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Tevatron Collider Monte Carlo Version 2.0 (for Run II) Elliott McCrory September 11, 2003

Tevatron Collider Monte Carlo

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Tevatron Collider Monte Carlo. Version 2.0 (for Run II) Elliott McCrory September 11, 2003. Outline. What’s going on here? Random numbers Assumptions Collider parameters Randomizations How does this work? What can we learn from this model? Web Interface, “beta” version. - PowerPoint PPT Presentation

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  • Tevatron Collider Monte CarloVersion 2.0 (for Run II)Elliott McCrorySeptember 11, 2003

    E. McCrory

  • OutlineWhats going on here?Random numbersAssumptionsCollider parametersRandomizationsHow does this work?What can we learn from this model?Web Interface, beta version

    E. McCrory

  • Whats going on here?Phenomenological (non-analytic) model of the Tevatron Collider ComplexBegan during Run I, with Vinod, GPJ & others helpingMcGinniss ordered me to revive it now.Incorporate randomnessDowntimeFor the Tevatron, stacking and the PBar SourceVariations in all realistic parametersE.g., transmissions during a shot, lifetimes, uncertainty in exactly how many pbars we extract, shot setup time, downtime, etc. Develop intuition for controlling storesBased on these assumptions and randomizationsMany already have this intuition, but not all.

    E. McCrory

  • Current FeaturesRepresents Run II performance, today.Easy to change to reflect tomorrows performanceMany algorithms for ending storesLinux, C++Pretty good random number generator: drand48()Can simulate 10,000 weeks in about 23 seconds Command-line arguments: scan a parameterEasily adaptable, through recompilation

    E. McCrory

  • LimitationsThis is a phenomenological model!L (t=0) = K Np(0) Npbar(0) / (p (0) + pbar (0))K = (1.331 10%) / * [cm]Downtime over 24 hours is not considered.Extended shutdowns are irrelevant.Performance in the model does not improve.Just random fluctuations around specified performance.

    E. McCrory

  • Random NumbersUnixs drand48( ); class RandomLinear

    E. McCrory

  • Class RandomLikely(0, 5, 2) and (-2, 12, 8)Product of these two distributions(Not shown): class RandomBoolean

    E. McCrory

  • AssumptionsCollider ParametersRandomizations

    E. McCrory

  • Collider Parameter AssumptionsStacking rate: 12 (1-S/300) [mA/hr]Stacking off:-0.001 S [mA/hr]Luminosity LifetimeL (t) = L (0) e -t/(t)(t) = (0) + C1 t C2C1 = 1.8 0.2C2 = 0.595 0.005

    E. McCrory

    Old Way

    Parameters and Randomizations in "simulate_week"

    ParameterDescriptionUnitsClassRandomizationRange

    K Beta*Variation in beta-star1LuminosityLinear0.8 to 1.0

    t0Initial Luminosity Lifetime multiplier1LuminosityLinear0.95 to 1.05

    LumUpTimeProbability that store is lost1/hourLuminosityboolean1%

    extraRecovery time from lost storehoursLuminosityLinear1 to 6

    extraWorse recovery time from lost storehoursLuminosityLinear6 to 24

    init_efficInitial Pbar efficiency (?)1ShotLinear0.82 to 1.0

    xmis[0]Initial extraction from source1ShotLinear0.975 to 1

    xmis[1]Transfer to MI1ShotLinear0.975 to 1

    xmis[2]Coalescing Efficiency1ShotLinear0.73 to 0.75

    xmis[3]Acceleration in MI1ShotLinear0.975 to 1

    xmis[4]Transfer to Tevatron1ShotLinear0.98 to 1

    xmis[5]at 150 in Tevatron1ShotLinear0.98 to 1

    xmis[6]Acceleration in Tevatron1ShotLinear0.98 to 1

    xmis[7]To initial squeeze in Tevatron1ShotLinear0.98 to 1

    xmis[8]To low beta in Tevatron1ShotLinear0.98 to 1

    g[0]Emittance growth factor, initial extraction1ShotLinear0 to 0.05

    g[1]Emit gwth, Transfer to MI1ShotLinear0 to 0.06

    g[2]Emit gwth, during Coalescing1ShotLinear0 to 0.06

    g[3]Emit gwth during acceleration in MI1ShotLinear0 to 0.06

    g[4]Emit gwth, Transfer to Tevatron1ShotLinear0.02 to 0.12

    g[5]Emit gwth at 150 in Tevatron1ShotLinear0.02 to 0.12

    g[6]Emit gwth, Acceleration in Tevatron1ShotLinear0.25 to 0.35

    g[7]Emit gwth, To initial squeeze in Tevatron1ShotLinear0 to 0.08

    g[8]Emit gwth, To low beta in Tevatron1ShotLinear0 to 0.06

    sDownStacking downtime now?1/hourStackboolean97%

    sOfftimeHow long is stacking off?hoursStackLinear0 to 0.83

    SOffTimeMoreMow much longer is stacking off?hoursStackLinear0.83 to 10

    sDropTimeProbability of dropping a stack during stacking downtime1Stackboolean40%

    reduceStkRtDo we reduce stacking rate?1Stackboolean40%

    sReduceAmount to reduce stacking rate1StackLinear0 to 0.5

    setupTimeJumpDo we increase the shot setup time this time?1mainboolean50%

    setupTimeHow much do we increase shot setuphoursmainLinear0 to 4

    stop_stackingStop stacking for a moment (?)1mainboolean50%

    New Way

    Parameters and Randomizations in "simulate_week"

    First crack at this9/11/03 9:06

    ParameterDescriptionUnitsClassRandomizationMinLikelyMax

    K Beta*Variation in beta-star1LuminosityLikely0.80.991

    t0Initial Luminosity Lifetime multiplier1LuminosityLikely0.911.05

    LumUpTimeProbability that store is lost1/hourLuminosityBoolean1%

    extraRecovery time from lost storehoursLuminosityLikely1224

    extraWorse recovery time from lost storehours

    init_efficInitial Pbar efficiency (?)1ShotLinear0.821

    xmis[0]Initial extraction from source1ShotLinear0.9751

    xmis[1]Transfer to MI1ShotLinear0.9751

    xmis[2]Coalescing Efficiency1ShotLikely0.730.80.95

    xmis[3]Acceleration in MI1ShotLinear0.9751

    xmis[4]Transfer to Tevatron1ShotLinear0.981

    xmis[5]at 150 in Tevatron1ShotLinear0.981

    xmis[6]Acceleration in Tevatron1ShotLinear0.981

    xmis[7]To initial squeeze in Tevatron1ShotLinear0.981

    xmis[8]To low beta in Tevatron1ShotLinear0.981

    g[0]Emittance growth factor, initial extraction1ShotLinear00.05

    g[1]Emit gwth, Transfer to MI1ShotLinear00.06

    g[2]Emit gwth, during Coalescing1ShotLinear00.06

    g[3]Emit gwth during acceleration in MI1ShotLinear00.06

    g[4]Emit gwth, Transfer to Tevatron1ShotLinear0.020.12

    g[5]Emit gwth at 150 in Tevatron1ShotLinear0.020.12

    g[6]Emit gwth, Acceleration in Tevatron1ShotLinear0.250.35

    g[7]Emit gwth, To initial squeeze in Tevatron1ShotLinear00.08

    g[8]Emit gwth, To low beta in Tevatron1ShotLinear00.06

    sDownStacking downtime now?1/hourStackBoolean97%

    sOfftimeHow long is stacking off?hoursStackLikely00.824

    SOffTimeMoreMow much longer is stacking off?hours

    sDropTimeProbability of dropping a stack during stacking downtime1StackBoolean40%

    reduceStkRtDo we reduce stacking rate?1StackBoolean40%

    sReduceAmount to reduce stacking rate1StackLikely00.040.05

    setupTimeJumpDo we increase the shot setup time this time?1mainBoolean50%

    setupTimeHow much do we increase shot setuphoursmainLikely014

    stop_stackingStop stacking for a moment (?)1mainboolean50%

    Parameter Assumptions

    ProtonEmittance20

    ProtonERange5

    ProtonIntensity27

    ProtonIRange5

    PBarEmittance15

    EmitVsStack0.02

    PBarEmitRange3

    MaxPBarEmit30

    EmitGrowthRange0.05

    ExtractPerStack0.0011

    ExtractRange0.08

    MinExtract0.3

    MaxExtract0.7

    TransFactorRange0.02

    ExtractEfficRange0.05

    ExtractEfficPerStack0.0003

    bunches36

    betastar35

    energy980

    kLong0.8

    ZeroStackRate12

    ZeroRateStack300

    Parameters

    ParameterDescriptionTypeSwitchDefaultUnits

    file of stacksz vs init lumPlot Directive-1off

    file of typical store dataPlot Directive-2off

    plot of stack rate vs stack sizePlot Directive-3off

    plot of coal effic vs stacksizePlot Directive-4off

    lum vs timePlot Directive-5off

    integ vs timePlot Directive-6off

    stack vs time & rate vs sizePlot Directive-7off

    figure_of_merit_vs_timePlot Directive-8off

    overall pbar effic vs stacksizePlot Directive-9off

    plot potential integ lum's vs timePlot Directive-Aoff

    Basic Coalescing Efficiencydouble-C0.7

    DZero_MR_off_at_beginningdouble-D0

    min_figure_of_meritdouble-F5

    glitching_stack_probabilityUsed twice: Turn off stacking for up to 10 hrs, and determine possiblility of dropping a stackdouble-G0.5

    include column headers in output filesBoolean-H

    shot_setup_timeDefault shot setup timedouble-I2hours

    Lifetime_growth_factorAmount the lifetime grows per hour. There are adjustments in Luminosity that are dependent on luminosity now.double-L1Hr/hr

    Maximum Store Lengthdouble-M24hours

    Random_number_seedint-R

    max_stackUsed in stack rate calculationdouble-S150E10

    Target_stack_sizeUsed in several end-of-store decision algorithmsdouble-T150E10

    uptime_for_storeProbability per hour that a store is lost by accidentdouble-U0.99

    Lum_ratio_factor_targetUsed in one of the end-of-store decision algorithms: When the "potential" for luminosity in the stack exceeds (1/this) time luminosity now, then end the store.double-V2.71828

    cut_flagWhich of 5 end-of-store algorithms to use, see "Decision Types" worksheetint-c1

    delta_timedouble-d0.1hours

    file_for_shot_parametersBasic parameters descibing shots, see "Basic Params" worksheetstring-fbasic-param-input

    Initial StackInitial stack sizedouble-i0E10

    k_betastar_constantCorrection to luminosity formula, taking into account betastar, hourglass, energy, etc. Makes the average initial luminosity equal to 40E30.double-k1.28

    initial_lifetimedouble-l10hours

    stack_rate_multiplier_for_DZerodouble-m0.5

    number_of_weeksint-n1weeks

    stack_rateZero-current stacking ratedouble-r4.5E10/hr

    small_stack_sizeMinimum acceptable stacksize from which we can actually shootdouble-s80E10

    uptime_for_stackingdouble-u0.97

    verboseShow lots of extra crap when runningBoolean-v

    lum_difference_targetUsed in decision #5double-w5E30

    extra_shot_setup_time_potentialIf shot setup time is increased, how much worse can it get?double-x4hours

    target_integrated_per_storeUsed in decisions 1, 2 and 3double-y600nb-1

    minimum_acceptible_luminositydouble-z1E30

    Decision Types

    TypeDescription

    1Vote

    2OR

    3Figure of Merit

    4Luminosity potential ratio

    5Luminosity potential difference

    Basic Params

    ParameterValue

    ProtonEmittance12

    ProtonERange5

    ProtonIntensity25

    ProtonIRange1

    PBarEmittance9.3

    EmitVsStack0.02

    PBarEmitRange3

    MaxPBarEmit16

    EmitGrowthRange0.05

    ExtractPerStack0.0011

    ExtractRange0.08

    MinExtract0.3

    MaxExtract0.7

    TransFactorRange0.02

    EfficRange0.18

    EfficPerStack0.0007

    bunches6

    kLong0.8

    Energy900

    betaStar35

    Lifetime Growth

    0.113043.25

    timeGrowthGrowth 2LifetimeLifetime 2SimulatedHoursReal 1

    000303043.25043.25473785

    0.10.06726727940.067571656230.067267279430.134838935642.81990123240.016666666743.70198059

    0.20.064018440.065067922630.131285719430.263925298242.39498128960.033333333343.49961853

    0.30.06097107610.063011000630.192256795530.387907374841.97512476950.0543.29367447

    0.40.05812381940.061265647430.250380614830.507296841741.56022236670.066666666743.36256409

    0.50.05547001960.059736944230.305850634430.622503805541.1501704820.083333333343.0820694

    0.60.0529998940.058359433830.358850528430.733863133340.74487081440.143.2231102

    0.70.05070201270.057088641530.409552541130.841653787540.34422995770.116666666742.57736588

    0.80.04856429310.055894752530.458116834230.946112833139.94815901460.133333333342.72679901

    0.90.04657464330.054758040530.504691477531.047445516839.55657323460.150277777842.24930954

    10.04472135950.053665631530.549412837131.145832507839.16939167910.166666666741.98022842

    1.10.0429933580.052609247730.592406195131.241435113638.78653691490.183333333341.76606369

    1.20.04138029440.051583654730.633786489531.334399062738.40793473550.200277777841.89092636

    1.30.03987261110.050585602130.673659100731.424857275938.03351390780.216666666741.85815048

    1.40.03846153850.049613108830.712120639131.512931923237.66320594390.233611111141.61022949

    1.50.03713906760.048664985230.749259706831.59873597637.29694489410.250277777841.70185089

    1.60.03589790790.047740516730.785157614731.682374400636.93466716090.266944444441.11171722

    1.70.03473143560.046839258130.819889050331.763945094336.57631133090.283611111140.99689865

    1.80.03363363970.045960901330.8535226931.843539635436.2218180220.300277777841.23522186

    1.90.03259906830.045105193430.886121758331.921243897135.8711297470.316944444441.01695251

    20.03162277660.044271887230.917744534931.997138560935.52419078820.333611111140.92507553

    2.10.0307002780.04346071430.948444812932.071299552935.18094708490.350277777840.79452896

    2.20.02982749930.042671369130.978272312232.143798421334.8413461310.366944444440.81176376

    2.30.02900073950.041903507631.007273051732.214702668434.50533688130.383611111140.26362991

    2.40.02821663240.041156744131.035489684132.284076044934.17286966660.400277777840.64550018

    2.50.02747211280.040430656631.062961796932.351978814333.84389611620.416944444440.12816238

    2.60.02676438640.039724791231.089726183332.418467991933.51836908660.433611111139.96654129

    2.70.02609090250.039038668331.115817085832.483597562733.19624259640.450277777840.25371933

    2.80.02544932990.038371787631.141266415832.547418680232.87747176630.466944444440.14395905

    2.90.0248375350.037723634331.166103950832.609979849632.56201276450.483611111140.12682343

    30.02425356250.037093683831.190357513332.671327095932.24982275550.500277777839.92819214

    3.10.0236956180.036481406331.214053131332.731504120231.94085985340.516944444439.48732758

    3.20.02316205270.035886270531.23721518432.790552443531.63508307850.533611111139.42820358

    3.30.02265134950.035307747431.259866533532.848511540431.33245231730.550277777839.40564728

    3.40.02216211040.034745312531.282028643932.905418963231.03292828510.566944444439.38661194

    3.50.02169304580.034198448631.303721689632.961310457630.7364724910.583611111139.35594177

    3.60.02124296440.033666647631.324964654133.016220069730.44304720630.600277777839.07408524

    3.70.02081076440.033149411731.345775418533.070180245830.15261543380.616944444439.37992096

    3.80.02039542540.03264625531.366170843933.123221926229.86514087970.633611111139.17922211

    3.90.01999600120.03215670431.386166845133.175374631529.58058792760.650277777839.45931625

    40.01961161350.031680298831.405778458633.226666543729.29892161350.666944444438.86359787

    4.10.01924144610.031216592631.425019904733.277124582429.02010760270.683611111138.68444443

    4.20.01888473940.030765153131.443904644133.32677447528.7441121680.700277777838.50307465

    4.30.01854078590.030325561831.4624454333.375640822728.47090216960.716944444438.90739441

    4.40.0182089260.029897414331.48065435633.423747163128.2004450350.733611111138.67290497

    4.50.01788854380.029480320231.498542899833.471116027127.93270874160.750277777838.57666779

    4.60.01757906380.029073902931.516121963733.517768993827.66766179880.766944444438.43847275

    4.70.01727994780.028677799331.533401911533.563726740927.40527323240.783611111138.04647064

    4.80.01699069170.028291659831.550392603133.609009092427.14551256850.800277777838.5905838

    4.90.0167108230.027915147531.567103426133.653635062926.88834981940.816944444438.60827255

    50.01643989870.027547938431.583543324933.697622926.63375546930.833611111137.84820938

    5.10.01617750270.027189720631.599720827633.740990123326.38170046160.850277777838.21746063

    5.20.01592324390.02684019431.615644071533.783753561326.13215618560.866944444438.29030991

    5.30.01567675440.026499070331.631320825933.82592938625.88509446560.883611111138.06151581

    5.40.0154376880.026166071831.646758513933.867533145825.64048754850.900277777837.80647278

    5.50.01520571840.025840931931.661964232333.908579796125.39830809330.916944444437.6652832

    5.60.01498053790.025523394131.676944770333.949083728125.15852916120.933611111137.78491974

    5.70.01476185620.025213211831.691706626533.989058796224.92112420470.950277777837.61775208

    5.80.0145493990.024910148131.706256025634.028518343324.68606705890.966944444437.42490387

    5.90.01434290720.024613974931.720598932834.067475225524.45333193210.983611111137.64581299

    60.01414213560.024324473331.734741068434.105941834424.22289339711.000277777837.15026855

    6.10.01394685220.024041432431.748687920634.14393011923.99472638281.016944444437.49407959

    6.20.01375683710.023764649831.762444757734.181451605823.76880616621.033611111137.22751617

    6.30.01357188210.023493930431.776016639934.218517418423.54510836461.050277777837.30598831

    6.40.01339178960.02322908731.789408429534.25513829523.32360892851.066944444437.3229332

    6.50.0132163720.022969939131.802624801534.291324606123.1042841341.083611111136.82713318

    6.60.01304545130.022716313431.815670252734.327086370722.88711057611.100277777837.20526123

    6.70.01287885810.022468042731.828549110834.362433271522.67206516221.116944444437.13778305

    6.80.01271643160.022224966531.841265542434.397374669622.45912510551.133611111137.0265007

    6.90.01255801860.0219869331.853823561134.431919618222.2482679191.150277777836.73488998

    70.01240347350.021753784231.866227034534.466076875922.03947140961.166944444436.81880569

    7.10.01225265720.021525385831.878479691734.499854918921.83271367191.183611111136.64274979

    7.20.01210543750.021301596431.890585129234.533261952821.62797308311.200277777836.68922043

    7.30.01196168830.02108228331.902546817534.566305924121.42522829761.216944444436.80484009

    7.40.0118212890.020867317331.914368106534.598994530321.22445824141.233611111136.39679337

    7.50.01168412480.020656575531.926052231234.631335230621.02564210741.250277777836.46526337

    7.60.01155008580.020449938531.937602317134.663335254920.82875935051.266944444436.63645935

    7.70.01141906730.020247291331.949021384334.695001613420.63378968251.283611111136.0165863

    7.80.01129096880.020048522931.960312353134.726341105120.4407130681.300277777836.14450455

    7.90.01116569450.019853526431.971478047634.75736032620.24950971971.316944444435.99098969

    80.01104315260.019662198531.982521200334.788065677220.06016009391.333611111135.81222916

    8.10.01092325520.019474439731.993444455434.81846337219.87264488651.350277777835.76277924

    8.20.01080591810.019290153632.004250373534.848559443719.68694502891.366944444436.0450325

    8.30.01069106060.019109247432.014941434134.878359751819.50304168391.383611111135.75501633

    8.40.01057860550.018931631432.025520039634.907869988719.3209162421.400277777835.75377655

    8.50.01046847850.018757218932.03598851834.93709568619.14055031751.416944444435.84567261

    8.60.01036060840.018585926232.046349126534.966042220618.96192574471.433611111135.67029572

    8.70.01025492710.018417672232.056604053534.994714819918.78502457491.450277777835.76482391

    8.80.01015136880.018252378732.066755422335.023118567418.6098290721.466944444435.35436249

    8.90.01004987060.018089970132.076805292935.05125840818.43632170991.483611111135.633461

    90.00995037190.017930373132.086755664835.079139153118.26448516911.500277777835.3983078

    9.10.00985281450.01777351732.096608479335.106765484618.09430233291.516944444435.59550476

    9.20.00975714240.017619333332.106365621735.134141960317.92575628481.533611111135.36579514

    9.30.00966330170.017467755632.116028923535.161273017717.75883030541.550277777835.36845398

    9.40.00957124070.017318719832.125600164135.188162978217.59350786911.566944444435.08853149

    9.50.00948090930.017172163732.135081073435.214816051217.42977264141.583611111135.04891205

    9.60.00939225950.017028027232.144473332935.241236337917.2676084761.600277777835.24380875

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    17.068333333313.97943592

    17.08514.00124168

    17.101666666713.88473034

    17.118333333314.01013851

    17.13513.90000057

    17.151666666713.76090431

    17.168333333313.95840645

    17.18513.85060024

    17.201666666713.90670395

    17.218333333313.91318035

    17.23513.75562763

    17.251666666713.91935349

    17.268333333313.90805721

    17.28513.6043644

    17.301666666713.66483021

    17.318333333313.75551128

    17.33513.96398354

    17.351666666713.83556557

    17.368333333313.89285278

    17.38513.82293797

    17.401666666713.75851631

    17.418333333313.8354826

    17.43513.65127945

    17.451666666713.60938931

    17.468333333313.70881462

    17.48513.65753269

    17.501666666713.50438309

    17.518333333313.57022476

    17.53513.67312336

    17.551666666713.54185104

    17.568333333313.68088531

    17.58513.48395824

    17.601666666713.57066154

    17.618333333313.5010004

    17.63513.86976528

    17.651666666713.64164925

    17.668333333313.62392902

    17.68513.59221172

    17.701666666713.44347191

    17.718333333313.27598

    17.735277777813.64695072

    17.751944444413.50283623

    17.768611111113.47944736

    17.785277777813.62517738

    17.801944444413.49198818

    17.818611111113.75905323

    17.835277777813.47889519

    17.851944444413.65232277

    17.868611111113.64040279

    17.885277777813.6016264

    17.901944444413.5188036

    17.918611111113.50452232

    17.935277777813.49757481

    17.951944444413.47674084

    17.968611111113.3836689

    17.985277777813.50345421

    18.001944444413.38092995

    18.018611111113.40538883

    18.035277777813.32876587

    18.051944444413.42348671

    18.068611111113.23351097

    18.085277777813.33568001

    18.101944444413.58446312

    18.118611111113.29972649

    18.135277777813.23176098

    18.151944444413.32409382

    18.168611111113.22381783

    18.185277777813.3124609

    18.201944444413.39387894

    18.218611111113.37002373

    18.235277777813.5829649

    18.251944444413.2044735

    18.268611111113.21652412

    18.285277777813.31930733

    18.301944444413.4314909

    18.318611111113.2906723

    18.335277777813.18883705

    18.351944444413.30826187

    18.368611111113.26598072

    18.385277777813.2987051

    18.401944444413.29770279

    18.418611111113.34982681

    18.435277777813.16357422

    18.451944444413.26079845

    18.468611111112.96113014

    18.485277777813.20944881

    18.501944444413.0261097

    18.518611111113.09730625

    18.535277777813.07851315

    18.551944444413.23396301

    18.568611111112.92534351

    18.585277777812.99745464

    18.601944444413.04012966

    18.618611111112.94508648

    18.635277777812.95637512

    18.651944444412.94663525

    18.668611111113.09061909

    18.685277777813.09812069

    18.701944444412.98729706

    18.718611111113.13414192

    18.735277777813.0708313

    18.751944444412.90974522

    18.768611111113.15935898

    18.785277777813.12060165

    18.801944444412.96215343

    18.818611111112.90971184

    18.835277777812.88626003

    18.851944444412.82519627

    18.868611111112.91126919

    18.885277777812.91588402

    18.901944444413.08214474

    18.918611111113.02514839

    18.935277777812.93502808

    18.951944444413.00338078

    18.968611111112.82611942

    18.985277777812.74302864

    19.001944444412.84940243

    19.018611111112.58844852

    19.035277777813.03172207

    19.051944444412.82693768

    19.068611111112.9210062

    19.085277777812.88530827

    19.101944444412.66778946

    19.118611111112.84358883

    19.135277777812.97083092

    19.151944444412.87074375

    19.168611111112.6012888

    19.185277777812.73940086

    19.201944444412.88330841

    19.218611111112.68031693

    19.235277777812.67644882

    19.251944444412.83911705

    19.268611111112.53409767

    19.285277777812.87083435

    19.301944444412.62736988

    19.318611111112.86158848

    19.335277777812.58549404

    19.351944444412.70528793

    19.368611111112.55032253

    19.385277777811.77162457

    Lifetime Growth

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    Lifetime

    Lifetime 2

    Comparison Real and Sim

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    Simulated

    Real 1

    RealLumData

    TimeHoursReal 1Real 2Sim 1Sim 2Sim 3Sim 4Sim 5

    296182043.25473785041.45302963041.746494043.513059049.852456038.305358040.725974

    2962420.016666666743.701980590.016666666741.735969540.10000841.0093270.09998442.8846820.10000849.283770.09998437.8711240.10000840.102402

    2963020.033333333343.499618530.033333333341.094245910.20001640.2950780.19999242.2719960.20001648.7270730.19999237.4467570.20001639.495356

    2963620.0543.293674470.0540.943611150.339.6026870.341.6744230.348.1819680.337.0318750.338.904189

    2964220.066666666743.362564090.066666666740.980278020.40000838.9311610.39998441.0914150.40000847.6480750.39998436.6261220.40000838.328285

    2964820.083333333343.08206940.083333333340.459411620.50001638.2795650.49999240.5224480.50001647.1250330.49999236.229160.50001637.767062

    2965420.143.22311020.140.889850620.637.6470240.639.9670270.646.6124970.635.8406680.637.219966

    2966020.116666666742.577365880.116666666741.049716950.70000837.032710.69998439.4246770.70000846.1101350.69998435.4603440.70000836.686475

    2966620.133333333342.726799010.133333333340.711528780.80001636.4358470.79999238.8949470.80001645.6176320.79999235.0879010.80001636.166087

    2967230.150277777842.249309540.1540.503723140.935.8557020.938.3774060.945.1346870.934.7230660.935.65833

    2967820.166666666741.980228420.166666666740.836257931.00000835.2915820.99998437.8716421.00000844.6610110.99998434.3655811.00000835.162752

    2968420.183333333341.766063690.183333333340.531059271.10001634.7428341.09999237.3772631.10001644.1963281.09999234.0152011.10001634.678924

    2969030.200277777841.890926360.240.213726041.234.208841.236.8938941.243.7403711.233.6716911.234.206436

    2969620.216666666741.858150480.216666666740.188186651.30000833.6890161.29998436.4211741.30000843.2928871.29998433.334831.30000833.744899

    2970230.233611111141.610229490.233333333340.374546051.40001633.1828071.39999235.9587621.40001642.8536321.39999233.0044051.40001633.293939

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