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Crystal Channeling. Fermilab. Crystal Collimation at the Tevatron. Nikolai Mokhov and Dean Still Fermilab. Accelerator Division Seminar FNAL January 12, 2006. OUTLINE. Introduction Crystal Extraction and Collimation: a Little History Towards Crystal Collimation at the Tevatron - PowerPoint PPT Presentation

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  • Crystal Collimation at the TevatronAccelerator Division Seminar FNALJanuary 12, 2006FermilabCrystal ChannelingNikolai Mokhov and Dean Still Fermilab

  • OUTLINEIntroductionCrystal Extraction and Collimation: a Little HistoryTowards Crystal Collimation at the TevatronCrystal Collaboration: Optimal Crystals and Expts

    Implementation and Commissioning at the Tevatron980-GeV Beam Crystal Channeling and CollimationEncouraging Results, Problems and Future PlansSummary

  • INRODUCTIONBent-crystal technique is well established for extraction and handling of high energy hadron and heavy-ion beams from accelerators. Such an extraction was successfully demonstrated for up to 900 GeV beams at JINR, IHEP, CERN and Fermilab, and measurements confirmed its high efficiency predicted in simulations.

    It was shown (SSC, 1991) that it is promising to apply this technique to a beam halo collimation at high energy colliders. A bent crystal, serving as a primary element, should coherently bend halo particles onto a secondary collimator. First successful measurements were performed at IHEP in 1998 for 1 to 70 GeV protons. Based on realistic modeling (1999, 2003), it was proposed to implement a bent crystal into the Tevatron collimation system. It was done, and first results are presented here.

  • CRYSTAL CHANNELINGChanneling/DechannelingCritical angle c = (2U/pv)1/2Bending: Ueff = U(x) pvkx, k=1/RDechanneling due to MCS & bending --> LD = 0.9m x p (TeV/c) --> LB = LD (1-F/3)2, F=3k/kc, kc~Z2/pv (well disappears)Channeling probability

    It was shown at CERN and IHEP that crystals are heat- and radiation-resistant. Deflection efficiency deteriorates at about 6%/1020 p/cm2 rateExtremely high interplanar electricfields from screened nuclei (a fewGV/cm) allow to bend and focus (cylindrically-shaped crystal exit)high-energy beams with very shortcrystals. Interplanar spacing ~ 2.

  • CHANNELING: EARLY DAYS (E. Tsyganov et al, 1976-1984)What will happen with the trajectory of the channeled particles if we bend the crystal? Up to some critical value of the bending radius a particle trajectory will repeat the shape of a bent crystal. This unexpected phenomenon caused by the fact that the particle in this case gradually goes to high electric field of the atoms. It then starts to be bent in the direction of the crystal bending. A stable trajectory in this case goes away from the potential minimum, in the region where electrical fields are strong enough to create the necessary transverse acceleration.First successful JINRexperiments in 1979.7.5-GeV proton bentcrystal extraction wasdemonstrated at JINRin 1984

  • Crystal Extraction at SPS: RD22 (W. Scandale et al)Multiple scattering and dechanneling determine the energy dependence of the extraction efficiency.For a given beam energy and crystal bending angle there is an optimal crystal length.

    Channelling efficiency consistently of the order of 10 % (more than an order on magnitude larger than in previous experiments)Experimental evidence of multiturn effect in extraction modeRobust method to evaluate the extraction efficiencyExperimental validation of simulation code at high energyExtraction of Lead ionsG. Arduini et al., CERN SL 97-031 and SL 97-0551991-1997

  • Crystal Extraction at Tevatron: E853 (R. Carrigan, T. Murphy et al)Bad:Interaction counters very sensitive to beam motionBeams in the 108 - 109 regime need special instrumentationBeam halo behavior is often non-linearLattice location important (RHIC difficult, Tevatron better but imperfect)Good:First parasitic TeV MHz beam extraction from colliderMeasured channeling and extraction efficiencies 33% and 23%, respectively Crystal extraction works well, robust (900 GeV)Extraction in diffusion modes means crystal collimation can workMultiple pass works900-GeV crystal extraction 6/6/95

  • Two-Stage Collimation with Target and CrystalCourtesy R. Assmann

  • FIRST PROPOSAL FOR CRYSTAL COLLIMATION (SSC, 1991)Fraction of outscattered protons (%) per one 20 TeV proton:Calculated beam loss in SSC lattice was drastically down with W target and especially with bent crystal (Maslov, Mokhov, Yazynin).

  • 1 to 70 GeV Crystal Collimation at IHEP: V. Biryukov et al (1998)Also crystal extraction, focusing, characterization, radiation damage and heating

  • Crystal Collimation at RHIC (2003) Measured bent crystal channeling for gold ions was 26% Crystal channeling worked as expected once lattice functions and halo distribution were understood Collimation was unsuccessful because lattice was not optimal in area of collimator and IP (high angular spread at crystal, phase advances): crystal caused background

  • TEVATRON COLLIMATION SYSTEM EVOLUTIONDesign report, commissioning, initial operation: a few single 0.9 to 1.8-m long SS collimators in front of SC magnets (Edwards, Pruss, Van Ginneken, 1979-1984).A set of two-unit collimators at optimal locations based on STRUCT/MARS modeling: 5-fold increase of 800-GeV proton beam intensity at fast resonant extraction (Drozhdin, Harrison, Mokhov, 1985).First two-stage system, two 2.5-mm thick L-shape tungsten targets with 0.3-mm offset relative to A0 scrapers: 5-fold reduction of beam loss rates upstream D0 and CDF detectors (Drozhdin, Mokhov et al., 1995).Genuine two-stage system proposed for Run-II with primary and secondary collimators at appropriate locations optimized in STRUCT/MARS runs (Church, Drozhdin, Mokhov, 1999).Current system with a tertiary collimator (Drozhdin, Mokhov,Still).Crystal collimation (Carrigan, Drozhdin, Mokhov, Still).

  • BENT CRYSTAL FOR TEVATRON COLLIMATION

    Biryukov, Drozhdin, Mokhov (PAC99) have shown and later calculations (2003) confirmed - that implementation of a silicon bent crystal instead of amorphous primary collimators (targets), can improve the Tevatron collimation system efficiency by a factor of:

    2 with one (horizontal) target replaced, and with contribution from beam-gas scattering unsuppressed3 with one (horizontal) target replaced, and with contribution from beam-gas scattering suppressedup to a factor of 10 for the horizontal scraping itself.

  • TEV BEAM LOSS REDUCTION WITH CRYSTAL (1999)10-fold hit rate reduction at D and B (horizontal component).4-fold reduction of radiation loads to downstream SC magnets.

  • TEVATRON: CRYSTAL ALIGNEMENT (1999)The crystal critical angle is 5 rad, therefore the efficiency depends strongly on the crystal alignment. With the alignment of -(104 - 111) rad the large amplitudeprotons are captured by the crystal over the next 32 turns after the first scattering.For poorer alignment it takes longer time for the scattered protons to get into the critical region, which increases background in the detectors.

  • PROPOSAL FOR CRYSTAL COLLIMATION (2003)Current collimation system in Tevatron is somewhat different comparedto the one planned before Run-II. Based on detailed modeling, Carrigan,Drozhdin, Mokhov and Still, proposed to implement a bent crystal in theE straight section. It was done in 2005, Dean Still will describe the implementation and show first results.

  • Crystal Channeling Workshop at CERN, Dec. 05A theoretical interpretation of the Tevatron results was given at the Crystal Channeling workshop at CERN on December 8-9, 2005. Yuri Ivanov (PNPI) has shown that the pure channeling, calculated from the crystal properties, is consistent with 2 to 3 passages of the proton beam through the crystal with a channeling efficiency of about 92%. Confirmed by IHEP modeling.The observed plateau is explained byreflections from atomic planes and corresponds to 6 to 9 beam passages. The volume capture is estimated to be negligible in the considered case.

    The consensus was reached that the TeV crystal needs to be replaced with the optimal one with a bending angle of about 0.15 mrad, that the beam diagnostics must be implemented to see the deflected beam (phosphorous screen, BPM, flying wires, secondary emission monitor etc), and that the characterization and knowledge of the additional crystal parameters (miscut angle, surface perfection) are vital for success of the studies.

  • Two identical characterized crystals for SPS and TeV It was proposed that PNPI will expressly fabricate a pair of identical crystals optimized for the Tevatron (about 1-mm thick, 0.12-mrad bending angle, minimal miscut angle), and ship them to INFN (Ferrara) for chemical etching and characterization. Then by mid-spring 2006, one crystal goes to Fermilab for installation in the Tevatron in the spring shutdown, and another one goes to CERN for beam characterization in the extracted beamline in June-July to use these data for optimal crystal use in the Tevatron starting about mid-summer. The crystal preparation, etching, characterization and beam tests will be done for INFN and INTAS money.

  • SPS H8 Beam Line105 protons/s 400 GeV/c 3rad 5mmx5mmBeam line parameters taken from C.Biino et al., PL B403(1997)163CrystalVacuum pipeScintillator S1 0.5 mm (1 rad)Silicon with X- and Y-strips X-position resolution 30 m 0.3 mm (1.5 rad)20 m2x30m/20m 2 rad20 mScintillators S2, S3critical 10 radbending 100 radAMS type detector

  • CRYSTAL COLLABORATION: EXPERIMENTSBeam-crystal experiments at CERN:Characterize TeV crystal to guarantee success at Tevatron: extracted beam at H8 or P0, summer 2006, approved, supported by INFN (400 keuro) and INTAS/CERN (130 keuro)Crystal collimation efficiency in SPS (ala Tevatron): 2007, based on success at Tevatron and extracted beamlinesResponsibility split between CERN, INFN, Fermilab, PNPI, JINR and IHEP in 7 areas: Tank (crystal, goniometer, integration), pipe, scintillators, silicon, calculations, analysis, and DAQ.Fermilab contribution to these experiments: calculations (crystal, track reconstruction and beam loss, Drozhdin & Mokhov), detectors (scintillating fibers, Alan Bross), data taking (Dean Still).In the spring shutdown: replace Tevatron crystal with an optimal characterized one, and perform measurements to come to a reliable conclusion about crystal collimation efficiency.We have a proposal from KEK to collaborate (Tevatron, J-PARC, ILC).

  • INTAS-2006 Project: Crystal Channeling Just ApprovedExperimental study of crystal channeling at CERN SPS for use at the LHC in diffractive physics and halo cleaning

    First station: deflection at large angles (some mrad)Extraction of ~450-GeV proton beam from SPS with a bent crystal:ala RD22 at CERN and 900-GeV E853 at Tevatron

  • Second station: deflection at small angles (0.2 mrad)

  • OTHER CRYSTAL CHANNELING APPLICATIONSSince early 80s, many successful applications at FNAL, CERN & IHEPCrystal-based beam linesBeam splitting (recent success at KEK with 12 GeV protons)Beam focusingBeam diagnostics

    Very recent proposals for LHC, ILC & J-PARCCalibration of CMS calorimeters with LHC beamTOTEM: larger acceptance for diffractive Higgs, reaching Coulomb regionBeam splitting at J-PARCCollimation at ILC with tests at ATF

  • MOTIVATION FOR CRYSTAL COLLIMATIONProton Halo LossLimitOver 2004 shutdown improved TevatronVacuum and alignment. Also installedCrystal collimator.

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    1973.444778.476

    1423.444111.254

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    348.444402.328

    CDF Proton Halo Loss

    D0 Proton Halo Loss

    Store #

    Loss rates (Hz)

    Proton Halo Rates at IP's

    pbar eff

    pbar eff

    23.5250178699166.2024975294

    33.6891260841193.2389863181

    26.54213360581.0134040359

    31.091866306210.8523092295

    31.57828914460.0000310494

    32.862221395195.5898158513

    26.963820657198.4420046007

    30.3297535766111.4990378365

    29.939782500881.9643047227

    27.985352984208.2914430369

    31.8270624567282.1921877321

    30.8585395661210.6426326876

    25.1031465924128.0266241043

    28.2643980523121.8390804598

    27.8774496274164.7785787848

    28.4667418264140.6518010292

    25.9851764008194.8395633477

    25.7345494146183.0785638109

    10.73901250562.8036064865

    2.57258677684.863147664

    10.197919269926.8160790948

    11.00169593979.0007035414

    11.00169593974.1451315362

    10.796296770456.1713069631

    10.197919269939.5803832855

    5.538007074752.9002884653

    6.9920101925145.8661089386

    2.801461798764.4947993458

    11.4046457744263.3687484201

    8.162191372585.9011785086

    8.2118661672153.6536917425

    8.5051855537135.4205034003

    10.275580701189.4294077396

    11.153260505479.2982386384

    9.996447847888.4119383718

    11.24622045695.3715852187

    11.7352750179123.8885968918

    10.3280154862.8653756304

    11.50186169374.829577414

    11.803714728323.709628772

    1.11518850547.8638604129

    1.6606345884141.9180319161

    1.4550567288149.5034675996

    2.0077736169219.6179433708

    1.2082675421171.6656405571

    1.4005594898137.0030272563

    1.7446384074106.2349293464

    1.7893294966175.2244025252

    8.21493689182.7901477852

    8.328097804124.3953934533

    6.804801579350.549653687

    6.6600376686117.9494318518

    5.843525296297.0028457684

    4.9917636109105.9701388622

    9.247916912256.6625818813

    8.112656796177.4290198564

    1.5745632254175.1098237861

    2.76931283818.8422271149

    0.795029950398.5615505084

    1.420365654527.5267982251

    2.350803830590.3479744824

    0.997044269955.5619657143

    10.046065693572.2480812093

    7.42419530272.0648750285

    10.5432174395111.6271524847

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    75.0423823713246.2652331541

    59.5841590921232.3419038264

    00

    00

    130.8314305736328.1711717599

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    103.1553081461150.9109831701

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    103.9469796741195.0157902012

    82.7062262248169.7957332578

    193.3102678827200.4739955048

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    819.76376804551

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    1.17340867390

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    272.0643431635234.3527738265

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    00

    3619

    59.37

    Store #

    Halo Loss Reduction

    Halo Removal Efficiency (Anitprotons)

    proton eff

    proton eff

    9.55227268430.9086214899

    10.44100316330.8199402318

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    00

    00

    17.20624436291.1005815969

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    8.78784857520.9059238261

    8.21852331141.0668616145

    8.11988872210.9924993409

    8.33666917490.7804201791

    3.91483313941.2954786165

    8.47592187370.9142743671

    8.90349398690.8107844929

    10.02484748270.7255881198

    9.53059246240.4396230896

    10.12486152460.4644457784

    10.33099830611.0220655924

    9.33337950090.5664258483

    8.9427218190.8940496914

    8.92306478950.3414516429

    17.50228371770.4962432015

    6.15124472370.7206764615

    8.2687447040.5790402115

    7.35488518990.6895848006

    9.24832522890.3398196711

    7.68923766750.3621648194

    7.49059980340.5407560969

    7.99200074970.5672273424

    8.03948384910.3900433946

    6.42379513420.5920163662

    10.33099830610.457105675

    10.46415114181.3288458656

    7.64579054110.4476908001

    3.86427862220.8535592148

    3.87373988680.8535540637

    2.08325612991.1726385644

    0.99709316653.359280817

    8.31265916370.7316817042

    8.76255628680.8636025109

    5.7582655211.45754822

    9.85009247541.0228249682

    10.94182525950.7371774304

    8.38151246580.8595696978

    7.46899911431.2259706076

    6.14277909310.9965022803

    7.30719237441.2043937421

    7.60941494960.2181545708

    3.45381937330.5564038497

    10.3418582218

    10.76952174582.1922678195

    4.3888773472.4289750462

    11.8028319090.7571107354

    12.04803999320.9710008618

    7.70382997910.8439514443

    1.46368449810.8551155101

    12.80831835672.8137222885

    11.0329514570.6232010501

    10.82696875432.5329879673

    12.41655190472.2369357382

    11.06301910730.6156344267

    10.60078111940.8182098579

    7.63141706850.3732704342

    20.20247917761.3384188683

    12.01238832262.71857743

    7.99200074970.9275864938

    5.2519604172.744995385

    14.1424708025

    12.37868936040.3628532945

    14.87313466520.3194293215

    12.49297612830.2850010353

    14.09832435920.6621138255

    11.6671428441.5430768391

    11.12364875530.308979061

    18.29089654033.6086023549

    14.55321075393.5403552158

    12.4546467792.3382163626

    13.95294963592.2490025148

    11.4049138951.0805494182

    15.03842991860.9467210467

    13.35615494760.7293591126

    12.80831835670.652028508

    13.7637170711.0166864007

    41.160822773945.0075233939

    30.083814148269.7382736778

    23.779849614875.5398126605

    1.127171435638.850832673

    10.606180384

    22.686331324421.7326432256

    73.891791414313.2580438926

    17.352651647321.7497761438

    18.712466995139.5401483352

    17.887902577625.5081322479

    14.001073610319.3194384086

    10.855922699414.7307404579

    4.22006342243.0118270859

    15.322240708826.3613596679

    5.791439466222.4642384013

    18.886586990818.4609336641

    14.196935555214.039369209

    18.712466995129.4213160543

    29.644434253325.9294907672

    20.303523099242.1981387294

    15.79931345224.6730372632

    29.347447795864.4775233249

    19.099660249257.0482103725

    150.35661218420.0020222447

    23.40735600280.0002585315

    20.2460984394113.9352398051

    26.1270333075102.6091103203

    26.2004683176102.6024961775

    24.9140632979143.6956546832

    22.3122525525123.2331569547

    36.9249254122109.6099023795

    70.0656858413124.955920161

    38.319139569110.5659466011

    33.2911069268112.633008328

    27.816256263111.4720043091

    28.0081751043124.7456187036

    43.2141941033118.3970522405

    36.5920813142108.1253262618

    29.6444342533120.7458750427

    37.6091156372121.1939172595

    38.319139569139.675381097

    41.8768122999120.1265768416

    32.7538832445135.3063295134

    21.71546911910.0298678257

    27.440202355694.9995789879

    30.5364146788113.6104500863

    29.8625080919142.146719283

    30.308424818795.1618399881

    32.4917213073147.9736017713

    31.729825164888.5150631942

    28.008175104331.3873265856

    31.729825164828.3604555189

    31.483738490691.359868503

    31.979789124779.6498416269

    37.9608077982126.7869503618

    28.4000688412110.0085268076

    31.2414395833116.2515564263

    33.56638200287.7864083137

    34.420216114346.4799594934

    39.822770793116.2378759716

    49.54303860519.7082304359

    34.71456298064.437937569

    65.540764898949.6685044434

    73.891791414358.2229441819

    63.490617101760.813268022

    50.155152611435.602152332

    94.5427243255106.3345130446

    57.22547252867.4614942455

    44.639815433959.8682013232

    79.694325606271.9657323057

    145.303736899480.3903790743

    88.368519034536.1152716006

    73.891791414317.1623901353

    46.693693867841.4939433746

    57.22547252844.5455936397

    51.425907045617.1366287076

    71.296255549931.7134857151

    50.155152611476.7353301245

    68.270164644139.6707112061

    65.540764898949.9682436335

    37.960807798280.2044640353

    52.762728236947.4281369714

    58.043708677480.6810189145

    46.162707192415.7502126387

    140.282458807986.3351161869

    81.290203774338.6360327958

    169.584155470957.1963256989

    64.49940385423.884287204

    62.512899768480.7588718105

    54.903563004579.7858436463

    57.22547252891.2860428888

    54.170905927189.8147197134

    79.694325606256.0226541353

    99.161594231242.1567493139

    64.98462668856.7110258771

    53.768017370112.5652775345

    45.262488274842.4746205996

    38.560506715323.1204247931

    57.2254725286.6280026062

    51.425907045643.786833154

    50.782581413593.6503797707

    60.6451034994123.5604316414

    60.6451034994147.7843182313

    52.7627282369122.4209797757

    78.159901112140.4863770547

    109.899876548654.7115775309

    65.040436844833.0366971735

    62.512899768466.6905213134

    88.368519034530.3784093974

    70.065685841361.9565644614

    121.363963373237.7289458323

    86.485838219350.1382193154

    73.891791414368.2838341732

    99.161594231221.0086681593

    69.521549574834.6820517931

    84.68170454924.1855781555

    99.1615942312174.5969677822

    101.6445074316105.0240127549

    119.614754137129.799307246

    176.9774379185119.2444917011

    116.191085821661.9601801889

    112.957951560540.9940531659

    81.290203774359.2980039783

    65.716108818631.5822889784

    162.783815603744.2753147001

    340.054758075347.0746073952

    213.038534087855.5083849101

    137.551041248718.8059883819

    122.860864211728.2789658636

    80.86545571833.8283037162

    63.173537701778.5463194803

    119.066694347449.6197565427

    128.8599165998102.463573563

    104.4978054241100.7007384039

    156.507837271168.4576876087

    169.584155470987.0551286568

    169.584155470987.0551286568

    145.3037368994167.3370483294

    117.619848344166.1406779258

    77.7804284128128.4421785832

    97.71892613106.0862174564

    130.1983485631110.7421921032

    54.5494993387162.5993010048

    120.9994548173191.4438980065

    91.7018143398136.1663937544

    11.0107885731

    93.5143650727138.0578120412

    105.964809040260.4966661237

    49.4389117558166.0523137595

    133.489426373163.9448759307

    137.7914346208206.4339410183

    131.2137231072178.8609008634

    95.0511075949188.7260736511

    149.3242783321206.3690375395

    67.8714918678129.3846353716

    155.3064400931139.3386572952

    159.0180202231116.5493782994

    175.3643659319103.5976219141

    151.6114706064152.3343975279

    109.8998765486213.1342407829

    176.9774379185158.435836976

    176.9774379185234.0867672404

    185.04474874191

    585.135735701177.4657067438

    284.4717012873205.4656376726

    235.810148886190.5409909578

    185.0447487419237.503378224

    340.0547580753174.566276634

    239.6701823163208.0138728269

    408.4927628401266.4134149646

    271.7596990146227.0836029452

    86.109234687221.7422915688

    226.3088529123193.8909765318

    156.507837271168.7751243766

    150.6978231171159.4312160342

    214.358613551993.6749868744

    214.358613551978.1382093439

    193.8826646798210.5450599354

    340.5169031597192.9537962459

    868.6605241772183.0221187239

    144.4500649549102.8846290579

    236.2096401935131.606404987

    374.3798985671206.9077209502

    259.5634398648216.722433913

    254.7082170465270.8937943133

    511.4187764564203.5536096896

    139.1802721088164.6058387902

    441.4260954797199.0458555383

    371.1451945582272.702789498

    479.5451622657181.5311045898

    371.1451945582260.0872975638

    408.4927628401162.3225776777

    511.418776456434.9852247789

    418.9533745077231.6483311071

    300.279176771852.4232577265

    304.946635002472.3558059025

    271.7596990146230.4362053145

    292.8830529549103.118510405

    239.6701823163230.5653965144

    346.3047093866101.0882185936

    49.052551537732.5917812964

    313.7705354934160.9661319043

    226.3088529123251.9509688675

    193.8826646798138.0945754839

    44.6398154339215.6063682429

    193.8826646798212.5279844254

    291.2580128573304.2627673358

    00

    CDF Protons

    D0 Protons

    Store #

    Halo Loss Reduction Factor

    Halo Removal Efficiency (Protons)

    store vs ratio

    9.552272684323.52501786990.9086214899166.2024975294

    10.441003163333.68912608410.8199402318193.2389863181

    9.927851062626.5421336051.007838128481.0134040359

    9.31009607131.09186630621.044412898510.8523092295

    8.74580028431.57828914460.00000243290.0000310494

    8.113467729832.86222139511.102363231895.5898158513

    7.785137601926.96382065711.027557287898.4420046007

    8.16264646930.32975357661.0463206731111.4990378365

    8.506409284629.93978250081.149578230281.9643047227

    8.343417189627.9853529840.9981469338208.2914430369

    11.010094403431.82706245670.7757677825282.1921877321

    10.661881135930.85853956610.8542651374210.6426326876

    9.736441282525.10314659240.9702421013128.0266241043

    7.333483493128.26439805230.7777938517121.8390804598

    8.296545667427.87744962740.9221912527164.7785787848

    9.019467762128.46674182640.9709343576140.6518010292

    10.203669279925.98517640080.909777313194.8395633477

    9.289064655625.73454941460.8213038989183.0785638109

    31.245306821310.7390125051.294497735662.8036064865

    79.70426671732.5725867761.468477871784.863147664

    33.295229228910.19791926991.227314690726.8160790948

    25.385062868511.00169593970.41255376529.0007035414

    18.359751811911.00169593970.1367238374.1451315362

    35.284265059410.79629677041.322524417656.1713069631

    26.546381031910.19791926992.553472802339.5803832855

    23.47632647915.53800707471.473831085952.9002884653

    33.85043879516.99201019251.9862628928145.8661089386

    25.07101306732.80146179871.318102511864.4947993458

    23.476326479111.40464577441.1776043754263.3687484201

    19.90775253138.16219137252.004476176185.9011785086

    40.22228483528.21186616721.38886033153.6536917425

    27.8196976358.50518555371.18875647135.4205034003

    31.245306821310.27558070111.570542023989.4294077396

    35.948528708611.15326050541.458847716979.2982386384

    32.23771343129.99644784781.491289186688.4119383718

    37.965511824111.2462204561.32747545995.3715852187

    30.087537402511.73527501791.2211689958123.8885968918

    32.757938677510.328015481.556282972962.8653756304

    3.437893716811.50186169371.48130714284.829577414

    15.740004323511.80371472831.39449563723.709628772

    38.32388826921.1151885051.050546363347.8638604129

    36.26967686971.66063458841.1076385447141.9180319161

    26.81296251281.45505672881.0682582151149.5034675996

    17.78944150742.00777361691.2027235839219.6179433708

    14.40564340351.20826754211.1085663925171.6656405571

    11.26189096541.40055948980.9924454865137.0030272563

    10.98114048931.74463840741.1426236951106.2349293464

    10.64184092931.78932949661.0304362004175.2244025252

    36.59661474318.214936891.9534635981182.7901477852

    35.63301781548.3280978041.4314929637124.3953934533

    36.92950031986.80480157931.464337259750.549653687

    39.82770701116.66003766861.6324357231117.9494318518

    41.45436478285.84352529621.33924878997.0028457684

    35.01832435264.99176361091.4424036435105.9701388622

    41.88200482129.24791691221.371238516456.6625818813

    38.68909499678.11265679611.416622632677.4290198564

    54.17763598261.57456322541.724036799175.1098237861

    36.59661474312.76931283814.16004714358.8422271149

    6.76594821920.79502995036.354881317998.5615505084

    13.54204118591.42036565455.910294398427.5267982251

    33.57053857232.35080383051.217894287390.3479744824

    25.86977084890.99704426991.274897739755.5619657143

    40.222284835210.04606569351.265201360872.2480812093

    35.94852870867.4241953021.06031154372.0648750285

    41.035369392710.54321743951.0674710693111.6271524847

    40.22228483529.45917722581.211396597856.1471303884

    37.96551182418.87827106171.577997421637.9826196553

    34.71886251748.80105823052.349636784437.6506377321

    31.24530682130.99704426992.46945793432.6913874709

    36.92950031989.09776472031.330677277465.3612598918

    37.26849739196.56814281761.179944721294.3067089242

    40.22228483529.92293331142.132812809246.49926359

    39.44079554281.93594372331.069337898595.8041415497

    40.22228483529.34993310811.333153409547.018341201

    38.32388826924.65825974431.188510852571.2612145836

    43.737869911411.73527501791.0250501787164.1704247548

    73.901000263616.39255261251.541930065986.5733458619

    44.645352985214.61678587522.95233325860.0902606791

    52.09221027310.71059772832.115513634267.5038836375

    58.893004564113.18814508232.539533078554.9276376464

    49.549189187111.12261442622.306758430775.0090066904

    46.168435043410.30173136912.545847523960.0407211606

    39.44079554289.97182227022.811296636168.6619054439

    24.615003790525.30948069756.850090260328.2942922333

    66.02310442536.12957267241.02125572126.9922777166

    61.572495902213.58830654221.263707755413.5366269841

    50.788887120813.14531775271.409125249910.8162253055

    47.24290019079.68525924111.28964433825.5497044032

    61.572495902214.10737944421.54648258924.3634846003

    14.877661057810.60210221471.87808175967.0255557843

    11.70414466253.12955404751.70371865089.1059541152

    26.20370895318.50518555370.8796695698158.3805771307

    39.827707011111.09213629950.9232496604234.3684929724

    36.26967686978.70641049471.4919657431158.1459680196

    58.050924310710.40767876390.149063106124.1622401075

    45.649324154811.37260463630.6294390163321.9069651148

    58.050924310713.27464241860.7139375922247.9782252013

    57.232585520313.01848859710.6935604541285.6308718466

    54.910384876311.87295739750.6022204283278.5424237336

    51.432293287113.18814508230.6023474562258.786681207

    15.324132572814.05838487232.488590921116.081898262

    15.679212597975.04864146520.8649882556223.7379521115

    75.271122587815.63286907730.8649882556223.7379521115

    15.98793435875.2918539020.995560448663.7009402044

    5.307541562315.94067833990.995560448663.7009402044

    13.313994994448.80707308341.543091302784.9494335097

    48.951761277613.27464241861.543091302784.9494335097

    13.357800022144.51339337161.2582475387200.357469067

    17.811618969481.06004463180.6784989726331.6630100417

    13.227241237353.30616011690.5971388726225.5175371261

    16.302835398156.06494375721.6273555855261.0677941203

    13.357800022172.36533904261.1079411787240.0703869899

    15.6744543331101.67410764731.3753539062208.6157973414

    14.66011722579.46868241721.5154010445217.3162932376

    11.342585076364.31676367291.1196202805190.909922384

    12.049523947573.68256885280.133890599146.198841048

    13.01522381461.39050422280.887007779265.6983371861

    11.374362577759.58324060111.0213516089240.8680903647

    7.869047884972.36533904260.911747677233.1315135624

    13.811197995109.58877585720.7105728918343.5735790687

    14.503009527876.46632482971.0509306658266.3894013669

    14.929666511796.52305620360.6885081629334.0161643278

    12.121474806162.3358822450.9628920147305.795997618

    12.809895954361.39050422280.6528964514324.7800338036

    14.820666020379.46868241721.0012218879291.574085684

    13.23145980921.15034719571.0771192483218.3416572697

    14.40889775062.29747074580.9823075906269.9383964234

    12.732061318211.585067767542.9511768224

    10.32817679721.2765940271.590064485542.7275887272

    17.30376555241.55815908061.474964738918.4250679823

    11.15884257821.59123402381.297678870429.3278657244

    11.51917203671.62118591381.9977330111188.6658457635

    11.35461578792.21209733520.1339258894218.7393465272

    9.60702103872.39252327961.4505723928193.52290041

    1.44111426961.30921143181.436122341397.2393945399

    6.65775601552.16131070590.8911719026202.4059349168

    4.74320721382.68802652581.2177550957165.8793869051

    5.54940590283.26758092341.0443368431124.1253495422

    59.58415909214.07766266291.871141237446.8442308883

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