A Monte Carlo Model of Tevatron Collider Operations Elliott McCrory, BD/(Linac Integration) 4, 5...

A Monte Carlo Model of Tevatron Collider Operations

Elliott McCrory, BD/(Linac & Integration)4, 5 December 2003

A phenomenological model of Tevatron Collider operations has been created. Key elements of the operation of the facility have been randomized in this model to reflect actual Run II performance. In particular, failures and downtimes occur randomly, in agreement with the rates observed in reality. Similarly, performances are randomized, also in agreement with the range of possibilities in reality. Some of the performance elements that have been randomized include: PBar transmission and emittance growth from the Accumulator to Low Beta, Shot Setup time, the Luminosity Lifetime, etc. A primary motivation for this model is to guide the Run Coordinator on how to manage the operation of the Collider. In particular, this model answers the question of how a particular criterion for ending stores affects the integrated luminosity.

4,5 December 2003 Elliott McCrory 2

Executive Summary

Tevatron Operations Model exists Uses randomizations, not beam physics,

to model the creation of luminosity The Model is normalized to real data

from the accelerator complex Predicts how best to operate the

Tevatron This talk available from “Beamdocs” database, http://beamdocs.fnal.gov


Outline

1. Model overview [13 slides]

a. Structure/Random numbersb. Collider Operational Performance

Matching Model to Reality

2. Developing Intuition/Model Predictions [10 slides]

a. Optimizing an End-Store criterionb. When should we end stores?c. Where do we integrate luminosity?

3. Conclusions [3 slides]


1. Model Overview Phenomenological, non-analytic model of Tevatron

Collider Operations Complexity Randomness

Downtime Variations in all realistic parameters

Adjust parameters of Model to match Reality “Shot data” is used Model parameters have

Appropriate range of randomizations Correlations

Model represents present and future Tevatron Operations Develop intuition/guidance for controlling stores

Many already have this intuition, but not all….


Model Assumptions

Performance does not improve Random fluctuations around a specific set of

parameters As performance changes, I’ll modify the Model

No shutdowns Only simulating running periods

Existing data on stores/shots are accurate Supplemented and supported by other sources


1a. Program Structure How does this work?

Step size = 0.1 hours Diminish the luminosity Stack Has anything failed?

Stacking stops? Stacking slows down? Lose a store? Lose a stack?

“End-store” criterion? Start shot setup. Shot Setup over? Generate luminosity

“Shot” process: Heavily randomized Based on Reality

Stack or store lost? Stack to reasonable stack size & shoot Reasonable ≈ 100 mA If a stack is lost, we could keep the store in for a long time!

Repeat for N weeks, dumping lots of relevant data.

C++/Linux (FRH 9.0) 5000 weeks in 40

seconds 100+ parameters


Model: Three Typical Weeks

Week #7Week #8Week #9

10000 1/nb

100 E30

200 mA


Random NumbersR

ando

mLi

kely

(10,

25,

12)

, “є P

”

Ratio of these two quantities

RandomLikely(150, 250, 200), “NP”

Linux drand48( )


1b. Collider Performance

Measurements of Operation Performance From our control system

Shot Data Acquisition (SDA) D44 data logger D18 downtime logger

From “Weekly Operations Data Sheets” Weekly hour usage Weekly integrated luminosity

Put it together: Matching Model to Reality Match to good weeks of running in 2003

Note: Only 35 weeks in 2003


Performance Data from SDA

Mostly from the “Super Table” Sample of data matched between Model & Reality

Tevatron Up Time Stacking rate Stacking Up Time

Proton Source Uptime and Lost Stacks Emittance of the PBars from the core PBars from the Accumulator to Low Beta

Efficiency, Emittance Growth Protons at Low Beta Stack Size vs. Initial Luminosity Initial Luminosity Lifetime Time in a store and between stores

Including Shot Setup time Stores that are lost during shot setup Recovery time from Tevatron failure

Ideas in development Turn-on delay at

experiments due to losses

Recycler tax Switchyard tax Time-of-day

dependencies


= 0.975 / hour

Tevatron Failure Rate

f(t) = e - t

σ = < t > = 1/

Time Between Tevatron Failures; Real Data

e - t

R ≈ 1 - ΔtΔt = 42 hours

Model data for Tevatron Failures


Failure Rate: Interpretation

is “Tevatron Up Time” is measured directly from real data

< t > = σ = 1/ Probability of having stores of:

1 hour: 0.975 2 hours: (0.975)2 = 0.951 10 hours: (0.975)10 = 0.776 20 hours: 0.603 30 hours: 0.459

Failures are Independent of Time This is a random process!!


Initial Luminosity vs. Stack Size

Stack size before first transfer

Initi

al L

umin

osity

(E30

) 2003 Stores

Simulated Stores


Initial Luminosity Lifetime

Initial Luminosity, E30 cm-2 sec-1

Lum

inos

ity L

ifetim

e (fi

rst 2

hou

rs),

hour

s

2003 Stores

Simulated Stores


Best Match of Model to Data

The parameters of the model have been adjusted to get this match.

Reality ModelHours RMS Hours Ratio

Tevatron Store 92.18 15.35 93 0.9%Shot Setup 16.77 3.78 17.53 4.5%Studies 18.76 10.46 18.86 0.5%

General Shutdown 7.11 5.02 7.41 4.3%Standby 1.60 1.83Failure 17.70 11.52Turn-around 12.13 5.20Startup 1.60 1.80Misc 0.18 0.38 31.63 -5.0%

Tevatron Luminosity 6810.40 1487.53 6814.63 0.1%Pbar Stacked 904.29 137.38 915.24 1.2%

Hours Stacking 120.82 16.62 121.2 0.3%


Model Params that Match Reality

Category Parameter Value Units Category Parameter Value Units Category Parameter Value UnitsProton ProtonEmitPerE9 0.0272 π mm mr Tevatron TevUpTime 0.975 Pbar Transmissions PBarTransmissions[0] 0.967

ProtonEmitPerE9Offset 18.052 π mm mr TevExtraDown 2.2 Hours PBarTransmissions[1] 0.999999ProtonEmitPercentRange 0.1 TevExtraDownOffset 0.2 Hours PBarTransmissions[2] 0.92ProtonIntensity 250 E9 TevRecoveryTimeMin 0 Hours PBarTransmissions[3] 0.91ProtonILower 230 E9 TevRecoveryTimeMax 16 Hours PBarTransmissions[4] 0.9ProtonIUpper 270 E9 TevTurnAroundTimeMin 0 Hours PBarTransmissions[5] 0.94ProtonLengthPerE9 0.0013 nSec TevTurnAroundTimeMax 4 Hours PBarTransmissionsMin[0] 0.94ProtonLengthPerE9Offset 1.4727 nSec TevTurnAroundTime 0.8 Hours PBarTransmissionsMin[1] 0.96ProtonLengthPercentRange 0.1 TevAccessTimeMin 1 Hours PBarTransmissionsMin[2] 0.82

Shot ShotLostPBarFraction 0.01 TevAccessTimeMax 14 Hours PBarTransmissionsMin[3] 0.84RemoveVary 0.93 TevStudyTimeMin 6 Hours PBarTransmissionsMin[4] 0.83RemoveVaryMin 0.86 TevStudyTimeMax 24 Hours PBarTransmissionsMin[5] 0.86RemoveVaryMax 0.96 Luminosity LumInitLife 9.5 Hours PBarTransmissionsMax[0] 0.99StackEmitQuadratic 0.00005 LumLifetimeVary 1 Hours PBarTransmissionsMax[1] 1StackEmitQuadraticMin 0.00001 LumLifetimeVarySpread 0.2 Hours PBarTransmissionsMax[2] 0.985StackEmitQuadraticMax 0.0001 LumLifetimeC1 1.8 PBarTransmissionsMax[3] 0.96StackEmitLinear 0.008 LumLifetimeC1Offset 0.2 PBarTransmissionsMax[4] 0.98

Stacking StackDowntimeOff 0.4 Hours LumLifetimeC2 0.595 PBarTransmissionsMax[5] 1StackDowntimeOffMin 0.2 Hours LumLifetimeC2Offset 0.005 Pbar Emit Growth PBarEmittanceGrowths[0] 2.8 π mm mrStackDowntimeOffMax 2 Hours bunches 36 PBarEmittanceGrowths[1] 0.000001 π mm mrStackBadDowntime 0.1 kLong 0.8 PBarEmittanceGrowths[2] 4.5 π mm mrStackingSucks 0.1 energy 980 GeV PBarEmittanceGrowths[3] 1.5 π mm mrStackingUpTime 0.921 betastar 35 cm PBarEmittanceGrowths[4] 1.8 π mm mrStackNotLost 0.64 KStarBeta 1 PBarEmittanceGrowthsMin[0] 2 π mm mrStackBadRateLower 0 mA/Hr Operations ExpNeedAccess 0.3 PBarEmittanceGrowthsMin[1] 0 π mm mrStackBadRateUpper 0.77 mA/Hr TevNeedsStudy 0.25 PBarEmittanceGrowthsMin[2] 1 π mm mrStackRateVaryMin 0.7 mA/Hr StopStackOnTevFailure 0.3 PBarEmittanceGrowthsMin[3] 0 π mm mrStackRateVaryMax 1.03 mA/Hr Shot Setup ShotSetupTime 2.3 Hours PBarEmittanceGrowthsMin[4] 0 π mm mrStackRateVary 0.95 mA/Hr ShotSetupLower 1.2 Hours PBarEmittanceGrowthsMax[0] 3.5 π mm mrZeroStackRate 13.4 mA/Hr ShotSetupUpper 3.6 Hours PBarEmittanceGrowthsMax[1] 2 π mm mrZeroRateStack 280 mA PBarEmittanceGrowthsMax[2] 7 π mm mr

PBarEmittanceGrowthsMax[3] 3 π mm mrPBarEmittanceGrowthsMax[4] 6 π mm mr


2. Developing Intuition/Predictions

a. Optimizing an “End-Store” criterion

b. When should we end a store and why? What is important? End-store criteria: Which is “best”?

Introducing the “Luminosity Potential Ratio” end-store criterion

c. Where we integrate luminosity


Maximize weekly integrated luminosity Simple End-Store Criteria

Store Duration Target Stack Size Minimum Luminosity

Optimization by eye Which of these three is best??

They all integrate about 7100 pb-1 per week Store Duration: 30 hours 7085 pb-1

Target stack size: 200 mA 7095 pb-1

Minimum luminosity: 10E30 7049 pb-1

Error bars: ~17 pb-1

Each is approximately as good as the others, for the running we have today

2a. Optimizing an End-Store Criterion

Store Duration, Hours

Ave

rage

Wee

kly

Inte

grat

ed

Lum

inos

ity, E

30 c

m-2 s

ec-1

Target Stack Size, mA

Minimum Luminosity, E30


2b. Which End-Store Criterion?

If Model is believable Can change the performance See how the End-Store criteria respond Find the Best criterion for ending stores for lots of parameters

How to decide which is the “Best” criterion? It integrates lots of luminosity It insensitive to many/most performance changes

Some performance changes may be unnoticed Random fluctuations or improvements?!

It is simple Everyone can understand it!

Some effective but complex schema have been rejected


Example: Sensitivity to PerformanceA

vera

ge W

eekl

y Lu

min

osity

, E30

Shoot when stack reaches this value, mA

Green: TevUp = 0.99

Red: TevUp = 0.975No Studies or Post-Store Accesses

Green/Magenta: TevUp = 0.99

Red/Blue: TevUp = 0.975

Note Shift!


Search Big Parameter SpaceStack(0) MaxStack Init Life Recov TurnArnd # Protons

Parameter Sets 12 13.4 280 9.5 16 4 250Parameter Sets 34 15 350 9.5 16 4 250Parameter Sets 56 15 350 12 16 4 250Parameter Sets 78 13.4 280 9.5 8 2 250Parameter Sets 9A 13.4 280 9.5 16 4 295Parameter Sets BC 15 350 9.5 16 4 295Parameter Sets DE 15 350 9.5 8 2 295

Details are unimportant for this talk But ask me!

Which criterion works “best,” independent of how we are running? Example: MaxStack and InitLife


Optimization Example: “MinLum”

Optimum shifts higher with better performance:We’d like a criterion that was insensitive to these changes

Sets 1, 2: 2003 RunningSets 7, 8: Reduced Recovery timeSets 3, 4: Enhanced StackingSets 5, 6: Enhanced Stacking, Improved Lum LifeSets 9, A: 25% more protonsSets B, C: More Protons,Enhanced stacking.

Sets D, E: More P, PBar;Reduced recovery


0

10

20

30

40

50

60

70

80

0 50 100 150 200 250 300 350 400 450

New: Luminosity Potential Use chart, here

Stack size L End store when

“Potential” / ”Actual” > V. Example:

If: Stack=180 mA Potential = 45E30

And: L (now) = 9 E30 Then: Ratio = 45/9 = 5.0

Assumption on “potential” curve?

May be a problem But it is changeable as

performance improves ACNET:

T:XPCTLU, T:XPLURAStack Size, mA

Initi

al L

umin

osity

, E30

LuminosityPotential

50 recent stores


Luminosity Potential: Ratio

(Likely Initial Luminosity) / (Actual Luminosity Now)

Ave

rage

Wee

kly

Inte

grat

ed L

umin

osity

, nb-1

Best: End store when 4 ≤ ratio ≤ 5


Luminosity Potential: Ratio

Optimum stays between 3 and 4;This criterion is less sensitive

to these changes in performance.

(Likely Initial Luminosity) / (Actual Luminosity Now)

Ave

rage

Wee

kly

Inte

grat

ed L

umin

osity

, nb-1


2c. Where we integrate Luminosity

Target Stack SizeStore DurationLuminosity RatioMinimum Luminosity


3. Conclusions

Operations Model of the Tevatron exists It matches Reality well

Hours per week Luminosity, luminosity lifetime, etc.

We will be using this Model to help us understand the Tevatron Complex

Model says: Use “Ratio” end-store criterion Store Duration, minimum luminosity, target stack size

work okay, but are not as robust Work Continues


Web Pages

http://mccrory.fnal.gov/montecarlo http://mccrory.fnal.gov/testForm.html This talk:

On “beamdocs” database, talk #913 Public access! Three versions

http://beamdocs.fnal.gov/cgi-bin/public/DocDB/ShowDocument?docid=913

http://mccrory.fnal.gov/montecarlo

http://mccrory.fnal.gov/testForm.html

http://beamdocs.fnal.gov/cgi-bin/public/DocDB/ShowDocument?docid=913


What’s Next?

Improve understanding of 2003 performance Historical “End-Store” criterion?? Knowledge of time of day

Further exploration of “Best” End-Store Criteria

Incorporate Recycler First: “Recycler Tax”

A Monte Carlo Model of Tevatron Collider Operations Elliott McCrory, BD/(Linac Integration) 4, 5...

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