measurement that the
chamber needs to make, it is also required to provide a measurement of the
position along the length of the straw, z, with reasonable resolution,
and to do dE/dx measurements to separate 
's and K's with total
momentum under about
.
A search of recent literature on straw tube chambers shows that the
2m length is fairly typical of modern chambers. A summary of
length, radius, and wall thickness for several chambers is given in
table 1. The main issue in making long tubes appears
to be related to keeping the wire well centered in the tube to make sure
that the electrostatic description of the cell is accurate. Two issues can
affect this, electrostatic deflection due to the wire being off center
in the tube, h, and gravitational sag of the the tube itself, y.
These are discussed in detail in [1] and only summarized
here. For a tube of length L, radius R, wire radius r, voltage V,
displacement of the wire from the center 
and tension of
the wire T, the sag at the center of the wire is given in equation
1. Similarly, if the tub is built from material of density
with elastic modulus E, then the gravitational sag at the
center of the tube is given in equation 2.
,
,
,
and
,
equation 1 yields a
displacement at the center
of the wire. For mylar,
and
.
From this, equation 2 yields
for a 
length. This latter effect is often reduced by putting internal
wire supports at about 
spacing inside the tubes, and gluing adjacent
tubes together to improve the overall rigidity. For a
length,
y is reduced to about
.
The straw tube radius is determined by an optimization between the number of
electronic channels, and the pile-up rate in the detector. Typical tube
radii vary between a few millimeters up to a couple of centimeters,
(table 1). A drift velocity of about
are typical for common gas mixtures.
The lead to maximum drift times of about
for a
radius, and about
for a
radius tube.
It should be noted that due to the magnetic field, we expect the actual drift times
to be longer than these. We also anticipate that the total hadronic rate
will be about
for
,
and
for
[7].
In table 2 we show the estimated pile-up rate under various
assumptions, where it is explicitly assumed that the total hadronic rate
will deposit ionization in the straw tube chamber. It should however be noted that
most of the hadronic rate comes low energy photons in the beam that excite the
near threshold. As such, the numbers given in the table are
pessimistic. From this we would conclude that there is no problem using
diameter straws, and somewhat larger tubes should be investigated.
|
The tube material itself is also an issue. Chambers have been built using both extruded stainless steel tubes, as well as metalized mylar or kapton sheets. The main criteria in Hall D is to have as little material as possible in the chamber volume, and this consideration tends to favor metalized mylar or kapton as the material of choice. It is also desirable to make the straws as thin as possible, however, they need to be able to support both them selves, as well as the tension of the anode wire. It is likely that the tubes can be glued together to improve rigidity, but to minimize the thickness of the end plates and the overall cylindrical shell of the chamber, they must be self supporting. The exact material composition and thickness remains to be optimized.
The issue of a z-measurement has also been addressed by several groups.
Charge division along the length of the wire can provide a measurement
with resolution on the order of 1% of the wire length. The JETSET
group [8] did this with their
long chamber,
achieving a z-resolution of about
.
They
read out two wires with the same electronics by bridging the ends of two
wires together with a resistor. This lead to an effective wire length of
on the order of a meter. Another method is to use stereo layers to provide an
effective z-measurement. If the stereo angle is ,
and the chamber has
an r-
resolution of 
,
then the z resolution is given as:
 |
(3) |
stereo layers in their
long chamber. With
resolution, this yields
a z resolution of about
.
The SDC collaboration are looking
at 
stereo layers in their 
long chamber. There has also
been some work looking at cathode readout on straw chambers to measure the position along
the length of the tube. A resolution of
has been achieved
for
long resistive kapton straws [9]. Also,
pitch cathode strips have been used to obtain a
[10]. 
stereo wires are currently the favored method of
achieving the needed z resolution in the chamber. However, we would like to investigate
the use of cathode strips on the inner most layer to provide an extremely accurate
z-measurement near the target.
The final aspect of the Hall D straw tube chamber is the ability to make reasonable
dE/dx measurements. While this has been discussed in the JETSET experiment [8],
it has never been implemented in the data analysis of an experiment. The major difficulty
is knowing the exact path length of a track. Tracks which pass close to the anode wire
have a long length, while those that pass far away have a much shorter length. In fact, the
length depends on both the distance from the anode as well as the polar angle of the track.
The former comes from the drift time measurement, while the latter requires reasonable
z information. This becomes more complicated when the the
magnetic field
is taken into account, and to fully integrate this information requires accurate track
reconstruction capabilities, but appears to be a tractable problem. The solution is likely
to require flexibility in the arrangement of the tracking layers in the chamber.
We would then proceed to a multi-tube prototype chamber with which we could perform some track reconstruction, and allow us to access dE/dx capabilities and resolution. This would require obtaining Flash-ADC modules, and corresponding electronics to allow triggering and readout. While many of these tests could be done with cosmics, we would also need test beams of protons and pions to fully access the capabilities of this chamber. This would require in beam tests at an accelerator facility such as TRIUMF or IUCF.
50% of a postdoc $40,000
Graduate student summer salary $4,200
Undergraduate salaries $5,000
Total Salaries $49,200
Travel for discussions $2,500
Total Travel $2,500
Material for tubes and test setups $8,000
Electronics to augment in house equipment $12,000
Total Equipment $20,000
Total $71,700
100% of a postdoc $80,000
Graduate student summer salary $4,200
Undergraduate salaries $5,000
Total Salaries $89,200
Travel for meetings and discussions $1,200
Travel for Equipment testing $5,000
Total travel $6,200
Material and Fabrication of multi-tube chamber $25,000
Electronics for chamber $32,000
Total Equipment and Material $57,000
Total $152,400
m resolution.
![$\displaystyle \frac{L^{2} \delta V^{2} (4\pi\epsilon) }{(9.8)(16)T R^{2}
\left[ \cosh^{-1}(R/2r)\right ] ^{2}}$](img19.gif)
