1. SCT readout limitation estimate with data
Susumu Oda (Kyushu)
Bruce Gallop (RAL)
Dave Robinson (Cambridge)
Steve McMahon (RAL)
SCT DAQ Upgrade for High-Mu

2. Introduction
ATLAS will need to take collision data under the following conditions until Phase-II Upgrade.
at sqrt(s)=14 TeV
with 25 ns bunch spacing
at <m>=80 (the mean number of interactions)
with 100 kHz Level-1 trigger rate
Where is the readout limitation of SCT with the current setting (90 RODs, expanded mode)?
How can we achieve 100 kHz at <m>=80?

3. Maximum rate is determined by data size.

4. ABCD data formats Data size of a link is
Header: 19 bits
Trailer: 16 bits
Data (chip/chan/XXX):
1hit cluster 17 bits
2hit cluster 21 bits
3hit cluster 25 bits
Data size of a link is
19+13<Nclusters>+4<Nstrips>+16 bits
<Nclusters>: The mean number of clusters of the link
<Nstrips>: The mean number of strips of the link.

5. ROD S-link Event Formats
One ABCD hit in BS is (reduced to) 16 bit
Condensed mode encodes 2 hit cluster in single 16bit word:
Cluster width
Expanded
Condensed 1 16 2 32 3
Plus, we have 9x32bit Header, and 5x32bit trailer

6. Data size of ROD output ROD header is 9x32bit words.
ROD trailer is 5x32bit words.
Link header is 1x16bit word.
Only for links which have hits.
The number of links with hits will not increase linearly with mu and will become the number of used links at high mu.
Link trailer is used as a 16bit padding word for a ROD to fill 16bit.
8bits on average
Cluster word (expanded) is 1x16bit word for 1-hit cluster, 2x16bit words for 2-hit cluster, 2x16bit word for 3-hit cluster, 3x16bit word for 4-hit cluster...
Cluster word (condensed) is 1x16bit word for 1-hit cluster, 1x16bit word for 2-hit cluster, 2x16bit words for 3-hit cluster, 2x16bit word for 4-hit cluster...
Linearly increase with mu.

7. Used data Stream Run Data format Hit pattern
express stream
Run
201191: Period A4, Apr 13
201289: Period A5, Apr 15
201489: Period A7, Apr 18
202668: Period B1, May 2
202712: Period B1, May 2
202798: Period B1, May 3
Data format
NTUP_SCT produced by Bulk processing (f-tag) at Tier-0.
Hit pattern
Online: XXX in Period A, X1X in Period B
Offline: X1X is required.
Luminosity underestimate in Period A
actualIntPerXing (= m) in NTUP_SCT is corrected by a factor

8. Linear extrapolation of data size and the number of cluster words
One run is divided into three sets based on m value.
Set A: m £ 1
Set B: 1 < m £ mthresh
Set C: mthresh < m
mthresh~16
Calculate mean data size and the number of cluster words in each mode for each link with set B and set C, vB and vC.
Calculate mean m values of set B and set C, mB and mC.
Linearly extrapolated using the mean values:
v(m) = [(vB-vC)m+(vCmB-vBmC)]/(mB-mC)
Use the average of slope and intercept of the six runs.
Negative or very large slope of one run compared to other five runs is excluded.

9. Non-linear increase of link header
Probability that a link has at least one hit is approximated by 1-p0*exp(-p1*mu).

10. Extrapolation to 14 TeV For inelastic scattering:
ALICE measurement, arXiv: , Charged-particle multiplicity measurement in proton-proton collisions at sqrt(s) = 7 TeV with ALICE at LHC
CMS measurement, arXiv: , Transverse-momentum and pseudorapidity distributions of charged hadrons in pp collisions at sqrt(s) = 7 TeV
ATLAS measurement, arXiv: , Charged-particle multiplicities in pp interactions measured with the ATLAS detector at the LHC
Model comparison, arXiv: , Charged-Particle Multiplicity in Proton-Proton Collisions, Jan Fiete Grosse-Oetringhaus, Klaus Reygers
For inelastic scattering:
lns ln2s
11.1% increase by sqrt(s)=8 TeV14 TeV
For Non-Single-Diffraction interaction:
lns ln2s
13.1% increase by sqrt(s)=8 TeV14 TeV
13.1% increase is used for extrapolation.

11. Bunch spacing change from 50 ns to 25 ns
We will see more hits with 25 ns bunch spacing than with 50 ns bunch spacing even at the same instantaneous luminosity.
25 ns bunch spacing runs were taken on 7 October, 2011.
01X mode with 25 ns bunch spacing gives 7% higher hit rate than X1X mode with 50 ns bunch spacing.
The following results are assumed 25 ns bunch spacing and 01X mode.
Run
50 ns spacing
1.0<m<=15.5
15.5<m
Slope
Ratio
<m>
14.393
16.608
<Nstrips (X1X)>
2.225x104
2.505x104
1.26x103 1
<Nstrips (01X)>
2.101x104
2.373x104
1.23x103
0.97
50ns
Run
25 ns spacing
1.0<m<=6.2
6.2<m
Slope
Ratio
<m>
5.357
7.167
<Nstrips (XXX)>
2.829x104
3.513x104
3.78x103
2.99
<Nstrips (X1X)>
1.472x104
1.805x104
1.84x103
1.45
<Nstrips (01X)>
1.014x104
1.258x104
1.35x103
1.07
25ns

12. Data size and maximum rate of links between ABCD-ROD
8176 links are plotted.
Maximum rate
= 40 MHz*90%/datasize [bit]
2.5% of links read 12 chips due to the TX failure.
However, all links are assumed to read 6 chips in this calculation.
100 kHz  <m>~87

13. ROD-ROS (Expanded mode)
Maximum rate
= 40 MHz*90%/datasize [32-bit]
90 RODs are plotted.
100 kHz  <m>~33

14. ROD-ROS (Condensed mode)
100 kHz  <m>~43

15. The number of words for clusters (including link header) for each ROD with Condensed mode at m=67 at 14 TeV
bit
words/module
corresponds to
100 kHz limit.
Blue: For individual module (=2 links)
Red: Average for group of 12 modules (=24 links)
Black: Average for ROD

16. Add more RODs and shuffle links
bit
words/module
corresponds to
100 kHz limit.
Use 128 RODs by adding 38 RODs to empty slots.
Shuffle groups of 24 links inside individual crates to minimize the maximum data flow per ROD.

17. ROD-ROS (Condensed mode) with 128 RODs and the shuffle
100 kHz  <m>~67
128 RODs are plotted.

18. Data size of ROD output with modified condensed mode
ROD header is 9x32bit words.
ROD trailer is 5x32bit words.
Link header is 1x16bit word.
Padding word is a 16bit word for a ROD to fill 16bit.
8bits on average
Cluster word is 1x16bit word for 1-hit—16-hit cluster, 2x16bit word for 17-hit—32-hit cluster, ...

19. ROD-ROS (modified condensed mode) with the current setting
100 kHz  <m>~50

20. ROD-ROS (modified condensed mode) with 128 RODs and the shuffle
100 kHz  <m>~87

21. Another possible modified algorithm more aggressive one
ROD header is 9x32bit words.
ROD trailer is 5x32bit words.
Link header is 8 bits.
Padding word to fill 32 bits will be 16 bits on average.
Cluster part is 14 bits for 1-hit cluster, 16 bits for 2-hit cluster, 18 bits for 3-hit cluster, 20 bits for 4-hit cluster, 22 bits for 5-hit cluster…
12 <Nclusters> + 2 <Nstrips> bits

22. ROD-ROS (modified algorithm) with the current setting
100 kHz  <m>~57

23. ROD-ROS (modified mode) with 128 RODs and the shuffle
100 kHz  <m>~95
Exceeds the “brick wall”
of ABCD-ROD, <m>~87.

24. Systematic error due to possible cluster size change by radiation damage
The limit rate is calculated with +/-20% change in the cluster size while keeping the number of clusters constant.
Condensed mode with 128 RODs and the shuffle
Cluster size +20%
100 kHz  <m>~58
100 kHz  <m>~67
Cluster size -20%
100 kHz  <m>~75

25. Summary SCT readout limit is estimated with data and extrapolation.
Average m value, <m>, with maximum L1 rate of 100 kHz at 14 TeV with 25 ns bunch spacing, 01X mode, 90% occupancy is as follows.
To take data at <m>=80, we need more RODs and need to modify the ROD firmware.
Average m value, <m>, with maximum L1 rate of 100 kHz at 14 TeV with 25 ns bunch spacing with 01X mode with 90% occupancy (+20%/-20% cluster size)
With 90 RODs with the current setting
With 128 RODs and the shuffle of links
ABCD-ROD
87 -1/+9
ROD-ROS (Expanded mode)
33 -4/+4
52 -7/+6
ROD-ROS (Condensed mode)
43 -6/+2
67 -9/+8
ROD-ROS (Modified condensed mode)
50 -0/+0
87 -2/+2
ROD-ROS (A possible modified algorithm)
57 -3/+1
95 -5/+4