1. 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.

2. 4,5 December 2003Elliott McCrory2 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

3. 4,5 December 2003Elliott McCrory3 Outline 1.Model overview [13 slides] a.Structure/Random numbers b.Collider Operational Performance  Matching Model to Reality 2.Developing Intuition/Model Predictions [10 slides] a.Optimizing an End-Store criterion b.When should we end stores?  c.Where do we integrate luminosity? 3.Conclusions [3 slides]

4. 4,5 December 2003Elliott McCrory4 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….

5. 4,5 December 2003Elliott McCrory5 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

6. 4,5 December 2003Elliott McCrory6 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

7. 4,5 December 2003Elliott McCrory7 Model: Three Typical Weeks Week #7Week #8Week #9 10000 1/nb 100 E30 200 mA

8. 4,5 December 2003Elliott McCrory8 Random Numbers RandomLikely(10, 25, 12), “є P ” Ratio of these two quantities RandomLikely(150, 250, 200), “N P ” Linux drand48( )

9. 4,5 December 2003Elliott McCrory9 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

10. 4,5 December 2003Elliott McCrory10 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

11. 4,5 December 2003Elliott McCrory11 = 0.975 / hour Tevatron Failure Rate f(t) = e - t σ = = 1/ Time Between Tevatron Failures; Real Data e - t R ≈ 1 - Δt Δt = 42 hours Model data for Tevatron Failures

12. 4,5 December 2003Elliott McCrory12 Failure Rate: Interpretation is “Tevatron Up Time” is measured directly from real data  = 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!!

13. 4,5 December 2003Elliott McCrory13 Initial Luminosity vs. Stack Size Stack size before first transfer Initial Luminosity (E30) 2003 Stores Simulated Stores

14. 4,5 December 2003Elliott McCrory14 Initial Luminosity Lifetime Initial Luminosity, E30 cm -2 sec -1 Luminosity Lifetime (first 2 hours), hours 2003 Stores Simulated Stores

15. 4,5 December 2003Elliott McCrory15 Best Match of Model to Data The parameters of the model have been adjusted to get this match.

16. 4,5 December 2003Elliott McCrory16 Model Params that Match Reality

17. 4,5 December 2003Elliott McCrory17 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

18. 4,5 December 2003Elliott McCrory18 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 Average Weekly Integrated Luminosity, E30 cm -2 sec -1 Target Stack Size, mA Minimum Luminosity, E30

19. 4,5 December 2003Elliott McCrory19 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

20. 4,5 December 2003Elliott McCrory20 Example: Sensitivity to Performance Average Weekly Luminosity, E30 Shoot when stack reaches this value, mA Green: TevUp = 0.99 Red: TevUp = 0.975 No Studies or Post-Store Accesses Green/Magenta: TevUp = 0.99 Red/Blue: TevUp = 0.975 Note Shift!

21. 4,5 December 2003Elliott McCrory21 Search Big Parameter Space Details are unimportant for this talk  But ask me! Which criterion works “best,” independent of how we are running?  Example: MaxStack and InitLife

22. 4,5 December 2003Elliott McCrory22 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 Stacking Sets 5, 6: Enhanced Stacking, Improved Lum Life Sets 9, A: 25% more protons Sets B, C: More Protons, Enhanced stacking. Sets D, E: More P, PBar; Reduced recovery

23. 4,5 December 2003Elliott McCrory23 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:XPLURA Stack Size, mA Initial Luminosity, E30 Luminosity Potential 50 recent stores

24. 4,5 December 2003Elliott McCrory24 Luminosity Potential: Ratio (Likely Initial Luminosity) / (Actual Luminosity Now) Average Weekly Integrated Luminosity, nb -1 Best: End store when 4 ≤ ratio ≤ 5

25. 4,5 December 2003Elliott McCrory25 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) Average Weekly Integrated Luminosity, nb -1

26. 4,5 December 2003Elliott McCrory26 2c. Where we integrate Luminosity Target Stack SizeStore DurationLuminosity RatioMinimum Luminosity

27. 4,5 December 2003Elliott McCrory27 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

28. 4,5 December 2003Elliott McCrory28 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://beamdocs.fnal.gov/cgi-bin/public/DocDB/ShowDocument?docid=913

29. 4,5 December 2003Elliott McCrory29 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”