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{"sheet":"Main","index":0,"n_rows":105,"n_cols":15,"rows_kept":105}
["Neutron and precursor levels as a function of time.",{"$nulls":13},"by Wm. J. Garland 2017-02-14"]
[null,"Calcs are preformed by VBA function 'Run' using semi-implicit numerical integration.",{"$nulls":12},"See any standard reactor physics text for the basic point kinetics equations"]
[null,"All input values are contained in the function 'Run'.",{"$nulls":12},"or visit http://www.nuceng.ca/ep4d3/ep4d3home.htm and go to the chapter on Kinetics."]
["t (s)","n","k","C1","C2","C3","C4","C5","C6",null,"To view the VBA code, ",{"$nulls":3},"or click on the link here ->"]
[0,1,0.95,395.11023622047236,887.2760252365929,214.9385281385281,172.922619047619,12.095606125661941,0.8866306846060479,null,"turn on the Developer Tab"]
[0.10000000000000007,0.11258671758287972,0.95,394.67014969743855,884.8115672250163,212.77241428838636,168.27863971157478,10.71125203287725,0.6367762510806285]
[0.20000000000000015,0.10893045753954571,0.95,394.22475312291937,882.322065979008,210.60238686766633,163.7154362676924,9.489691793509381,0.4640829064091417]
[0.3000000000000002,0.1056868580928946,0.95,393.7781969507752,879.8307848291423,208.4487889930509,159.27366073275968,8.421923631446166,0.3457737827123236]
[0.4000000000000003,0.10277174361882728,0.95,393.3306671826518,877.3387627184622,206.3123400439898,154.95154360346592,7.488482261365141,0.2645194512457062]
[0.5000000000000003,0.10012289023277321,0.95,392.8823132528717,874.846831860549,204.19357237116827,150.74698647668964,6.672325510554921,0.20852516318977227]
[0.6000000000000004,0.09769361238229743,0.95,392.4332573596137,872.3556703846414,202.09287912822575,146.6576699921377,5.958547584464152,0.16976187260106232]
[0.7000000000000005,0.09544832325360728,0.95,391.9836010992526,869.8658397793383,200.01054834342304,142.6811301688035,5.334121297646642,0.14276281372518515]
[0.8000000000000006,0.09335944769998931,0.95,391.53343022981016,867.3778117887589,197.9467874362456,138.81481277259977,4.787668069502872,0.12380480072722945]
[0.9000000000000007,0.09140526380113487,0.95,391.0828181300161,864.8919879534235,195.90174106428972,135.05611233390766,4.309253831959547,0.11035124020633148]
[1.0000000000000007,0.08956838360388045,0.95,390.63182834340756,862.4087139904503,193.87550428490871,131.40240037222594,3.8902086857233042,0.1006731797401725]
[1.1009999999999895,0.0878178179414234,0.95,390.17600190170583,859.9035016060886,191.84815405116814,127.81604046180148,3.5195341814130594,0.0935307970389983]
[1.2009999999999785,0.08617649670042028,0.95,389.72441455751664,857.4262246719762,189.85985898744053,124.36540964827402,3.197920874716369,0.08825544791431872]
[1.3009999999999675,0.08461688741132602,0.95,389.27259835948666,854.9522970609428,187.89044820295808,121.01189801510026,2.9157039964317772,0.08421734369449495]
[1.4009999999999565,0.08313079589272707,0.95,388.82059244233136,852.4819256925298,185.93989601710555,117.75294371368791,2.66787093897679,0.08104181791824451]
[1.5009999999999455,0.08171123615049875,0.95,388.3684320989369,850.0152955962465,184.0081583825211,114.58602328604604,2.450050493038881,0.07847216783059045]
[1.6009999999999345,0.08035220146564682,0.95,387.9161493304972,847.5525730341565,182.0951757791812,111.50865624017763,2.258430963538705,0.07633214723394097]
[1.7009999999999235,0.07904848912802996,0.95,387.463773295478,845.0939080509548,180.20087558084114,108.51840842605321,2.089688642719811,0.07450042606336121]
[1.8009999999999124,0.0777955641552924,0.95,387.0113306805057,842.6394365819535,178.3251740129131,105.6128944910296,1.94092536245572,0.07289319355280566]
[1.9009999999999014,0.07658945170440486,0.95,386.5588460100669,840.1892822144225,176.4679777890988,102.78977961992115,1.8096139950753687,0.07145230393014626]
[2.0009999999998906,0.07542665089562157,0.95,386.10634190754627,837.7435576730319,174.62918549168265,100.0467807127768,1.693550905746486,0.07013719492867598]
[2.1009999999998796,0.07430406485362397,0.95,385.6538393170044,835.3023660826321,172.8086887444329,97.38166711614753,1.5908144797123314,0.06891937496379352]
[2.2009999999998686,0.07321894322010147,0.95,385.20135769288794,832.8658020490221,171.00637321559552,94.79226099672128,1.499728954997909,0.0677786595799062]
[2.3009999999998576,0.07216883440520844,0.95,384.748915163231,830.4339525892209,169.2221194801251,92.27643742654419,1.41883288644358,0.066700599534033]
[2.4009999999998466,0.07115154555825265,0.95,384.29652867073537,828.0068979360706,167.4558037641624,89.83212423449504,1.3468516510908488,0.06567472097403193]
[2.5009999999998356,0.07016510874357987,0.95,383.8442140952243,825.5847122369945,165.70729859018516,87.45730166775189,1.2826734790875063,0.06469331934150652]
[2.6009999999998246,0.06920775216956138,0.95,383.39198636030045,823.1674641629662,163.9764733377868,85.15000189867042,1.22532855943181,0.06375063107952379]
[2.7009999999998136,0.06827787558048565,0.95,382.9398595265285,820.7552174408457,162.26319473236214,82.90830840604835,1.173970827020961,0.0628422633321439,null,"Notes:"]
[2.8009999999998025,0.06737402911298537,0.95,382.48784687306323,818.3480313199888,160.56732727190337,80.73035525469912,1.1278620875193839,0.061964800007324794,null,null,"In the default input values, k = .95 (ie quite subcritical) for the first half of the calculation."]
[2.9009999999997915,0.06649489506103462,0.95,382.0359609693266,815.9459609822472,158.8887336004423,78.61432629322864,1.0863581803494369,0.06111552856557169,null,null,"Notice that the neutron level drops off quickly and the delayed precursors are, well, delayed!"]
[3.0009999999997805,0.06563927210080917,0.95,381.58421373809136,813.5490579030511,157.22727483535414,76.55845428666177,1.0488969183817636,0.060292249590798985,null,null,"For the second half of the calculation, k = 1.001 (ie supercritical but not prompt critical)."]
[3.1009999999997695,0.06480606160871404,0.95,381.1326165111191,811.1573701700927,155.58281085465006,74.56101999791004,1.0149875763362293,0.05949314324843336,null,null,"Notice the prompt jump in neutron level when k jumps."]
[3.2009999999997585,0.06399425576955897,0.95,380.6811800783277,808.7709427651897,153.95520054949364,72.62035122988213,0.984201729094192,0.058716674942475296,null,null,"If k > 1.006 (prompt critical) the neutron is supercritical without the aid of precursors and so "]
[3.3009999999997475,0.06320292722205378,0.95,380.22991473133544,806.3898178140946,152.34430204643576,70.73482183821528,0.9561652665972725,0.05796152807515209,null,null,"rises exponentially with a very short time constant (life time = 0.00005 seconds in the default example."]
[3.4009999999997365,0.06243122002892756,0.95,379.7788303020997,804.0140348083634,150.74997290323495,68.9028507230717,0.930551434232616,0.05722655562484651]
[3.5009999999997254,0.061678341791499086,0.95,379.3279361972757,801.6436308028226,149.17207028160558,67.12290080715404,0.9070747669896778,0.05651074485825105]
[3.6009999999997144,0.06094355675519987,0.95,378.877241428834,799.2786405917141,147.6104510997872,65.39347800599235,0.8854858025784799,0.055813191267746316]
[3.7009999999997034,0.06022617977466218,0.95,378.4267546414042,796.9190968661651,146.06497216744407,63.71313019562164,0.8655664734391171,0.05513307903790371]
[3.8009999999996924,0.05952557102548234,0.95,377.9764841367521,794.5650303552951,144.53549030507423,62.08044618196634,0.8471260904229185,0.05446966617482435]
[3.9009999999996814,0.05884113136536629,0.95,377.52643789574097,792.2164699529735,143.0218624498254,60.494054675562964,0.829997842128126,0.05382227300063536]
[4.000999999999671,0.05817229826059815,0.95,377.07662359808637,789.8734428319665,141.52394574936832,58.95262327466186,0.814035743638051,0.05319027310586323]
[4.100999999999704,0.05751854220506531,0.95,376.62704864016996,787.5359745469976,140.0415976452673,57.45485745924309,0.7991119769212364,0.05257308612111396]
[4.200999999999738,0.05687936356874855,0.95,376.1777201511462,785.2040891280521,138.57467594710354,55.99949959804556,0.7851145725719076,0.05197017185501737]
[4.300999999999771,0.05625428982090636,0.95,375.7286450075463,782.8778091650775,137.12303889844753,54.58532797033208,0.7719453890349265,0.05138102547398863]
[4.400999999999804,0.05564287308035819,0.95,375.2798298465535,780.5571558850918,135.68654523563728,53.21115580379188,0.7595183510948851,0.050805173488915195]
[4.500999999999838,0.05504468795147312,0.95,374.8312810781101,778.2421492225855,134.26505424020138,51.87583032970397,0.7477579143203898,0.05024217037661623]
[4.600999999999871,0.054459329609840144,0.95,374.38300489598595,775.9328078839852,132.85842578565683,50.57823185624513,0.7365977264350076,0.04969159570817806]
[4.700999999999905,0.05388641210625293,0.95,373.93500728793117,773.6291494068531,131.46652037932375,49.31727286062322,0.7259794603167325,0.049153051687756195]
[4.800999999999938,0.053325566861684465,0.95,373.48729404501387,771.3311902144147,130.08919919971666,48.09189710053875,0.7158517965788946,0.04862616102805387]
[4.900999999999971,0.052776441329439046,0.95,373.039870770235,769.0389456659268,128.72632413000753,46.901078745329755,0.7061695365186863,0.04811056510512371]
[5.000000000000004,0.09952906902769093,1.001,372.59747676540616,766.7767470635285,127.39247943738972,45.75805876086683,0.6978720087435004,0.04779090701829958]
[5.100000000000038,0.5097328579700733,1.001,372.3722810469248,765.7371266644774,127.14916669438983,46.97392280361309,1.3889722976855936,0.17450869475459413]
[5.200000000000071,0.5244895989563801,1.001,372.1730259196197,764.8443835768932,127.03454958986713,48.421000285817044,2.0675538465256067,0.27363826596008894]
[5.300000000000105,0.5376775589141085,1.001,371.9813844157488,763.9956845121031,126.9574730431929,49.90144216528567,2.680804799027779,0.3451480104047761]
[5.400000000000138,0.549630382834405,1.001,371.79661253054286,763.1867779960226,126.91389244638926,51.40648414584183,3.2349375574418273,0.397478615197642]
[5.500000000000171,0.5605906524826385,1.001,371.6181168255875,762.4142638361157,126.90054584644525,52.92920753305016,3.7358235318756745,0.4364490054275092]
[5.600000000000205,0.5707398468626181,1.001,371.4454155704802,761.6753739074899,126.91475470667102,54.46407516165394,4.188916542851197,0.4660751111467969]
[5.700000000000238,0.5802158124550463,1.001,371.27811125543076,760.9678170281379,126.95428265701226,56.00660084317463,4.599221614442445,0.48913249821535737]
[5.800000000000272,0.5891249504872325,1.001,371.11587087383526,760.2896676383095,127.01723392500725,57.55311046720699,4.971292050253096,0.5075429774598054]
[5.900000000000305,0.5975507547275939,1.001,370.95841163631235,759.6392851059405,127.10197953423373,59.10056740505498,5.30924381679055,0.5226403129162777]
[6.000000000000338,0.6055598239467433,1.001,370.8054904994192,759.0152545465673,127.2071030304001,60.64644327794423,5.616779939087419,0.5353528830924337]
[6.100000000000372,0.613206123179745,1.001,370.65689638913494,758.4163428456853,127.33136002440293,62.18862094733339,5.897220113022947,0.5463292919394488]
[6.200000000000405,0.6205340273279347,1.001,370.5124443414813,757.8414655002236,127.47364758440601,63.72532058016985,6.153532430795235,0.556024783701933]
[6.300000000000439,0.6275805152020886,1.001,370.37197101868776,757.2896612258097,127.63298071101813,65.25504239944665,6.388365256216647,0.564760724170244]
[6.400000000000472,0.6343767683084749,1.001,370.2353312222474,756.7600721947434,127.80847395975954,66.77652163634698,6.604078050303379,0.5727655708988707]
[6.500000000000505,0.6409493503594916,1.001,370.1023951368799,756.2519284045335,127.99932684920293,68.2886925200064,6.802770455135159,0.5802031178768411]
[6.600000000000539,0.6473210895546248,1.001,369.9730461174599,755.7645351167253,128.20481209115613,69.79065905689359,6.986309277414088,0.5871919890861947]
[6.700000000000572,0.6535117485031672,1.001,369.84717888517054,755.2972626112685,128.42426595580963,71.28167098939878,7.1563532288038525,0.5938191115787488]
[6.800000000000606,0.6595385410115435,1.001,369.7246980368896,754.8495377144936,128.6570802775828,72.76110376866957,7.314375416413847,0.6001490444343667]
[6.900000000000639,0.6654165372378619,1.001,369.6055167982186,754.4208367076235,128.90269574235518,74.22844168937337,7.461683659922041,0.6062304532058739]
[7.000000000000672,0.6711589864527221,1.001,369.4895559691071,754.010679327343,129.16059619172532,75.68326355473,7.5994387596551025,0.6121006164085808]
[7.100000000000706,0.6767775781395556,1.001,369.37674302413643,753.6186236439124,129.43030374715053,77.12523039698853,7.72867086458248,0.6177885737312724]
[7.200000000000739,0.6822826562521676,1.001,369.2670113388576,753.2442616549567,129.7113746047553,78.55407489090639,7.85029409883569,0.6233173354138909]
[7.3000000000007725,0.6876833973186686,1.001,369.16029952027367,752.8872154708883,130.00339538609475,79.96959217912143,7.965119605558525,0.6287054415178522]
[7.400000000000806,0.6929879601873042,1.001,369.0565508244186,752.5471339953581,130.3059799552489,81.3716318878387,8.073867161328181,0.6339680699721753]
[7.500000000000839,0.6982036131706091,1.001,368.9557126475504,752.2236900242987,130.61876663108418,82.76009115539468,8.177175505516704,0.6391178305142484]
[7.600000000000873,0.7033368428980336,1.001,368.8577360801252,751.9165777020826,130.94141573730644,84.13490852946494,8.275611518399323,0.6441653391687194]
[7.700000000000906,0.7083934481532359,1.001,368.76257551471986,751.6255102846709,131.27360744334985,85.49605861403582,8.369678370602108,0.6491196386853546]
[7.8000000000009395,0.7133786212260749,1.001,368.6701883006052,751.3502181682825,131.61503985718386,86.84354736694218,8.459822755272219,0.6539885102407692]
[7.900000000000973,0.7182970187649471,1.001,368.5805344388637,751.0904471488808,131.96542733738795,88.17740796429584,8.546441303549743,0.6587787078520656]
[8.000000000001005,0.7231528237129202,1.001,368.4935763128892,750.845956883141,132.3244989968298,89.4976971605637,8.629886273748102,0.6634961373965387]
[8.10000000000095,0.7279497996098,1.001,368.4092784498661,750.6165195258508,132.6919973743006,90.80449208317175,8.710470595227212,0.6681459955369039]
[8.200000000000895,0.732691338313126,1.001,368.32760730944597,750.4019185222264,133.06767725375693,92.09788740885271,8.788472339313493,0.6727328792927676]
[8.30000000000084,0.7373805020140186,1.001,368.24853109634995,750.2019475365264,133.45130461354518,93.37799287591923,8.864138681781844,0.6772608738417927]
[8.400000000000784,0.7420200602847381,1.001,368.1720195940535,750.0164095007813,133.84265569027343,94.64493109251806,8.937689414337637,0.681733623942243]
[8.500000000000728,0.7466125227838873,1.001,368.09804401707424,749.8451157695227,134.24151614394205,95.89883560593131,9.009320056176172,0.686154392842465]
[8.600000000000673,0.7511601681552865,1.001,368.02657687968787,749.687885368146,134.64768031259757,97.13984920228108,9.079204611000073,0.6905261114762752]
[8.700000000000617,0.7556650695827012,1.001,367.9575918791732,749.5445443240543,135.06095054620724,98.36812240970734,9.147498009785872,0.6948514199942797]
[8.800000000000562,0.7601291174011373,1.001,367.8910637919033,749.4149250710459,135.48113661068658,99.58381218130963,9.21433827505306,0.6991327031522808]
[8.900000000000507,0.7645540391136927,1.001,367.82696838081023,749.2988659185266,135.90805515408988,100.78708073695196,9.279848438349378,0.703372120701743]
[9.000000000000451,0.768941417119004,1.001,367.76528231292014,749.1962105781422,136.3415292279112,101.97809454548903,9.344138239073636,0.7075716336575646]
[9.100000000000396,0.7732927044166729,1.001,367.7059830858091,749.1068077412732,136.78138785727066,103.15702343112517,9.40730562956607,0.7117330271229636]
[9.20000000000034,0.7776092385255967,1.001,367.6490489619653,749.0305107016192,137.22746565448074,104.32403978951567,9.469438108562526,0.7158579302081203]
[9.300000000000285,0.7818922538219603,1.001,367.5944589101575,748.9671770177436,137.67960247112381,105.4793179008851,9.530613902594668,0.7199478334729142]
[9.40000000000023,0.7861428924791317,1.001,367.54219255301666,748.9166682110646,138.13764308433588,106.62303332891197,9.590903012687937,0.7240041042440328]
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