research article time-dependent neutronic analysis of a

Research ArticleTime-Dependent Neutronic Analysis of a Power-Flattened GasCooled Accelerator Driven System Fuelled with ThoriumUranium Plutonium and Curium Dioxides TRISO Particles

Gizem BakJr1 Gamze Genccedil2 and Huumlseyin YapJcJ2

1Cumhuriyet Universitesi Teknoloji Fakultesi 58140 Sivas Turkey2Erciyes Universitesi Muhendislik Fakultesi 38039 Kayseri Turkey

Correspondence should be addressed to Huseyin Yapıcı yapicierciyesedutr

Received 14 July 2016 Accepted 3 August 2016

Academic Editor Eugenijus Uspuras

Copyright copy 2016 Gizem Bakır et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This study presents the power flattening and time-dependent neutronic analysis of a conceptual helium gas cooled AcceleratorDriven System (ADS) loaded with TRISO (tristructural-isotropic) fuel particles Target material is lead-bismuth eutectic (LBE)ThO2 UO2 PuO

2 and CmO

2TRISO particles are used as fuel PuO

2and CmO

2fuels are extracted from PWR-MOX spent fuel

Subcritical core is radially divided into 10 equidistant subzones in order to flatten the power produced in the core Tens of thousandsof these TRISO fuel particles are embedded in the carbon matrix fuel pebbles as five different cases The high-energy Monte Carlocode MCNPX 27 with the LA150 library is used for the neutronic calculations Time-dependent burnup calculations are carriedout for thermal fission power (119875th) of 1000 MW using the BURN card The energy gain of the ADS is in the range of 9998ndash14864at the beginning of a cycle Furthermore the peak-to-average fission power density ratio is obtained between 1021 and 1029 at thebeginning of the cycle These ratios show a good quasi-uniform power density for each case Furthermore up to 1551 g 233U and1036 g 239Pu per day can be produced The considered system has a high neutronic capability in terms of energy multiplicationfissile breeding and spent fuel transmutation with thorium utilization

1 Introduction

Currently Light Water Reactors (LWRs) and Canada Deu-terium Uranium (CANDU) reactors which use uraniumsources generate the most of nuclear electricity Commercialnuclear reactors produce highly radioactivematerials as high-level wastes They mainly contain transuranic isotopes (NpPu Am and Cm) and long-lived fission products Mostcountries prefer to bury thesewastes in concrete containers inthe sea bed On the other hand transmutation of these wastesby driving high-energetic neutron andor proton source isan improved approach Lawrence [1] is the first to transmutethorium to 233U by releasing fast neutrons from a spallationtarget bombarded with high-energetic protons The poten-tials of nuclear fuel transmutation in various fusion-fissionhybrid reactors fuelledwith several spent fuels extracted fromconventional nuclear reactors are investigated in our previousstudies (Yapıcı et al [2 3])

Many studies on transmutation of nuclear waste andfissile fuel breeding in ADSs have been performed in recentyears Barros et al investigated potentials of fissile breedingand transmutation for a lead cooled ADS loaded with tho-rium and reprocessed fuel [4 5] Their results show that theuse of ThO

2and reprocessed fuel combination enabled ura-

nium (233U) production without the initial 233U enrichmentVu and Kitada [6] propose a conceptual design of ADS uti-lizing thorium fuel and reprocessed fuel for transmutation ofnuclear waste and production of energy Abanades and Perez-Navarro [7] examine the transmutation of nuclear waste in agas cooled ADS moderated with graphite TRISO is formedfrom nuclear wastes and they show that 95 of plutoniumcan be transmuted (except 242Pu) Garcıa et al [8] evaluatethe real number of pebbles fitting in a cylindrical ADS corein detail The transmutation of MA in a lead-bismuth cooledADS is analyzed by Takizuka et al [9] and Tsujimoto et al[10] Takizuka et al indicate that the waste transmutation

Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2016 Article ID 2612459 11 pageshttpdxdoiorg10115520162612459

2 Science and Technology of Nuclear Installations

of 250 kgyear is obtained by 80 plant factor According toTsujimoto et al their ADS design productively transmutesand burns the MA when the effective neutron multiplicationfactor is 097 A uranium spallation target in an ADS loadedwith MA is considered by Ismailov et al [11] Lead-bismuth(PbBi) target and uranium target are compared in their studyand results show that the limited geometrical size of uraniumtarget has better neutron multiplication than that of lead-bismuth (PbBi) target The criticality of the targets made ofpure 241Am and 243Am is investigated by applying the MonteCarlo code for ADS [12]The neutronic data of several infinitetarget mediums irradiated with a proton source of 1000MeVis studied by Yapıcı et al [13] to attain a real ADS designYapıcı et al [14] and Bakir et al [15] bring out that a highneutronic performance in nuclearwaste transmutation fissilebreeding and energy generation can be obtained for variousconsidered configurations and fuel compositions of an ADSMartınez et al [16] claim that high-energetic neutrons arenecessitated for transmutation of transuranium (TRU) andlong-lived fission products in ADS There are several otherstudies of various types of ADS for energy productionand transmutation of radioactive wastes (Adam et al [17]Artisyuk et al [18] Brolly and Vertes [19] Haeck et al [20]Mukaiyama et al [21] Park et al [22] Seltborg andWallenius[23] Tsujimoto et al [24] Wade et al [25] Wallenius andEriksson [26] Westlen and Wallenius [27])

The main cause of temperature and radiation damagegradients in an ADS is the nonuniform fission power densityTherefore power flattening can help cooling of fuel core andreduce material stresses To obtain a uniform fission powerdensity profile peak-to-average fission power density ratio(D) is expected to be reduced to 100 Power flattening ofthe helium-cooled DT driven blanket in the Prometheus-H(heavy ion) breeder reactor fuelled with various mixed fuels(UCndashThC UO

2ndashThO

2 UCndashC UO

2ndashC and 244CmO

2ndashUO2)

and nuclear waste actinide are studied by Yapıcı and Ubeyli[28] According to their results high amounts of energy fissilefuel and self-sufficient tritium production for (D T) fusionreaction are obtained Fissile fuel breeding and a flat fissionpower density are examined by Yapıcı [29] in a blanket-driven ICF (inertial confinement fusion) neutron and basedon SiCfSiC composite material In order to accomplish a flatfission power density the blanket is fuelled with ThO

2and

UO2mixed by several different mixing methods and cooled

with natural lithium (LiF)2BeF2 Li17Pb83 and 4He for the

nuclear heat transfer Peak-to-average fission power densityratio of the blanket is decreased to almost 11 Bakır et al[30] have investigated the medical radioisotope productionperformance of a power-flattened ADS fuelled with UO

2

and PuO2 Their results show that a good quasi-uniform

power density is achieved and good neutronic performancein terms of energy production radioisotope production andthe transmutation of spent fuel is also achieved

In this study power flattening and time-dependent neu-tronic analysis of a conceptual helium gas cooled ADSloaded with TRISO fuel particles are presented The paper isorganized as follows In Section 2 the computational modelof a conceptual gas cooled ADS is explained Calculation

TargetSubc

ritic

al co

re

Subc

ritic

al co

re

Prot

on b

eam

IS50keV

RFQ3MeV

DTL40MeV

CCDTL100MeV

SC LINAC1GeV

Figure 1 Layout of the 1 GeV LINAC for ADS (IS ion source RFQradio frequency quadrupol DTL drift tube LINAC CCDTL cavitycoupled DTL SC LINAC superconducting linear accelerator)

1GeV sim30mA)Proton beam (

200

300

370

5 55 100 60 30

z

r

21 3 4

Figure 2 Cross-sectional view of the investigated ADS (A SNTspallation neutron target B SCZ Subcritical Core Zone C RZreflector zoneD SZ shielding zone dimensions are in cm)

procedure is outlined in Section 3 Numerical results andconclusions are presented in Sections 4 and 5 respectively

2 Conceptual Gas Cooled AcceleratorDriven System

Figure 1 demonstrates the layout of 1000MeV linear acceler-ator (LINAC) for an ADS As is apparent from this figurea proton of 50 keV is accelerated to 1000MeV in four stepsion source (IS) of 50 keV is accelerated firstly to 3MeV byradio frequency quadrupole (RFQ) secondly to 40MeV bydrift tube LINAC (DTL) thirdly to 100MeVby cavity coupledDTL (CCDTL) and finally to 1000MeV by superconductinglinear accelerator (SC LINAC)

Figures 2 and 3 show the cross-sectional view of theinvestigated conceptual cylindrical ADS and TRISO coatedfuel particles in the fuel pebble sphere respectively Thereare four parts in the considered ADS as follows spallationneutron target (SNT) subcritical core (SC) reflector zone(RZ) and shielding zone (SZ) In order to obtain flattenedpower profiles in SC this core is radially divided into 10equidistant subzones (see Figure 2) The isotopic percentages

Science and Technology of Nuclear Installations 3

Outer PyCSiC layerInner PyCPyC bufferFuel kernel

Fuel pebble sphere sectionD = 60mm

TRISO coated fuel particleD = 092mm

Fuel kernelD = 05mm

Figure 3 Fuel pebble sphere and TRISO coated fuel particle (PyC pyrocarbon SiC silicon carbide)

Table 1 Isotopic percentages and densities of the materials used inthe investigated ADS

Material Density [gcm3] Nuclide Percentage

LBE 11344 Pb 44598 Bi 555

He 01786 He 100ThO2

988 232Th 100

UO2

1054235U 75 15 225238U 925 85 775

lowastPuO2

1150

238Pu 353535239Pu 450154240Pu 263505241Pu 159640242Pu 913483

lowastCmO2

1055

242Cm 391520243Cm 004721244Cm 855422245Cm 954125246Cm 095413

Graphite 210 12C 100

B4C 252

10B 1843111B 81569

lowastDischarged PWR-MOX fuel with plutonium recycle 1000MWe reactor80 capacity factor 33MWdkg 25 thermal efficiency and 150 days afterdischarge [32 p 370 Table 85]

Table 2 Characteristics of a TRISO particle [31]

Layer Size [120583m] Material Density [gcm3]Fuel kernel 250 (radius) UO

21055

PyC buffer 95 (thickness) CC 105Inner PyC 40 (thickness) CC 190SiC layer 35 (thickness) SiC 318Outer PyC 40 (thickness) CC 190

and densities of the materials used in this ADS are given inTable 1 Geometric characteristics of a TRISO particle (Kimet al [31]) are given in Table 2

Spallation Neutron Target The target is liquid lead- (Pb-)bismuth (Bi) eutectic (LBE 445Pb-555Bi eutectic) Dueto its good neutron release characteristic and thermal andchemical properties the LBE is the most preferable target

material for ADS designs amongmany target materials in theliterature [33] The radius of the target is optimized as 55 cmin terms of spallation neutrons A continuous uniformprotonbeam of 1000MeV and a source radius of 4 cm bombardsthe target to release a few tens of high-energy spallationneutrons In this work the target radius is gradually increasedto optimize neutron leakage It is determined as 55 cm andneutron leakage is calculated as about 30 neutrons per protonThe release neutrons penetrate through SC to activate fissionand breeding reactions

Subcritical Core Tristructural-isotropic (TRISO) fuel is orig-inated from a kernel made of fuel such as uranium car-bideuranium oxide and surrounded by carbon and ceramiclayerTheTRISO fuel is an attractive fuel for high temperaturenuclear reactors due to the fact that it has a quite highneutronic performance and good burn-up ability in hightemperatures As is apparent from Figure 3 and Table 2 amicrospherical tristructural-isotropic (TRISO) fuel particleis designed as five layers from the inside out as follows (1) fuelkernel (2) Porous Carbon Buffer (3) Inner Pyrolytic Carbon(IPyC) (4) silicon carbide (SiC) and (5) Outer Pyrolytic(OPyC) (see Figure 3) (Kim et al [31]) Dimensions of theselayers are given in Table 2 These TRISO composite particlesare embedded inside a spherical carbon matrix fuel pebblewith a determined packing fraction which can be up to 32(Conway and Sloane [34]) Spherical fuel pebble is made ofcarbonmatrix having a 60mmdiameter (see Figure 3)Thesecarbon matrix fuel pebbles are located in a cylindrical SCwith a determined packing fraction which can be up to 74(Conway and Sloane [34]) In this study to produce fissile fueland energy and to transmute PWR-MOX spent fuel tens ofthousands of six different TRISO fuel particles (ThO

2 average

9 enrichment UO2 15 enriched UO

2 225 enriched

UO2 PuO

2 and CmO

2) are embedded in the carbon matrix

fuel pebbles with a packing factor of 29 as five differentcases as follows and the embedding percentages of differentTRISO fuel particles in the carbonmatrix fuel pebbles in eachsubzone are given in Table 3

Case 1 (a) Only UO2TRISO particles with different enrich-

ment percentages (320ndash1125) are embedded in the car-bon matrix fuel pebbles and tens of thousands of these fuelpebbles are located in the ten equidistant layers according totheir enrichment percentages

(b) ThO2and 15 enriched UO

2TRISO particles are

separately embedded in the carbon matrix fuel pebbles with


Table 3 Enrichment percentages of UO2TRISO particles (Case 1(a)) and embedding percentages of 15 enrichedUO

2 225 enrichedUO

2

PuO2 andCmO

2TRISOparticles inCases 1(b) 1(c) 2 and 3 in the fuel pebbles in the fuel subzones at the beginning of cycle [119875th = 1000MW]

Case Number of the subzones1 2 3 4 5 6 7 8 9 10 1ndash10lowast

1(a) 852 932 982 1025 1075 1125 1125 992 647 320 751(b) 7000 7850 8300 8650 8900 9300 9450 9300 6350 2800 71001(c) 4700 5600 6050 6350 6650 6850 6950 6600 4300 1825 46002 2030 2600 2790 2885 2976 3140 3365 3555 2680 676 26503 790 780 780 790 810 831 831 742 601 404 645lowastConstant enrichment percentage or constant embedding percentages in all subzones

different embedding percentages and tens of thousands ofthese fuel pebbles are located in the ten equidistant layersaccording to their embedding percentages

(c) ThO2and 225 enriched UO


separately embedded in the carbon matrix fuel pebbles withdifferent embedding percentages and tens of thousands ofthese fuel pebbles are located in the ten equidistant layersaccording to their embedding percentages

Case 2 ThO2and PuO

2TRISO particles are separately

embedded in the carbon matrix fuel pebbles with differentembedding percentages and tens of thousands of these fuelpebbles are located in the ten equidistant layers according totheir embedding percentages

Case 3 ThO2and CmO



Packing factor of the carbon matrix fuel pebbles in SC is60This core is cooled with helium gas whose percentage is40 PuO

2and CmO

2fuels mentioned above are extracted

from PWR-MOX spent fuels (Manson et al [32]) fuel withplutonium recycle 1000MWe reactor 80 capacity factor33MWdkg 325 thermal efficiency and 150 days afterdischarge

Neutron Safety The last two zones (RZ and SZ) serve forneutron safety Reflector part is the zone made of graphitereflecting neutrons leaking from the SC zone to increase fis-sion and breeding reactions The graphite is selected becauseits scatter cross section is much greater than its absorptioncross section Additionally it is a good neutron moderatorand is high temperature resistant Because of these propertiesthe graphite is widely preferable in nuclear applicationsShielding part is the last zone made of boron carbide (B

4C)

absorbing the neutrons leaking from RZ Due to the fact thatboron has a quite high absorption cross section and B

4C has

good thermomechanical properties B4C is usually used in

nuclear reactors

3 Calculation Procedure

The numerical calculations have been computed byusing the high-energy Monte Carlo code MCNPX 27

(Pelowitz et al [35]) with the LA150 library (Chadwick etal [36]) ldquoThe library consists of evaluated reaction cross-sections and emission spectra up to 150MeV for incidentneutrons and protons for over 40 target isotopes importantin SNTs structural materials and shieldingrdquo (Yapıcı etal [14]) Model for the intranuclear cascade of spallationreactions is selected as Bertini INC model (Bertini [37])The literature and our previous studies (Yapıcı et al [13 14])bring out that the energy gain (119866) is at the maximum levelat proton energy (119864

119901) of 1000MeV Therefore source proton

energy is assumed as 1000MeV (see Figure 2) The BURNcard of the MCNPX 27 code (Pelowitz et al [35]) is usedfor time-dependent calculations and these calculations areperformed for the power-flattened cases

4 Numerical Results

41 Effective Neutron Multiplication Coefficient The effectiveneutron multiplication coefficient (119896eff) is the ratio of onegeneration of neutrons to the next generationThis coefficientis less than 1 in the subcritical systems The compositions ofthe fuels in this study are determined in all cases so that 119896eff is098 at the beginning of the burn cycleThermal fission power(119875th) is considered as 100 300 500 700 and 1000MW for theburn-up calculations Figures 4ndash6 demonstrate the variationsof 119896eff with the operation time (a) and the burn cycle timescalculated according to the decrease of 119896eff from 095 to 90(b) for all fuel cases

As is apparent from (a) of Figures 4ndash6 the profiles of119896eff gradually decline with the operation time in all 119875thrsquosand fuel cases These profiles indicate that fissile isotopes areconsumed by burning with the operation time For all valuesof 119896eff (090ndash095) the operation times shorten exponentiallywith the increase of 119875th (see (b) of Figures 4ndash6) For 119875th =1000MW the times that 119896eff decreases from 098 to 095 are075 125 and 125 days in Cases 1(a) 1(b) and 1(c) (includingnatural 15 and 225 enriched UO

2TRISO particles)

respectively These times are 30 days and half a day in Cases2 and 3 (PuO

2and CmO

2spent fuel TRISO particles) To

prevent energy gain (119866) fromdecreasing significantly the fuelpebbles are refreshed when the value of 119896eff decreases from098 to 095

42 Fission Power Density Large numbers of energetic spal-lation and fission neutrons are released in SNT and SC ofan ADS and in turn more fission reactions occur in SC


Pth (MW)

kef

fk

eff

Operation time (day)

Case 1(b)

Case 1(c)

Case 1(a)

090

091

092

093

094

095

096

097

098

099

100

60 120 180 240 300 360 4200


090

091

092

093

094

095

096

097

098

099

100

600540480420360300240180120600

090

091

092

093

094

095

096

097

098

099

100

kef

f

360240120 480 600 7200


100

300

500

700

1000

(a)

Case 1(a)

Case 1(b)

Case 1(c)

Pth (MW)1000900800700600500400300200100

Pth (MW)1000900800700600500400300200100

100

Pth (MW)1000900800700600500400300200

keff090

091

092

093

094

095

0

60

120

180

240

300

360

420

480

540

600

Ope

ratio

n tim

e (da

y)

0

60

120

180

240

300

360

420

480

540

600

660

720

780

Ope

ratio

n tim

e (da

y)

0

60

120

180

240

300

360

420

Ope

ratio

n tim

e (da

y)

(b)

Figure 4 (a) Variations of the effective neutron multiplication in the various cases of thermal power depending on the operation time (b)The operation time at which effective neutron multiplication reached various values (090ndash095) versus the thermal power


Pth (MW)100

300

500

700

1000


090

091

092

093

094

095

096

097

098

099

100

kef

f

15001350120010509007506004503001500

Case 2

(a)

keff

0

150

300

450

600

750

900

1050

1200

1350

1500

Ope

ratio

n tim

e (da

y)Pth (MW)

1000900800700600500400300200100

090

091

092

093

094

095

Case 2

(b)


Case 3

Pth (MW)100

300

500

700

1000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 200Operation time (day)

090

091

092

093

094

095

096

097

098

099

100

kef

f

(a)

Pth (MW)1000900800700600500400300200100

095

094

093

092

091

090

0

2

4

6

8

10

12

14

16

18

20

Ope

ratio

n tim

e (da

y)

keff

Case 3

(b)



BOC

BOC

After 30 days

keff = 098

keff = 098

keff = 095

keff = 090

Γ = 1021

Γ = 1973

Γ = 1173

Γ = 1443

16015014013012011010090807060

Radius (cm)

00E + 00

10E minus 05

20E minus 05

30E minus 05

40E minus 05

50E minus 05

60E minus 05

70E minus 05

80E minus 05

After 1 day

Case 1(c)

BOC

BOC

After 075 daysAfter 25 days

keff = 098

keff = 098

keff = 095

keff = 090

Γ = 1027

Γ = 1868

Γ = 1182

Γ = 1464

16015014013012011010090807060

Radius (cm) Radius (cm)

00E + 00

10E minus 05

20E minus 05

30E minus 05

40E minus 05

50E minus 05

60E minus 05

70E minus 05

80E minus 05 Case 1(a)

RfD

(rea

ctio

nsc

m3)

BOC

BOC


keff = 098

keff = 098

keff = 095

keff = 090

Γ = 1029

Γ = 1973

Γ = 1191

Γ = 1454

1601501401301201101009080706000E + 00

10E minus 05

20E minus 05

30E minus 05

40E minus 05

50E minus 05

60E minus 05

70E minus 05

80E minus 05 Case 1(b)

RfD

(rea

ctio

nsc

m3)

RfD

(rea

ctio

nsc

m3)

Figure 7 Variations of fission densities in the fuel core at the beginning and at the end of the cycle versus the core radius (solid lines indicatethe flattened power case)

From inner side to outer side of SC in radial directionprofile of the fission power density declines exponentiallybecause of the decrease of neutron fluxes in this directionThis nonuniformity of fission power density causes radiationdamage and large temperature gradients that result in coolingand material issues This situation is usually observed inADSs and similar nuclear power systems On the contrarya uniform fission power density would help preventing ofthese cooling and material damage problems A measure ofuniformity of fission power density profile is determinedwith the peak-to-average fission power density ratio Thisratio must be 100 for an exact uniform fission power densityprofile

In this work in order to achieve a uniform power profilein SC this core is radially divided into 10 equidistant subzones(see Figure 2) and the embedding percentages of differentTRISO fuel particles in the carbon matrix fuel pebbles ineach subzone of SC are adjusted in radial direction Theembedding percentages are optimized after many computa-tional trials of percentages (see Table 3) The fission powerdensity profiles obtained in the cases without percentageadjustments (constant percentages in all subzones) and in thecases with percentage adjustments (varying percentages in allsubzones) are plotted in Figures 7ndash9 for all fuel cases Dashedlines in these figures indicate the cases without percentageadjustments In general uniformity of power profiles ofthe cases without percentage adjustments breaks down (theprofiles sharply increase) in the last subzones because ofneutrons reflecting from RZ On the other hand in theoptimized adjustment cases quasi-uniform power profiles

BOC

BOC Γ = 1029

Γ = 1899

Γ = 1246Γ = 1569


Radius (cm)16015014013012011010090807060

Case 2

RfD

(rea

ctio

nsc

m3)

keff = 098

keff = 098

keff = 095

keff = 090

00E + 00

10E minus 05

20E minus 05

30E minus 05

40E minus 05

50E minus 05

60E minus 05

70E minus 05

80E minus 05

Figure 8 Variations of fission densities in the fuel core at thebeginning and at the end of the cycle versus the core radius (solidlines indicate the flattened power case)

are achieved for all fuel cases At the beginning of cycle(BOC) the values of D are reduced to between 1021 and1029 in Cases 1(a)ndash1(c) and as to Cases 2 and 3 these valuesare 1029 and 1024 respectively It is important to note thatthese values are lower with respect to the values obtainedfrom Yapıcı and Ubeyli [28] (D = 1051ndash1069) and Yapıcı[29] (D = 1131ndash1403) The uniformity of power profile doesnot deteriorate significantly until 119896eff decreases to 095Thesevalues and power profiles bring out that the power of theinvestigated ADS is flattened for all fuel cases

43 Fuel Burn-up Burn-up (BU) is defined as the totalenergy generated per initial unit mass of initially loaded fueland its unit is GWdMTU (GWd gigawatt days MTU per


Table 4 Increase of burn-up with the thermal power and time

BU(119875th 119905) = 120572 sdot 10minus4sdot 119875th sdot 119905 [GWdMTU]

[119875th = 100ndash1000MW]Case 1(a) 1(b) 1(c) 2 3120572 279 287 283 286 297

BOCBOC

keff = 098

keff = 098

keff = 095

keff = 090

Γ = 1024

Γ = 1630

Γ = 1307Γ = 1477


Radius (cm)16015014013012011010090807060

Case 3

RfD

(rea

ctio

nsc

m3)

00E + 00

10E minus 05

20E minus 05

30E minus 05

40E minus 05

50E minus 05

60E minus 05

70E minus 05

80E minus 05


metric ton of uranium) So it is directly related to the fissionreactions and calculated as follows

BU (119905 + Δ119905) = BU (119905) +Fission Energy

MTUΔ119905 (1)

where 119905 is operation time and Δ119905 is time intervalThe calculations emphasize that the values of BU increase

quasi-linearly in all 119875thrsquos with operation time In order to findan empirical relation for BU curve-fitting method is usedCurve-fittingmethod gives the relation between independentvariables and dependent variable by applying the best fit todata The coefficients of the BU profiles obtained by thismethod are given in Table 4 for all fuel cases The operationtime limits in this BU(119875th 119905) expression are between the BOCand the end of cycle (EOC) which varies depending on thefuel cases (see footnote of Table 5) The longest EOC time isin Case 2 and it is 30 days for 119896eff = 095 In this operationtime the BU value is 858GWdMTU for 119875th = 1000MW

44 Gain The energy gain proportional to fission reactions(119877119891) occurring in SC is one of the most major parameters

of an ADS It can be defined as the ratio of the total fissionenergy production in the core to Ep and calculated as follows

119866 =

119877119891119864119891

119864119901

(2a)

or

119866 =119875thPE (2b)

where 119864119891is the energy per fission (200MeV) and PE is the

proton beam powerThe gain values of the investigated ADS calculated for119875th = 1000MWat the BOC and the EOC are given in Table 5

While these values vary in the range of 9998ndash14864 at theBOC depending on the fuel case this range is 1568ndash5271 atthe EOC (119896eff = 095) Case 1(b) (including 15 enrichedUO

2

TRISO particles) among Cases 1(a)ndash1(c) is the best fuel casein terms of the energy gain As for the spent fuel cases Case2 (including PuO

2TRISO particles) is the best In order to

maintain 119875th = 1000MW the value of proton flux (PF) isvaried in the range of 0420 sdot 1017ndash0624 sdot 1017 protonss at theBOC depending on the fuel case and during the operationPF is increased to the range of 1184 to 3981 times 1017 protonss1017 protons of 1000MeV of energy per second correspond toa PE of 1602MW

45 Thorium Utilization As known thorium utilizationmeans production of fissile 233U This production reaction isas follows

232Th (n 120574) 233Th120573

997888rarr233Pa

120573

997888rarr233U (3)

Masses of isotopes which are loaded to SC at the BOCand produced in this core at the EOC are given in Tables6ndash8 for all fuel cases Although the highest thorium load(3114 kgHM) is in Case 3 (including CmO

2TRISO particles)

the best thorium utilization is realized in Case 2 As for thecaseswith uraniumCase 1(c) (including 225 enrichedUO

2

TRISO particles) is the best case among Cases 1(a)ndash1(c) dueto the fact that it has more enrichment uranium Fissile fuel233U of 1551 g per day (4653 kg30 days) and 61 g per day(7619 sdot 10minus3 kg125 days) is produced by utilizing thoriumfor 119896eff = 095 in Cases 2 and 1(c) respectively

In addition to these fissile fuel 239Pu of 1036 g perday (1295 sdot 10minus1 kg125 days) and 776 g per day (9697 sdot10minus2 kg125 days) is produced by utilizing uranium for 119896eff =095 in Cases 1(b) and 1(c) respectively Reaction of 239Puproduced from 238U is as follows

238U (n 120574) 239U120573

997888rarr239Np

120573

997888rarr239Pu (4)

5 Conclusion

One way of transmutation of nuclear wastes is using ADSsby driving high-energetic proton source In this study a con-ceptual LBE target-ADS has been investigated to transmutespent fuel with thorium and to flatten the fission powerdensity of the fuel core as well as energy production Manytime-dependent computational trials have been performedto obtain optimum neutronic data by using MCNPX 27computer code The major results are in brief as follows

(i) The optimized radius (55 cm) of LBE target is thebest size in terms of spallation neutrons (about 30neutrons)

(ii) The longest and shortest times when 119896eff decreases to095 are in Case 2 (including ThO

2and PuO

2TRISO

particles) and Case 3 (including theThO2and CmO

2

TRISO particles) which are 05 days and 30 daysrespectively After these times the fuel pebbles shouldbe refreshed


Table 5 Neutronic data at the beginning and at the end of the cycle

119875th = 1000MW Case1(a) 1(b) 1(c) 2 3

FissionBOClowast 69217 74324 67564 61568 49992EOClowastlowast 263561 234393 248735 179487 78389

EOClowastlowastlowast 109812 106884 107486 94018 473410

119866

BOC 13843 14864 13513 12314 9998EOC 5271 4688 4975 3590 1568EOC 2196 2138 2150 1880 947

PE [MW]BOC 722 673 740 812 1000EOC 1897 2133 2010 2785 6377EOC 4554 4677 4651 5319 10560

PF times 1017 [ps]BOC 0451 0420 0462 0507 0624EOC 1184 1331 1255 1738 3981EOC 2843 2919 2903 3320 6592

lowast119896eff = 098

lowastlowast119896eff = 095 and

lowastlowastlowast119896eff = 090

1After 075 days 2After 25 days3After 125 days 4After 30 days5After 125 days 6After 30 days7After 30 days 8After 165 days9After 05 days 10After 25 days

Table 6 Masses of actinide isotopes [kgHM] at the beginning and at the end of the cycle (Cases 1(a)ndash1(c))

Case 1(a) 1(b) 1(c)Isotopes BOC EOC1 EOC2 BOC EOC3 EOC4 BOC EOC5 EOC6231Th mdash mdash mdash mdash 7448Eminus 5 1597Eminus 4 mdash 1680Eminus 4 2989Eminus 4232Th mdash mdash mdash 8015E+ 2 8012E+ 2 7941E+ 2 1519E+ 3 1519E+ 3 1507E+ 3233Th mdash mdash mdash mdash 5405Eminus 3 5611Eminus 3 mdash 9076Eminus 3 9442Eminus 3233Pa mdash mdash mdash mdash 2861Eminus 1 4904E+ 0 mdash 4844Eminus 1 8354E+ 0233U mdash mdash mdash mdash 4488Eminus 3 2002E+ 0 mdash 7619Eminus 3 3456E+ 0234U mdash 7634Eminus 6 8355Eminus 4 mdash 4174Eminus 4 2331Eminus 1 mdash 6433Eminus 4 3748Eminus 1235U 3120E+ 2 3110E+ 2 2807E+ 2 4051E+ 2 4034E+ 2 3663E+ 2 4372E+ 2 4355E+ 2 3978E+ 2236U mdash 2194Eminus 1 6952E+ 0 mdash 3892Eminus 1 8978E+ 0 mdash 3954Eminus 1 9181E+ 0237U mdash 3845Eminus 4 5459Eminus 2 mdash 5932Eminus 4 6547Eminus 2 mdash 4674Eminus 4 6445Eminus 2238U 3276E+ 3 3275E+ 3 3252E+ 3 2325E+ 3 2324E+ 3 2304E+ 3 1525E+ 3 1524E+ 3 1509E+ 3239U mdash 2151Eminus 2 2274Eminus 2 mdash 1574Eminus 2 1675Eminus 2 mdash 1175Eminus 2 1240Eminus 2238Pu mdash mdash 1053Eminus 3 mdash mdash 1629Eminus 3 mdash mdash 1494Eminus 3239Pu mdash 6525Eminus 2 1768E+ 1 mdash 1295Eminus 1 1615E+ 1 mdash 9697Eminus 2 1224E+ 1240Pu mdash 7266Eminus 4 9220Eminus 1 mdash 1359Eminus 3 7479Eminus 1 mdash 9769Eminus 4 5428Eminus 1241Pu mdash mdash 1733Eminus 1 mdash mdash 1435Eminus 1 mdash mdash 1008Eminus 1Total 3588E+ 3 3586E+ 3 3559E+ 3 3532E+ 3 3529E+ 3 3498E+ 3 3481E+ 3 3480E+ 3 3448E+ 31After 075 days (119896eff = 095)

2After 25 days (119896eff = 090)3After 125 days (119896eff = 095)


6After 30 days (119896eff = 090)

(iii) A quasi-uniform fission power density profile isobtained for each fuel case (D = 1021ndash1029 at theBOC)

(iv) Burn-up profiles increase quasi-linearly in all 119875thrsquoswith operation time The highest value is 858GWdMTU

(v) Case 1(b) (including ThO2and 15 enriched UO

2

TRISO particles) is the best fuel case in terms of theenergy gain (119866 = 14864)

(vi) 233U and 239Pu fissile fuels can be produced up to1551 g and 1036 g per day respectively

In conclusion the ADS flattened fission power density hasa good neutronic performance in terms of effective utiliza-tions of thorium and spent fuel and energy productionFurthermore this work would light the way for obtaininga uniform fission power density profile for similar futureworks


Table 7 Masses of actinide isotopes [kgHM] at the beginning andat the end of the cycle (Case 2)

Isotopes BOC EOC1 EOC2231Th mdash 6711Eminus 4 6574Eminus 4232Th 2468E+ 3 2451E+ 3 2374E+ 3233Th mdash 1231Eminus 2 1297Eminus 2233Pa mdash 1100E+ 1 1995E+ 1233U mdash 4653E+ 0 5359E+ 1234U mdash 4039Eminus 1 5973E+ 0235U mdash 8541Eminus 3 6315Eminus 1238Pu 3632E+ 1 3520E+ 1 3045E+ 1239Pu 4644E+ 2 4360E+ 2 3256E+ 2240Pu 2730E+ 2 2696E+ 2 2516E+ 2241Pu 1661E+ 2 1648E+ 2 1535E+ 2242Pu 9543E+ 1 9525E+ 1 9465E+ 1243Pu mdash 3420Eminus 2 3485Eminus 2244Pu mdash 7213Eminus 4 4449Eminus 3241Am mdash 6296Eminus 1 2790E+ 0242Am mdash 1944Eminus 3 3276Eminus 2243Am mdash 3129E+ 0 1345E+ 1244Am mdash 4735Eminus 3 1914Eminus 2Total 3503E+ 3 3472E+ 3 3326E+ 31After 30 days (119896eff = 095)2After 165 days (119896eff = 090)


Isotopes BOC EOC1 EOC2231Th mdash 4644Eminus 4 1414Eminus 3232Th 3114E+ 3 3113E+ 3 3110E+ 3233Th mdash 3370Eminus 2 3608Eminus 2233Pa mdash 7145Eminus 1 3730E+ 0233U mdash 4390Eminus 3 1170Eminus 1234U mdash 7117Eminus 4 2635Eminus 2235U mdash mdash 1304Eminus 4242Cm 9990E+ 0 9961E+ 0 9848E+ 0243Cm 1210Eminus 1 1258Eminus 1 1453Eminus 1244Cm 2201E+ 2 2198E+ 2 2187E+ 2245Cm 2465E+ 1 2428E+ 1 2284E+ 1246Cm 2475E+ 0 2553E+ 0 2863E+ 0Total 3371E+ 3 3370E+ 3 3368E+ 31After 05 days (119896eff = 095)

2After 25 days (119896eff = 090)

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

This study is supported by the Research Fund of the ErciyesUniversity Project no FDK-2015-5811

References

[1] E O Lawrence ldquoAEC research and development report facil-ities for electronuclear (MTA) programrdquo Report LWS-247361953

[2] H Yapıcı N Demir andG Genc ldquoNeutronic analysis for trans-mutation of minor actinides and long-lived fission products ina Fusion-Driven Transmuter (FDT)rdquo Journal of Fusion Energyvol 25 no 3-4 pp 225ndash239 2006

[3] H Yapıcı G Genc andN Demir ldquoTransmutation-incinerationpotential of transuraniums discharged from PWR-UO

2spent

fuel in modified PROMETHEUS fusion reactorrdquo Fusion Engi-neering and Design vol 81 no 18 pp 2093ndash2108 2006

[4] G P Barros C Pereira M A F Veloso and A L CostaldquoThorium and reprocessed fuel utilization in an accelerator-driven systemrdquo Annals of Nuclear Energy vol 80 pp 14ndash202015

[5] G D P Barros C Pereira M A F Veloso and A L CostaldquoStudy of an ADS loaded with thorium and reprocessed fuelrdquoScience and Technology of Nuclear Installations vol 2012 ArticleID 934105 12 pages 2012

[6] TM Vu and T Kitada ldquoTransmutation strategy using thorium-reprocessed fuel ADS for future reactors in Vietnamrdquo Scienceand Technology of Nuclear Installations vol 2013 Article ID674638 5 pages 2013

[7] A Abanades and A Perez-Navarro ldquoEngineering design stud-ies for the transmutation of nuclear wastes with a gas-cooledpebble-bed ADSrdquo Nuclear Engineering and Design vol 237 no3 pp 325ndash333 2007

[8] L Garcıa J Perez C Garcıa A Escriva J Rosales and AAbanades ldquoCalculation of the packing fraction in a pebble-bedADS and redesigning of the Transmutation Advanced Devicefor Sustainable Energy Applications (TADSEA)rdquo Nuclear Engi-neering and Design vol 253 pp 142ndash152 2012

[9] T Takizuka K Tsujimoto T Sasa K Nishihara andH TakanoldquoDesign study of lead-bismuth cooledADS dedicated to nuclearwaste transmutationrdquo Progress in Nuclear Energy vol 40 no 3-4 pp 505ndash512 2002

[10] K Tsujimoto T Sasa K Nishihara H Oigawa and H TakanoldquoNeutronics design for lead-bismuth cooled accelerator-drivensystem for transmutation of minor actiniderdquo Journal of NuclearScience and Technology vol 41 no 1 pp 21ndash36 2004

[11] K Ismailov M Saito H Sagara and K Nishihara ldquoFeasibilityof uranium spallation target in accelerator-driven systemrdquoProgress in Nuclear Energy vol 53 no 7 pp 925ndash929 2011

[12] Y Malyshkin I Pshenichnov I Mishustin and W GreinerldquoMonte Carlo modeling of spallation targets containing ura-nium and americiumrdquo Nuclear Instruments and Methods inPhysics Research Section B Beam Interactions with Materialsand Atoms vol 334 pp 8ndash17 2014

[13] H Yapıcı G Genc and N Demır ldquoNeutronic limits in infinitetarget mediums driven by high energetic protonsrdquo Annals ofNuclear Energy vol 34 no 5 pp 374ndash384 2007

[14] H Yapıcı G Genc and N Demir ldquoA comprehensive study onneutronics of a lead-bismuth eutectic cooled accelerator-drivensub-critical system for long-lived fission product transmuta-tionrdquo Annals of Nuclear Energy vol 35 no 7 pp 1264ndash12732008

[15] G Bakır B S Selcuklu G Genc and H Yapıcı ldquoNeutronicanalysis of LBE-uranium spallation target accelerator drivensystem loaded with uranium dioxide in TRISO particlesrdquo ActaPhysica Polonica A vol 129 no 1 pp 30ndash32 2016


[16] A H Martınez Y Kadi and G Parks ldquoTransmutation ofnuclear waste in accelerator-driven systems thermal spectrumrdquoAnnals of Nuclear Energy vol 34 no 7 pp 550ndash563 2007

[17] J Adam K Katovsky A Balabekyan et al ldquoTransmutation of129I 237Np 238Pu 239Pu and 241Am using neutrons produced intarget-blanket system lsquoEnergy plus Transmutationrsquo by relativis-tic protonsrdquo Pramana vol 68 no 2 pp 201ndash212 2007

[18] V Artisyuk A Chmelev M Saito M Suzuki and Y Fujii-E ldquo244Cm transmutation in accelerator-driven systemrdquo Journal ofNuclear Science and Technology vol 36 no 12 pp 1135ndash11401999

[19] A Brolly and P Vertes ldquoConcept of a small-scale electronaccelerator driven system for nuclear waste transmutation part2 Investigation of burnuprdquo Annals of Nuclear Energy vol 32no 4 pp 417ndash433 2005

[20] W Haeck E Malambu V P Sobolev and H Aıt AbderrahimldquoAssessment of americium and curium transmutation in mag-nesia based targets in different spectral zones of an experimentalaccelerator driven systemrdquo Journal of Nuclear Materials vol352 no 1ndash3 pp 285ndash290 2006

[21] TMukaiyama H Takano T Ogawa T Takizuka andMMizu-moto ldquoPartitioning and transmutation studies at JAERI bothunder OMEGA program and high-intensity proton acceleratorprojectrdquoProgress inNuclear Energy vol 40 no 3-4 pp 403ndash4132002

[22] W S Park T Y Song B O Lee and C K Park ldquoA preliminarydesign study for the HYPER systemrdquo Nuclear Engineering andDesign vol 219 no 3 pp 207ndash223 2003

[23] P Seltborg and J Wallenius ldquoProton source efficiency forheterogeneous distribution of actinides in the core of anaccelerator-driven systemrdquo Nuclear Science and Engineeringvol 154 no 2 pp 202ndash214 2006

[24] K Tsujimoto T Sasa K Nishihara T Takizuka and HTakano ldquoAccelerator-driven system for transmutation of high-level wasterdquo Progress in Nuclear Energy vol 37 no 1ndash4 pp 339ndash344 2000

[25] D CWade W S Yang and H Khalil ldquoATW neutronics designstudiesrdquo Progress in Nuclear Energy vol 40 no 3-4 pp 497ndash504 2002

[26] J Wallenius and M Eriksson ldquoNeutronics of minor-actinideburning accelerator-driven systems with ceramic fuelrdquo NuclearTechnology vol 152 no 3 pp 367ndash381 2005

[27] D Westlen and J Wallenius ldquoNeutronic and safety aspects of agas-cooled subcritical core for minor actinide transmutationrdquoNuclear Technology vol 154 no 1 pp 41ndash51 2006

[28] H Yapıcı and M Ubeyli ldquoPower flattening in Prometheusbreeder reactor using nuclear fuel and waste actiniderdquo Annalsof Nuclear Energy vol 30 no 2 pp 159ndash173 2003

[29] H Yapıcı ldquoPower flattening of an inertial fusion energy breederwith mixed ThO

2ndashUO2fuelrdquo Fusion Engineering and Design

vol 65 no 1 pp 89ndash108 2003[30] G Bakır S B Selcuklu and H Yapıcı ldquoMedical radioisotope

production in a power-flattened ADS fuelled with uraniumand plutonium dioxidesrdquo Science and Technology of NuclearInstallations vol 2016 Article ID 5302176 11 pages 2016

[31] H-C Kim S Y Kim J K Kim and J M Noh ldquoMonteCarlo benchmark calculations for 400MWth PBMR corerdquo inProceedings of the 13th International Conference on EmergingNuclear Energy Systems (ICENES rsquo07) pp 498ndash502 IstanbulTurkey June 2007

[32] B Manson H P Thomas and W L Hans Nuclear ChemicalEngineering McGraw-Hill New York NY USA 1981

[33] S T Mongelli J R Maiorino S Anefalos A Deppman andT Carluccio ldquoSpallation physics and the ADS target designrdquoBrazilian Journal of Physics vol 35 no 3 pp 894ndash897 2005

[34] J H Conway and N J A Sloane Sphere-Packings Lattices andGroups Springer New York NY USA 3rd edition 1999

[35] D B Pelowitz ldquoMCNPX userrsquos manual version 260rdquo TechRep LA-CP-07-1473 Los Alamos National Laboratory 2008

[36] M B Chadwick P G Young S Chiba et al ldquoCross-sectionevaluations to 150 MeV for accelerator-driven systems andimplementation in MCNPXrdquo Nuclear Science and Engineeringvol 131 no 2-3 pp 293ndash328 1999

[37] H W Bertini ldquoLow-energy intranuclear cascade calculationrdquoPhysical Review vol 131 no 4 p 1801 1963

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of


Journal ofPetroleum Engineering


Industrial EngineeringJournal of


Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of


Journal of


Renewable Energy

Submit your manuscripts athttpwwwhindawicom


StructuresJournal of


RotatingMachinery


EnergyJournal of


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy


Nuclear InstallationsScience and Technology of


Solar EnergyJournal of


Wind EnergyJournal of


Nuclear EnergyInternational Journal of


High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


of 250 kgyear is obtained by 80 plant factor According toTsujimoto et al their ADS design productively transmutesand burns the MA when the effective neutron multiplicationfactor is 097 A uranium spallation target in an ADS loadedwith MA is considered by Ismailov et al [11] Lead-bismuth(PbBi) target and uranium target are compared in their studyand results show that the limited geometrical size of uraniumtarget has better neutron multiplication than that of lead-bismuth (PbBi) target The criticality of the targets made ofpure 241Am and 243Am is investigated by applying the MonteCarlo code for ADS [12]The neutronic data of several infinitetarget mediums irradiated with a proton source of 1000MeVis studied by Yapıcı et al [13] to attain a real ADS designYapıcı et al [14] and Bakir et al [15] bring out that a highneutronic performance in nuclearwaste transmutation fissilebreeding and energy generation can be obtained for variousconsidered configurations and fuel compositions of an ADSMartınez et al [16] claim that high-energetic neutrons arenecessitated for transmutation of transuranium (TRU) andlong-lived fission products in ADS There are several otherstudies of various types of ADS for energy productionand transmutation of radioactive wastes (Adam et al [17]Artisyuk et al [18] Brolly and Vertes [19] Haeck et al [20]Mukaiyama et al [21] Park et al [22] Seltborg andWallenius[23] Tsujimoto et al [24] Wade et al [25] Wallenius andEriksson [26] Westlen and Wallenius [27])

The main cause of temperature and radiation damagegradients in an ADS is the nonuniform fission power densityTherefore power flattening can help cooling of fuel core andreduce material stresses To obtain a uniform fission powerdensity profile peak-to-average fission power density ratio(D) is expected to be reduced to 100 Power flattening ofthe helium-cooled DT driven blanket in the Prometheus-H(heavy ion) breeder reactor fuelled with various mixed fuels(UCndashThC UO

2ndashThO

2 UCndashC UO

2ndashC and 244CmO

2ndashUO2)

and nuclear waste actinide are studied by Yapıcı and Ubeyli[28] According to their results high amounts of energy fissilefuel and self-sufficient tritium production for (D T) fusionreaction are obtained Fissile fuel breeding and a flat fissionpower density are examined by Yapıcı [29] in a blanket-driven ICF (inertial confinement fusion) neutron and basedon SiCfSiC composite material In order to accomplish a flatfission power density the blanket is fuelled with ThO

2and

UO2mixed by several different mixing methods and cooled

with natural lithium (LiF)2BeF2 Li17Pb83 and 4He for the

nuclear heat transfer Peak-to-average fission power densityratio of the blanket is decreased to almost 11 Bakır et al[30] have investigated the medical radioisotope productionperformance of a power-flattened ADS fuelled with UO

2

and PuO2 Their results show that a good quasi-uniform

power density is achieved and good neutronic performancein terms of energy production radioisotope production andthe transmutation of spent fuel is also achieved

In this study power flattening and time-dependent neu-tronic analysis of a conceptual helium gas cooled ADSloaded with TRISO fuel particles are presented The paper isorganized as follows In Section 2 the computational modelof a conceptual gas cooled ADS is explained Calculation

TargetSubc

ritic

al co

re

Subc

ritic

al co

re

Prot

on b

eam

IS50keV

RFQ3MeV

DTL40MeV

CCDTL100MeV

SC LINAC1GeV

Figure 1 Layout of the 1 GeV LINAC for ADS (IS ion source RFQradio frequency quadrupol DTL drift tube LINAC CCDTL cavitycoupled DTL SC LINAC superconducting linear accelerator)

1GeV sim30mA)Proton beam (

200

300

370

5 55 100 60 30

z

r

21 3 4

Figure 2 Cross-sectional view of the investigated ADS (A SNTspallation neutron target B SCZ Subcritical Core Zone C RZreflector zoneD SZ shielding zone dimensions are in cm)

procedure is outlined in Section 3 Numerical results andconclusions are presented in Sections 4 and 5 respectively

2 Conceptual Gas Cooled AcceleratorDriven System

Figure 1 demonstrates the layout of 1000MeV linear acceler-ator (LINAC) for an ADS As is apparent from this figurea proton of 50 keV is accelerated to 1000MeV in four stepsion source (IS) of 50 keV is accelerated firstly to 3MeV byradio frequency quadrupole (RFQ) secondly to 40MeV bydrift tube LINAC (DTL) thirdly to 100MeVby cavity coupledDTL (CCDTL) and finally to 1000MeV by superconductinglinear accelerator (SC LINAC)

Figures 2 and 3 show the cross-sectional view of theinvestigated conceptual cylindrical ADS and TRISO coatedfuel particles in the fuel pebble sphere respectively Thereare four parts in the considered ADS as follows spallationneutron target (SNT) subcritical core (SC) reflector zone(RZ) and shielding zone (SZ) In order to obtain flattenedpower profiles in SC this core is radially divided into 10equidistant subzones (see Figure 2) The isotopic percentages





Fuel kernelD = 05mm




LBE 11344 Pb 44598 Bi 555

He 01786 He 100ThO2

988 232Th 100

UO2

1054235U 75 15 225238U 925 85 775

lowastPuO2

1150

238Pu 353535239Pu 450154240Pu 263505241Pu 159640242Pu 913483

lowastCmO2

1055

242Cm 391520243Cm 004721244Cm 855422245Cm 954125246Cm 095413


B4C 252

10B 1843111B 81569




21055






2 average


2 225 enriched

UO2 PuO

2 and CmO










2 225 enrichedUO

2

PuO2 andCmO








Case 2 ThO2and PuO



Case 3 ThO2and CmO




2and CmO




4C)


4C has


nuclear reactors






4 Numerical Results



2TRISO particles)


2and CmO





Pth (MW)

kef

fk

eff


Case 1(b)

Case 1(c)

Case 1(a)

090

091

092

093

094

095

096

097

098

099

100

60 120 180 240 300 360 4200


090

091

092

093

094

095

096

097

098

099

100

600540480420360300240180120600

090

091

092

093

094

095

096

097

098

099

100

kef

f

360240120 480 600 7200


100

300

500

700

1000

(a)

Case 1(a)

Case 1(b)

Case 1(c)

Pth (MW)1000900800700600500400300200100

Pth (MW)1000900800700600500400300200100

100

Pth (MW)1000900800700600500400300200

keff090

091

092

093

094

095

0

60

120

180

240

300

360

420

480

540

600

Ope

ratio

n tim

e (da

y)

0

60

120

180

240

300

360

420

480

540

600

660

720

780

Ope

ratio

n tim

e (da

y)

0

60

120

180

240

300

360

420

Ope

ratio

n tim

e (da

y)

(b)



Pth (MW)100

300

500

700

1000


090

091

092

093

094

095

096

097

098

099

100

kef

f

15001350120010509007506004503001500

Case 2

(a)

keff

0

150

300

450

600

750

900

1050

1200

1350

1500

Ope

ratio

n tim

e (da

y)Pth (MW)

1000900800700600500400300200100

090

091

092

093

094

095

Case 2

(b)


Case 3

Pth (MW)100

300

500

700

1000


090

091

092

093

094

095

096

097

098

099

100

kef

f

(a)

Pth (MW)1000900800700600500400300200100

095

094

093

092

091

090

0

2

4

6

8

10

12

14

16

18

20

Ope

ratio

n tim

e (da

y)

keff

Case 3

(b)



BOC

BOC

After 30 days

keff = 098

keff = 098

keff = 095

keff = 090

Γ = 1021

Γ = 1973

Γ = 1173

Γ = 1443

16015014013012011010090807060

Radius (cm)

00E + 00

10E minus 05

20E minus 05

30E minus 05

40E minus 05

50E minus 05

60E minus 05

70E minus 05

80E minus 05

After 1 day

Case 1(c)

BOC

BOC


keff = 098

keff = 098

keff = 095

keff = 090

Γ = 1027

Γ = 1868

Γ = 1182

Γ = 1464

16015014013012011010090807060


00E + 00

10E minus 05

20E minus 05

30E minus 05

40E minus 05

50E minus 05

60E minus 05

70E minus 05


RfD

(rea

ctio

nsc

m3)

BOC

BOC


keff = 098

keff = 098

keff = 095

keff = 090

Γ = 1029

Γ = 1973

Γ = 1191

Γ = 1454

1601501401301201101009080706000E + 00

10E minus 05

20E minus 05

30E minus 05

40E minus 05

50E minus 05

60E minus 05

70E minus 05


RfD

(rea

ctio

nsc

m3)

RfD

(rea

ctio

nsc

m3)




BOC

BOC Γ = 1029

Γ = 1899

Γ = 1246Γ = 1569


Radius (cm)16015014013012011010090807060

Case 2

RfD

(rea

ctio

nsc

m3)

keff = 098

keff = 098

keff = 095

keff = 090

00E + 00

10E minus 05

20E minus 05

30E minus 05

40E minus 05

50E minus 05

60E minus 05

70E minus 05

80E minus 05








BOCBOC

keff = 098

keff = 098

keff = 095

keff = 090

Γ = 1024

Γ = 1630

Γ = 1307Γ = 1477


Radius (cm)16015014013012011010090807060

Case 3

RfD

(rea

ctio

nsc

m3)

00E + 00

10E minus 05

20E minus 05

30E minus 05

40E minus 05

50E minus 05

60E minus 05

70E minus 05

80E minus 05




MTUΔ119905 (1)





119866 =

119877119891119864119891

119864119901

(2a)

or

119866 =119875thPE (2b)




2





232Th (n 120574) 233Th120573

997888rarr233Pa

120573

997888rarr233U (3)


2TRISO particles)


2



238U (n 120574) 239U120573

997888rarr239Np

120573

997888rarr239Pu (4)

5 Conclusion




2and PuO

2TRISO


2




119875th = 1000MW Case1(a) 1(b) 1(c) 2 3



119866

BOC 13843 14864 13513 12314 9998EOC 5271 4688 4975 3590 1568EOC 2196 2138 2150 1880 947

PE [MW]BOC 722 673 740 812 1000EOC 1897 2133 2010 2785 6377EOC 4554 4677 4651 5319 10560










6After 30 days (119896eff = 090)




2









2After 25 days (119896eff = 090)

Competing Interests


Acknowledgments


References




2spent











































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of





















Fuel kernelD = 05mm




LBE 11344 Pb 44598 Bi 555

He 01786 He 100ThO2

988 232Th 100

UO2

1054235U 75 15 225238U 925 85 775

lowastPuO2

1150

238Pu 353535239Pu 450154240Pu 263505241Pu 159640242Pu 913483

lowastCmO2

1055

242Cm 391520243Cm 004721244Cm 855422245Cm 954125246Cm 095413


B4C 252

10B 1843111B 81569




21055






2 average


2 225 enriched

UO2 PuO

2 and CmO










2 225 enrichedUO

2

PuO2 andCmO








Case 2 ThO2and PuO



Case 3 ThO2and CmO




2and CmO




4C)


4C has


nuclear reactors






4 Numerical Results



2TRISO particles)


2and CmO





Pth (MW)

kef

fk

eff


Case 1(b)

Case 1(c)

Case 1(a)

090

091

092

093

094

095

096

097

098

099

100

60 120 180 240 300 360 4200


090

091

092

093

094

095

096

097

098

099

100

600540480420360300240180120600

090

091

092

093

094

095

096

097

098

099

100

kef

f

360240120 480 600 7200


100

300

500

700

1000

(a)

Case 1(a)

Case 1(b)

Case 1(c)

Pth (MW)1000900800700600500400300200100

Pth (MW)1000900800700600500400300200100

100

Pth (MW)1000900800700600500400300200

keff090

091

092

093

094

095

0

60

120

180

240

300

360

420

480

540

600

Ope

ratio

n tim

e (da

y)

0

60

120

180

240

300

360

420

480

540

600

660

720

780

Ope

ratio

n tim

e (da

y)

0

60

120

180

240

300

360

420

Ope

ratio

n tim

e (da

y)

(b)



Pth (MW)100

300

500

700

1000


090

091

092

093

094

095

096

097

098

099

100

kef

f

15001350120010509007506004503001500

Case 2

(a)

keff

0

150

300

450

600

750

900

1050

1200

1350

1500

Ope

ratio

n tim

e (da

y)Pth (MW)

1000900800700600500400300200100

090

091

092

093

094

095

Case 2

(b)


Case 3

Pth (MW)100

300

500

700

1000


090

091

092

093

094

095

096

097

098

099

100

kef

f

(a)

Pth (MW)1000900800700600500400300200100

095

094

093

092

091

090

0

2

4

6

8

10

12

14

16

18

20

Ope

ratio

n tim

e (da

y)

keff

Case 3

(b)



BOC

BOC

After 30 days

keff = 098

keff = 098

keff = 095

keff = 090

Γ = 1021

Γ = 1973

Γ = 1173

Γ = 1443

16015014013012011010090807060

Radius (cm)

00E + 00

10E minus 05

20E minus 05

30E minus 05

40E minus 05

50E minus 05

60E minus 05

70E minus 05

80E minus 05

After 1 day

Case 1(c)

BOC

BOC


keff = 098

keff = 098

keff = 095

keff = 090

Γ = 1027

Γ = 1868

Γ = 1182

Γ = 1464

16015014013012011010090807060


00E + 00

10E minus 05

20E minus 05

30E minus 05

40E minus 05

50E minus 05

60E minus 05

70E minus 05


RfD

(rea

ctio

nsc

m3)

BOC

BOC


keff = 098

keff = 098

keff = 095

keff = 090

Γ = 1029

Γ = 1973

Γ = 1191

Γ = 1454

1601501401301201101009080706000E + 00

10E minus 05

20E minus 05

30E minus 05

40E minus 05

50E minus 05

60E minus 05

70E minus 05


RfD

(rea

ctio

nsc

m3)

RfD

(rea

ctio

nsc

m3)




BOC

BOC Γ = 1029

Γ = 1899

Γ = 1246Γ = 1569


Radius (cm)16015014013012011010090807060

Case 2

RfD

(rea

ctio

nsc

m3)

keff = 098

keff = 098

keff = 095

keff = 090

00E + 00

10E minus 05

20E minus 05

30E minus 05

40E minus 05

50E minus 05

60E minus 05

70E minus 05

80E minus 05








BOCBOC

keff = 098

keff = 098

keff = 095

keff = 090

Γ = 1024

Γ = 1630

Γ = 1307Γ = 1477


Radius (cm)16015014013012011010090807060

Case 3

RfD

(rea

ctio

nsc

m3)

00E + 00

10E minus 05

20E minus 05

30E minus 05

40E minus 05

50E minus 05

60E minus 05

70E minus 05

80E minus 05




MTUΔ119905 (1)





119866 =

119877119891119864119891

119864119901

(2a)

or

119866 =119875thPE (2b)




2





232Th (n 120574) 233Th120573

997888rarr233Pa

120573

997888rarr233U (3)


2TRISO particles)


2



238U (n 120574) 239U120573

997888rarr239Np

120573

997888rarr239Pu (4)

5 Conclusion




2and PuO

2TRISO


2




119875th = 1000MW Case1(a) 1(b) 1(c) 2 3



119866

BOC 13843 14864 13513 12314 9998EOC 5271 4688 4975 3590 1568EOC 2196 2138 2150 1880 947

PE [MW]BOC 722 673 740 812 1000EOC 1897 2133 2010 2785 6377EOC 4554 4677 4651 5319 10560










6After 30 days (119896eff = 090)




2









2After 25 days (119896eff = 090)

Competing Interests


Acknowledgments


References




2spent











































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



















2 225 enrichedUO

2

PuO2 andCmO








Case 2 ThO2and PuO



Case 3 ThO2and CmO




2and CmO




4C)


4C has


nuclear reactors






4 Numerical Results



2TRISO particles)


2and CmO





Pth (MW)

kef

fk

eff


Case 1(b)

Case 1(c)

Case 1(a)

090

091

092

093

094

095

096

097

098

099

100

60 120 180 240 300 360 4200


090

091

092

093

094

095

096

097

098

099

100

600540480420360300240180120600

090

091

092

093

094

095

096

097

098

099

100

kef

f

360240120 480 600 7200


100

300

500

700

1000

(a)

Case 1(a)

Case 1(b)

Case 1(c)

Pth (MW)1000900800700600500400300200100

Pth (MW)1000900800700600500400300200100

100

Pth (MW)1000900800700600500400300200

keff090

091

092

093

094

095

0

60

120

180

240

300

360

420

480

540

600

Ope

ratio

n tim

e (da

y)

0

60

120

180

240

300

360

420

480

540

600

660

720

780

Ope

ratio

n tim

e (da

y)

0

60

120

180

240

300

360

420

Ope

ratio

n tim

e (da

y)

(b)



Pth (MW)100

300

500

700

1000


090

091

092

093

094

095

096

097

098

099

100

kef

f

15001350120010509007506004503001500

Case 2

(a)

keff

0

150

300

450

600

750

900

1050

1200

1350

1500

Ope

ratio

n tim

e (da

y)Pth (MW)

1000900800700600500400300200100

090

091

092

093

094

095

Case 2

(b)


Case 3

Pth (MW)100

300

500

700

1000


090

091

092

093

094

095

096

097

098

099

100

kef

f

(a)

Pth (MW)1000900800700600500400300200100

095

094

093

092

091

090

0

2

4

6

8

10

12

14

16

18

20

Ope

ratio

n tim

e (da

y)

keff

Case 3

(b)



BOC

BOC

After 30 days

keff = 098

keff = 098

keff = 095

keff = 090

Γ = 1021

Γ = 1973

Γ = 1173

Γ = 1443

16015014013012011010090807060

Radius (cm)

00E + 00

10E minus 05

20E minus 05

30E minus 05

40E minus 05

50E minus 05

60E minus 05

70E minus 05

80E minus 05

After 1 day

Case 1(c)

BOC

BOC


keff = 098

keff = 098

keff = 095

keff = 090

Γ = 1027

Γ = 1868

Γ = 1182

Γ = 1464

16015014013012011010090807060


00E + 00

10E minus 05

20E minus 05

30E minus 05

40E minus 05

50E minus 05

60E minus 05

70E minus 05


RfD

(rea

ctio

nsc

m3)

BOC

BOC


keff = 098

keff = 098

keff = 095

keff = 090

Γ = 1029

Γ = 1973

Γ = 1191

Γ = 1454

1601501401301201101009080706000E + 00

10E minus 05

20E minus 05

30E minus 05

40E minus 05

50E minus 05

60E minus 05

70E minus 05


RfD

(rea

ctio

nsc

m3)

RfD

(rea

ctio

nsc

m3)




BOC

BOC Γ = 1029

Γ = 1899

Γ = 1246Γ = 1569


Radius (cm)16015014013012011010090807060

Case 2

RfD

(rea

ctio

nsc

m3)

keff = 098

keff = 098

keff = 095

keff = 090

00E + 00

10E minus 05

20E minus 05

30E minus 05

40E minus 05

50E minus 05

60E minus 05

70E minus 05

80E minus 05








BOCBOC

keff = 098

keff = 098

keff = 095

keff = 090

Γ = 1024

Γ = 1630

Γ = 1307Γ = 1477


Radius (cm)16015014013012011010090807060

Case 3

RfD

(rea

ctio

nsc

m3)

00E + 00

10E minus 05

20E minus 05

30E minus 05

40E minus 05

50E minus 05

60E minus 05

70E minus 05

80E minus 05




MTUΔ119905 (1)





119866 =

119877119891119864119891

119864119901

(2a)

or

119866 =119875thPE (2b)




2





232Th (n 120574) 233Th120573

997888rarr233Pa

120573

997888rarr233U (3)


2TRISO particles)


2



238U (n 120574) 239U120573

997888rarr239Np

120573

997888rarr239Pu (4)

5 Conclusion




2and PuO

2TRISO


2




119875th = 1000MW Case1(a) 1(b) 1(c) 2 3



119866

BOC 13843 14864 13513 12314 9998EOC 5271 4688 4975 3590 1568EOC 2196 2138 2150 1880 947

PE [MW]BOC 722 673 740 812 1000EOC 1897 2133 2010 2785 6377EOC 4554 4677 4651 5319 10560










6After 30 days (119896eff = 090)




2









2After 25 days (119896eff = 090)

Competing Interests


Acknowledgments


References




2spent











































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















Pth (MW)

kef

fk

eff


Case 1(b)

Case 1(c)

Case 1(a)

090

091

092

093

094

095

096

097

098

099

100

60 120 180 240 300 360 4200


090

091

092

093

094

095

096

097

098

099

100

600540480420360300240180120600

090

091

092

093

094

095

096

097

098

099

100

kef

f

360240120 480 600 7200


100

300

500

700

1000

(a)

Case 1(a)

Case 1(b)

Case 1(c)

Pth (MW)1000900800700600500400300200100

Pth (MW)1000900800700600500400300200100

100

Pth (MW)1000900800700600500400300200

keff090

091

092

093

094

095

0

60

120

180

240

300

360

420

480

540

600

Ope

ratio

n tim

e (da

y)

0

60

120

180

240

300

360

420

480

540

600

660

720

780

Ope

ratio

n tim

e (da

y)

0

60

120

180

240

300

360

420

Ope

ratio

n tim

e (da

y)

(b)



Pth (MW)100

300

500

700

1000


090

091

092

093

094

095

096

097

098

099

100

kef

f

15001350120010509007506004503001500

Case 2

(a)

keff

0

150

300

450

600

750

900

1050

1200

1350

1500

Ope

ratio

n tim

e (da

y)Pth (MW)

1000900800700600500400300200100

090

091

092

093

094

095

Case 2

(b)


Case 3

Pth (MW)100

300

500

700

1000


090

091

092

093

094

095

096

097

098

099

100

kef

f

(a)

Pth (MW)1000900800700600500400300200100

095

094

093

092

091

090

0

2

4

6

8

10

12

14

16

18

20

Ope

ratio

n tim

e (da

y)

keff

Case 3

(b)



BOC

BOC

After 30 days

keff = 098

keff = 098

keff = 095

keff = 090

Γ = 1021

Γ = 1973

Γ = 1173

Γ = 1443

16015014013012011010090807060

Radius (cm)

00E + 00

10E minus 05

20E minus 05

30E minus 05

40E minus 05

50E minus 05

60E minus 05

70E minus 05

80E minus 05

After 1 day

Case 1(c)

BOC

BOC


keff = 098

keff = 098

keff = 095

keff = 090

Γ = 1027

Γ = 1868

Γ = 1182

Γ = 1464

16015014013012011010090807060


00E + 00

10E minus 05

20E minus 05

30E minus 05

40E minus 05

50E minus 05

60E minus 05

70E minus 05


RfD

(rea

ctio

nsc

m3)

BOC

BOC


keff = 098

keff = 098

keff = 095

keff = 090

Γ = 1029

Γ = 1973

Γ = 1191

Γ = 1454

1601501401301201101009080706000E + 00

10E minus 05

20E minus 05

30E minus 05

40E minus 05

50E minus 05

60E minus 05

70E minus 05


RfD

(rea

ctio

nsc

m3)

RfD

(rea

ctio

nsc

m3)




BOC

BOC Γ = 1029

Γ = 1899

Γ = 1246Γ = 1569


Radius (cm)16015014013012011010090807060

Case 2

RfD

(rea

ctio

nsc

m3)

keff = 098

keff = 098

keff = 095

keff = 090

00E + 00

10E minus 05

20E minus 05

30E minus 05

40E minus 05

50E minus 05

60E minus 05

70E minus 05

80E minus 05








BOCBOC

keff = 098

keff = 098

keff = 095

keff = 090

Γ = 1024

Γ = 1630

Γ = 1307Γ = 1477


Radius (cm)16015014013012011010090807060

Case 3

RfD

(rea

ctio

nsc

m3)

00E + 00

10E minus 05

20E minus 05

30E minus 05

40E minus 05

50E minus 05

60E minus 05

70E minus 05

80E minus 05




MTUΔ119905 (1)





119866 =

119877119891119864119891

119864119901

(2a)

or

119866 =119875thPE (2b)




2





232Th (n 120574) 233Th120573

997888rarr233Pa

120573

997888rarr233U (3)


2TRISO particles)


2



238U (n 120574) 239U120573

997888rarr239Np

120573

997888rarr239Pu (4)

5 Conclusion




2and PuO

2TRISO


2




119875th = 1000MW Case1(a) 1(b) 1(c) 2 3



119866

BOC 13843 14864 13513 12314 9998EOC 5271 4688 4975 3590 1568EOC 2196 2138 2150 1880 947

PE [MW]BOC 722 673 740 812 1000EOC 1897 2133 2010 2785 6377EOC 4554 4677 4651 5319 10560










6After 30 days (119896eff = 090)




2









2After 25 days (119896eff = 090)

Competing Interests


Acknowledgments


References




2spent











































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















Pth (MW)100

300

500

700

1000


090

091

092

093

094

095

096

097

098

099

100

kef

f

15001350120010509007506004503001500

Case 2

(a)

keff

0

150

300

450

600

750

900

1050

1200

1350

1500

Ope

ratio

n tim

e (da

y)Pth (MW)

1000900800700600500400300200100

090

091

092

093

094

095

Case 2

(b)


Case 3

Pth (MW)100

300

500

700

1000


090

091

092

093

094

095

096

097

098

099

100

kef

f

(a)

Pth (MW)1000900800700600500400300200100

095

094

093

092

091

090

0

2

4

6

8

10

12

14

16

18

20

Ope

ratio

n tim

e (da

y)

keff

Case 3

(b)



BOC

BOC

After 30 days

keff = 098

keff = 098

keff = 095

keff = 090

Γ = 1021

Γ = 1973

Γ = 1173

Γ = 1443

16015014013012011010090807060

Radius (cm)

00E + 00

10E minus 05

20E minus 05

30E minus 05

40E minus 05

50E minus 05

60E minus 05

70E minus 05

80E minus 05

After 1 day

Case 1(c)

BOC

BOC


keff = 098

keff = 098

keff = 095

keff = 090

Γ = 1027

Γ = 1868

Γ = 1182

Γ = 1464

16015014013012011010090807060


00E + 00

10E minus 05

20E minus 05

30E minus 05

40E minus 05

50E minus 05

60E minus 05

70E minus 05


RfD

(rea

ctio

nsc

m3)

BOC

BOC


keff = 098

keff = 098

keff = 095

keff = 090

Γ = 1029

Γ = 1973

Γ = 1191

Γ = 1454

1601501401301201101009080706000E + 00

10E minus 05

20E minus 05

30E minus 05

40E minus 05

50E minus 05

60E minus 05

70E minus 05


RfD

(rea

ctio

nsc

m3)

RfD

(rea

ctio

nsc

m3)




BOC

BOC Γ = 1029

Γ = 1899

Γ = 1246Γ = 1569


Radius (cm)16015014013012011010090807060

Case 2

RfD

(rea

ctio

nsc

m3)

keff = 098

keff = 098

keff = 095

keff = 090

00E + 00

10E minus 05

20E minus 05

30E minus 05

40E minus 05

50E minus 05

60E minus 05

70E minus 05

80E minus 05








BOCBOC

keff = 098

keff = 098

keff = 095

keff = 090

Γ = 1024

Γ = 1630

Γ = 1307Γ = 1477


Radius (cm)16015014013012011010090807060

Case 3

RfD

(rea

ctio

nsc

m3)

00E + 00

10E minus 05

20E minus 05

30E minus 05

40E minus 05

50E minus 05

60E minus 05

70E minus 05

80E minus 05




MTUΔ119905 (1)





119866 =

119877119891119864119891

119864119901

(2a)

or

119866 =119875thPE (2b)




2





232Th (n 120574) 233Th120573

997888rarr233Pa

120573

997888rarr233U (3)


2TRISO particles)


2



238U (n 120574) 239U120573

997888rarr239Np

120573

997888rarr239Pu (4)

5 Conclusion




2and PuO

2TRISO


2




119875th = 1000MW Case1(a) 1(b) 1(c) 2 3



119866

BOC 13843 14864 13513 12314 9998EOC 5271 4688 4975 3590 1568EOC 2196 2138 2150 1880 947

PE [MW]BOC 722 673 740 812 1000EOC 1897 2133 2010 2785 6377EOC 4554 4677 4651 5319 10560










6After 30 days (119896eff = 090)




2









2After 25 days (119896eff = 090)

Competing Interests


Acknowledgments


References




2spent











































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















BOC

BOC

After 30 days

keff = 098

keff = 098

keff = 095

keff = 090

Γ = 1021

Γ = 1973

Γ = 1173

Γ = 1443

16015014013012011010090807060

Radius (cm)

00E + 00

10E minus 05

20E minus 05

30E minus 05

40E minus 05

50E minus 05

60E minus 05

70E minus 05

80E minus 05

After 1 day

Case 1(c)

BOC

BOC


keff = 098

keff = 098

keff = 095

keff = 090

Γ = 1027

Γ = 1868

Γ = 1182

Γ = 1464

16015014013012011010090807060


00E + 00

10E minus 05

20E minus 05

30E minus 05

40E minus 05

50E minus 05

60E minus 05

70E minus 05


RfD

(rea

ctio

nsc

m3)

BOC

BOC


keff = 098

keff = 098

keff = 095

keff = 090

Γ = 1029

Γ = 1973

Γ = 1191

Γ = 1454

1601501401301201101009080706000E + 00

10E minus 05

20E minus 05

30E minus 05

40E minus 05

50E minus 05

60E minus 05

70E minus 05


RfD

(rea

ctio

nsc

m3)

RfD

(rea

ctio

nsc

m3)




BOC

BOC Γ = 1029

Γ = 1899

Γ = 1246Γ = 1569


Radius (cm)16015014013012011010090807060

Case 2

RfD

(rea

ctio

nsc

m3)

keff = 098

keff = 098

keff = 095

keff = 090

00E + 00

10E minus 05

20E minus 05

30E minus 05

40E minus 05

50E minus 05

60E minus 05

70E minus 05

80E minus 05








BOCBOC

keff = 098

keff = 098

keff = 095

keff = 090

Γ = 1024

Γ = 1630

Γ = 1307Γ = 1477


Radius (cm)16015014013012011010090807060

Case 3

RfD

(rea

ctio

nsc

m3)

00E + 00

10E minus 05

20E minus 05

30E minus 05

40E minus 05

50E minus 05

60E minus 05

70E minus 05

80E minus 05




MTUΔ119905 (1)





119866 =

119877119891119864119891

119864119901

(2a)

or

119866 =119875thPE (2b)




2





232Th (n 120574) 233Th120573

997888rarr233Pa

120573

997888rarr233U (3)


2TRISO particles)


2



238U (n 120574) 239U120573

997888rarr239Np

120573

997888rarr239Pu (4)

5 Conclusion




2and PuO

2TRISO


2




119875th = 1000MW Case1(a) 1(b) 1(c) 2 3



119866

BOC 13843 14864 13513 12314 9998EOC 5271 4688 4975 3590 1568EOC 2196 2138 2150 1880 947

PE [MW]BOC 722 673 740 812 1000EOC 1897 2133 2010 2785 6377EOC 4554 4677 4651 5319 10560










6After 30 days (119896eff = 090)




2









2After 25 days (119896eff = 090)

Competing Interests


Acknowledgments


References




2spent











































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of





















BOCBOC

keff = 098

keff = 098

keff = 095

keff = 090

Γ = 1024

Γ = 1630

Γ = 1307Γ = 1477


Radius (cm)16015014013012011010090807060

Case 3

RfD

(rea

ctio

nsc

m3)

00E + 00

10E minus 05

20E minus 05

30E minus 05

40E minus 05

50E minus 05

60E minus 05

70E minus 05

80E minus 05




MTUΔ119905 (1)





119866 =

119877119891119864119891

119864119901

(2a)

or

119866 =119875thPE (2b)




2





232Th (n 120574) 233Th120573

997888rarr233Pa

120573

997888rarr233U (3)


2TRISO particles)


2



238U (n 120574) 239U120573

997888rarr239Np

120573

997888rarr239Pu (4)

5 Conclusion




2and PuO

2TRISO


2




119875th = 1000MW Case1(a) 1(b) 1(c) 2 3



119866

BOC 13843 14864 13513 12314 9998EOC 5271 4688 4975 3590 1568EOC 2196 2138 2150 1880 947

PE [MW]BOC 722 673 740 812 1000EOC 1897 2133 2010 2785 6377EOC 4554 4677 4651 5319 10560










6After 30 days (119896eff = 090)




2









2After 25 days (119896eff = 090)

Competing Interests


Acknowledgments


References




2spent











































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



















119875th = 1000MW Case1(a) 1(b) 1(c) 2 3



119866

BOC 13843 14864 13513 12314 9998EOC 5271 4688 4975 3590 1568EOC 2196 2138 2150 1880 947

PE [MW]BOC 722 673 740 812 1000EOC 1897 2133 2010 2785 6377EOC 4554 4677 4651 5319 10560










6After 30 days (119896eff = 090)




2









2After 25 days (119896eff = 090)

Competing Interests


Acknowledgments


References




2spent











































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of






















2After 25 days (119896eff = 090)

Competing Interests


Acknowledgments


References




2spent











































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of














































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of

















research article time-dependent neutronic analysis of a

Documents