SCT Endcap Material

I have considered the possibility of rotating modules in the SCT Endcaps so as to avoid the lining-up of material, in particular associated with the cooling blocks.

This was proposed by Allan Clark and Alan Poppleton and included in the ID TDR Simulation, but never incorporated into the Engineering Designs.

Physics Considerations

The optimal distributions of material in a detector are:

Uniform or
Localised to a small number of well defined places of small dimensions (hence low probability of lying in the path of a track) which can be excluded by fiducial cuts.

The SCT material distribution (in eta-phi) is really nasty since it is very lumpy with significant amounts of material O(10%) X0 with a significant probability of being crossed O(10%) and located at many places with a fairly complicated distribution. The largest source of lumpiness is the cooling blocks. With such a distribution, there is a significant probability of tracks crossing more than one cooling block.

Question: Is it better to avoid the situation where blocks line up, or is the converse true ?

Photons

These go in straight lines. If they encounter material, they may convert to an e+e- pair. A single photon can only convert once, and so it doesn't matter whether material lines up or not. However, if the material does, there is a chance that a high-pT electron from an asymmetric pair may hit a subsequent block.

High-pT Charged Particles

The scale for high-pT is that particles deflect by no more than a few mm (the cooling blocks are O(10)mm) over the radius of the SCT. The deflection of a particle is:

Delta(Rphi) = 0.3 * R**2 / pT

where R is radius of detector. For example, for Delta(Rphi) = 0.003m and R = 0.5m, then pT = 25GeV. Chose your favourite numbers ... but we are talking of pT's in excess of 10 GeV.

The track parameters estimated for muons and pions are degraded by multiple scattering. It is not obvious whether it is better to have more tracks with degraded parameters of fewer tracks with even greater degradation. (But one should bear in mind the actual numbers which will be reported later. Tails might be O(10%), while "extreme" tails due to double interactions might be O(1%).) At very high pT, the multiple scattering is irrelevant. For the average material distribution, the transition to high pT occurs at O(40) GeV. When large lumps of material are concerned, this transition will be at higher pT.

Electrons will also suffer bremsstrahlung (photon emission). The fraction of brem is approximately independent of energy, so all electrons will be affected. Is it better to have more electrons in a smaller brem tail, or fewer electrons in a longer tail ? (See comment in parenthesis in last paragraph.) Might depend on the strength of the brem recovery procedures and the tightness of electron cuts.

Hence this is likely to be an effect for high-pT physics such as W/Z and low mass Higgs.

Low-pT Charged Particles

These will be liable to multiple-scattering and brem (for electrons). Corresponding physics will be B-physics and b-tagging. However, for sufficiently low-pT particles, their curvature will ensure that they will tend not to cross cooling blocks which are lined up as far as straight tracks are concerned. Of course there will be random correlations of material. If there is some systematic lining-up of material for straight tracks, and this correlation is broken by a rotation of detectors (see below), it will cause a certain class of lower-pT tracks, characterised by a momentum range (dependent on the charge sign) to see a correlation.

I feel that the low-pT tracks are less important than the high-pT tracks.

Where all this leaves us is not obvious. However my personal feeling is that it would be preferable to avoid excessive correlations of material.

Possible Engineering Design

Rotate Wheels

In the design proposed by Clark and Poppleton, it was proposed that each successive wheel should be rotated by 1/3rd of an outer module.

It seems likely that this could be achieved, however it would require quite a lot of redesign.

Comparing with the current Engineering Design (08/01/01):

The routing of the services would be more complicated (at least compared with current thinking), since power tapes would have to be modified to bring them out to the same place on the support barrel. This would probably result in extra expense in tapes (due to large number of different configurations) and connectors, but should be possible. It would require further study.
If it was required that the supports for the wheels were at the same azimuthal location, then they would need to have a different position with respect to the items mounted on the wheel - not a big issue.
The current scheme for the FSI proposed for the z measurements of disks would need to be modified. It is proposed to have composite jewels (containing quills for the laser light delivery/capture and reflectors) associated with holes in the disks to allow the connection of alternate wheels. Were the wheels to be rotated, the alignment paths would be lost. Todd Huffman has conceptual ideas which would permit the separation of the quills and reflectors and could accommodate the rotations; however this would require further design work.

Rotate Rings

A potentially simpler scheme which would avoid the problems listed above would be to rotate the middle ring of modules relative to the inner and outer rings by 1/2 of an inner module. This would require redesigning the routing of the power tapes and cooling circuits. Initial indications from Steve Temple and John Noviss are that this is feasible. It apprears easier to rotate the inner/outer rings, and in looking at this, they have effectively redone the deign.

My Simulation

I have made some very simple studies. These have been implemented in standalone F77 (not using Geant).

I consider:

The current layout (08/01/01) as proposed in December 2000 SCT Week.
Only the effects in the Endcap are considered, and a cut-off at eta=2.5 is used.
Only primary and secondary cooling blocks.
These are by far the largest contribution to the inhomogeneity in eta-phi.
I do not consider silicon overlaps.
An extra 300um of silicon corresponds to 0.3%.
I do not consider pipes, which corresponds to roughly 0.5%.
Only normal incidence.
For angled tracks, the material seen is greater when the whole thickness is crossed, but is reduced for those tracks entering/exiting at the edge.
The simulation is done in bins of eta x phi.
At R=500mm, the bins are approximately 0.4mm x 0.5mm in R x Rphi.
The bin sizes in the corresponding histograms are larger.

Cooling Blocks

The description of the blocks is very conservative.

The blocks are made of Aluminium.
The blocks are described by the rectangle in R and Rphi which contains the main part of the block - the attachment "wings" and associated pipe connections are ignored.
The fact that the blocks are chamfered and have their corners removed is ignored - conservative.
Allowance is made for the high (11.5mm = 13% X0) and low (6.8mm = 8% X0) alternation of blocks.
Allowance is made for the fact that the centre of the blocks is displaced in z from the centre of the wheels.
Allowance is made for the slightly different positions arising from the u-phi, v-phi, u-phi ... geometry.

The primary (secondary) blocks are taken as 19mm x 14mm (4mm x 20mm) in R x Rphi. There are no secondary blocks for the inner modules.

Studies

I have only considered infinite momentum particles, corresponding to photons or high energy electrons.

I looked at the variation arising from tracks with different starting positions in z. While there are effects in the precise location of the correlations of material, the net effect integrated over all eta appears to be smallish. Therefore, I have considered only tracks from z=0.

I have only studied the current layout. My suspicion is that moving the wheels in z or changing the location of the first inner ring (on Wheel 1 or 2), will probably not make a big difference to the net effect.

Results

Scatter plots show material in eta (1 to 2.5) vs phi (0 to 90 degrees).

Material in Wheels

The material distributions for material in the first 8 wheels (material in wheel 9 is beyond |eta|=2.5).
The primary and secondary cooling blocks can be seen.
The small stagger due to high/low blocks is just visible, and is correlated with the intensity of shading, which measures the thickness.
(For reasons I don't understand, this plot is made with z0=2*sig_vtx - rest have z0=0.)

Material Distributions for Current Engineering Design

Top left: scatter plot of material.
Bottom left: scatter plot of material, above 15% X0.
Bottom right: scatter plot of material, above 25% X0.
Top right: histogram of material seen in each eta-phi bin. In scatter plot with 15% threshold, note bands at eta of 1.7 (2.0) due to overlap of blocks from inner ring on Wheel 2 (5) with middle ring on Wheel 4 (6). If z position from which tracks start is varied, these bands move.

Material Distributions when Rotate Middle Ring

The plots show the effect of rotating this ring by 1/2 a module.

Note that the bands seen for the Current Design are largely removed.

Material Distributions when Rotate Wheels

The plots show the effect of rotating successive wheels by 1/3 module.

Note that the bands seen for the Current Design are largely removed.

Table of Results

The table tries to quantify the results shown in the plots. In looking at the numbers, one must bear in mind the many approximations made.

Two thresholds are set: 1% (low) and 15% (high) X0. The first is sensitive to material in the cooling blocks; the second is sensitive to the overlap in eta-phi of blocks (since individually, single blocks are less than 15% X0).

1st column: Fraction of eta-phi bins above threshold.
2nd column: Mean amount of material for bins above threshold.
3rd column: Mean amount of material above threshold, averaged over complete wheel.

It is not obvious what quantities to look at. I choose to focus on the 1st column: for the high threshold, it shows the probability for a high-pT particle to hit two or more blocks. With the three configurations, the amount of material is the same, only its distribution is different. This corresponds to the observation that the numbers in the 3rd column for the low threshold should be the same, not those in the first column (to understand this, consider overlapping blocks).


Current Design
 X0>1%       0.164     12.00      1.96
 X0>15%      0.020     20.84      0.42

Rotate Middle Ring
 X0>1%       0.171     11.48      1.97
 X0>15%      0.014     20.02      0.27

Rotate Wheels
 X0>1%       0.175     11.24      1.97
 X0>15%      0.010     21.36      0.21

Initial observations:

The probability to hit one block is distressingly large ~17%.
The probability to hit two blocks is fairly small <2%.
Further, this probability is probably significantly over-estimated (by a factor of 2, 3, .. ?), since overlaps will tend to be at the block edges and this is where my description of a block is conservative.

Other Considerations

The rotations of the rings or wheels would remove the correlations between the inner and middle rings for the detector overlaps at the edge of the modules. Is this and advantage/disadvantage for the pattern recognition or alignment ? I cannot think of any strong arguments either way.

Rotations of rings/wheels have the potential to open up small triangular holes in the coverage when going from one ring to another due to the trapezoid silicon detectors. This was never a consideration in my study for the positioning of the wheels in z - I assumed fan-shaped detectors (Poppleton did consider trapezoids). However, the difference in radius for an inner module between the centre of the outer edge and the corner is O(1)mm. I consider such effects to be small and probably would be smaller than other approximations I have made. I could go into much deeper considerations here; however, I don't think it is helpful.

Conclusions

The probabilities of a track hitting two or more sets of blocks as determined by this study are:

Current Design         2.0%     
Rotate Middle Ring     1.4%
Rotate Wheels          1.0%

Recall that these numbers are conservative in so far as the area of the blocks has been overestimated, although the effect of other contributions to the material inhomogeneity has been ignored. However, it is hoped that these numbers still give a feel for relative differences which might be seen with different SCT wheel configurations.

I would suggest that the effect of correlations in material arising from the cooling blocks is not big and it is not actually clear what is optimal for physics (increasing or decreasing the correlations).

Nevertheless, it would seem to me beneficial to reduce the material correlations. I would propose we should rotate the inner/outer rings (equivalent to rotating middle ring) by 1/2 of an inner ring and at the moment, there appear to be no Engineering reasons which would prevent this. To rotate the wheels would require much more design work, and these results suggest that the benefit is not so great. (These statements are made with the caveats that only the "Current Engineering Design" has been considered and with tracks starting from z=0.)

Stephen Haywood                                 12 Jan 2001