only single Coulomb scattering applied. Red
trace shows profile before fly, blue trace -- after.

IV. **Conclusions and the present status.**

Some progress was achieved during 2002:

i.  The monitoring program was brought to the level where it could run
    substantial time without crashes.

ii. The motion control reached the state with fairly low rate of
    hardware errors.

iii. A part of VME position and analog modules necessary for operation
     was maintained in working state.

iv. The entire system was operating synchronously with the Tevatron
    complex, wire flies were taking place on trigger certain time after
    each shot set up and results were logged with Lamberjack.

There were also some important lessons from random operation in 2002:

1.  A large irreducible offset in time between the gates and the loss
    monitor signal was observed in some stations (most notably- Low
    Dispersion wire). This is most probably the software bug, however it
    also looks very much similar to a angular offset of the fork in rest
    with respect to its normal parking position. In the latter case an
    eye inspection is necessary to determine a cause of this offset.

2.  The beam profile measured with the same beam and same width doesn't
    give the same answer for different flies. The reason for this is not
    well understood. Possible suspects could be loose wire or loose
    feedthrough connection of the fork with its drive. Those can be
    addressed by visual inspection of wires and examining one of the
    stations at the test stand.

The way this system was operating in 2002 was not very practical: VME
modules used are too old and ceased support at Fermilab. There are no
spare modules, performance of existing ones was very unstable and
failures were hard to track down and fix. The only way to make system
operational is to upgrade it. There is a variety of upgrade scenarios,
this paper presented just one of those, which is the most realistic in
author's point of view.

> **Upgrade of the Flying wires (out of date).**

In order to bring the system up to the level of normal operation, all
the VME based electronics in AP30 must be replaced with the standard
presently supported at Fermilab. VME chassis should be replaced too
along with its power supply. Nuclear Instruments do not support any more
the standard currently used for the motion control- this should be
updated too. PC instead of a Power PC station seems to be a natural
step, as a new interface to motion control is suggested in PCI
framework. There seems to be no special reason to build the Accumulator
FW principally different mechanically and electronically from that used
in Tevatron and Main Injector. In order to accomplish this unification
the belt drives with optical encoders will be replaced by direct drives
with resolvers. Currently, the drives, encoders and RIPFIFO modules are
already in hands and substantial testing had been performed by the
Recycler team. The complete work-list for the upgrade is presented in
Appendix I.

It doesn't make much sense now to continue maintaining intermittent DAQ
of present FW system, in fact, these attempts have been stopped de-facto
after the January shutdown, therefore upstairs part of the upgrade work
may be started right away. The bulk work of the upgrade is suggested be
made during the August 2003 shutdown. This work WILL NOT require vacuum
intervention, however, there is a strong motivation to open vacuum and
do wires inspection before completion of the upgrade.

There is no need in all 6 stations installed currently in the
Accumulator. It is suggested that one of them, the central orbit
horizontal wire be removed during vacuum intervention and placed at the
test stand with dual encoder/resolver readout to study possible free
walk of the fork around its axis.

**Appendix I. List of works that need to be done during the Accumulator
FW upgrade.**

1.  Replace belt drives/encoders with direct drives/resolvers

2.  RIPFIFO instead of position logics.

3.  Replace the VME crate with PS.

4.  Build a new DAQ and position logic with RIPFIFO.

5.  Replace Macintosh with a PC

6.  Replace the motion control system.

7.  Redo the terminations for cables coming to AP30 from the tunnel.

8.  Clone the LabView program from that used in Main Injector.