Monte Carlo modeling of spallation targets containing uranium and americium
Yury Malyshkin, Igor Pshenichnov, Igor Mishustin, Walter Greiner
MMonte Carlo modeling of spallation targets containing uranium andamericium
Yury Malyshkin a , Igor Pshenichnov a,b , Igor Mishustin a,c , Walter Greiner a a Frankfurt Institute for Advanced Studies, J.-W. Goethe University, 60438 Frankfurt am Main, Germany b Institute for Nuclear Research, Russian Academy of Sciences, 117312 Moscow, Russia c National Research Center “Kurchatov Institute”, 123182 Moscow, Russia
Abstract
Neutron production and transport in spallation targets made of uranium and americium are studied witha Geant4-based code MCADS (Monte Carlo model for Accelerator Driven Systems). A good agreementof MCADS results with experimental data on neutron- and proton-induced reactions on
Am and
Amnuclei allows to use this model for simulations with extended Am targets. It was demonstrated that MCADSmodel can be used for calculating the values of critical mass for , U, Np,
Pu and
Am. Severalgeometry options and material compositions (U, U+Am, Am, Am O ) are considered for spallation targetsto be used in Accelerator Driven Systems. All considered options operate as deep subcritical targets havingneutron multiplication factor of k ∼ .
5. It is found that more than 4 kg of Am can be burned in onespallation target during the first year of operation.
Keywords: spallation reactions, minor actinides, neutron sources, Accelerator Driven Systems, radioactivewaste
1. Introduction
Many neutrons can be produced in spallation nu-clear reactions [1, 2] induced by energetic protonsin collisions with heavy target nuclei like W, Ta, Biand Pb due to their enhanced neutron content withrespect to lighter nuclei. This method to create anintense flux of neutrons is known for decades and itis already employed in several existing [3, 4] spalla-tion neutron sources and will be used in the facili-ties to be constructed, e.g., in the ESS project [5].Such facilities are dedicated to neutron imaging andscattering experiments [6]. Accelerator Driven Sys-tems (ADS) aimed at energy production in subcrit-ical assemblies of fissile materials or burning nu-clear waste [7, 8] also use an intense proton beam toproduce neutrons in spallation targets. The designof a spallation target is a challenging part of suchprojects in view of high energy deposited by theproton beam and secondary particles and the radi-
Email addresses: [email protected] (Yury Malyshkin), [email protected] (IgorPshenichnov) ation damage of the target material. The perfor-mance of a target irradiated by a megawatt-powerproton beam was the subject of a dedicated exper-iment [9].Heavy materials like W, Ta, Bi and Pb are com-monly used in the design of spallation targets. Al-though the fission of such nuclei can, in principle, beinduced by energetic protons [10], its role in neu-tron production is negligible. However, an alter-native approach can be also considered to involvefissionable,
Th,
U [11], or even fissile, U, Am [12], materials in the design of a spallationtarget. The difference between these two groups ofmaterials consists in the capability of fissile mate-rial to sustain a nuclear chain reaction once a criti-cal mass of this material is accumulated. Such ma-terials can be either directly irradiated by a pro-ton beam, or used as a blanket surrounding a non-fissionable material impacted by protons. In bothcases neutron production is boosted due to addi-tional fission neutrons. As recently demonstratedby our calculations [13], the number of neutronsproduced per beam proton is about 3 times higherin a uranium target compared to one made of tung-
Preprint submitted to Elsevier August 22, 2018 a r X i v : . [ phy s i c s . i n s - d e t ] M a y ten, while the energy deposition calculated perproduced neutron remains comparable in both tar-gets. Therefore, a less powerful beam is needed toachieve the same neutron flux in the uranium tar-get as in the tungsten target, and the total energydeposition in both targets [13] remain comparable.Thermal energy released in fission reactions can beconverted to electricity and then support, at leastin part, the operation of the accelerator.Apart from the need to build intense neutronsources, using fissile materials in spallation tar-gets opens the possibility to transmute them infission reactions induced by primary protons andsecondary nucleons. Indeed, in addition to unuseduranium, each 1000 kg of spent nuclear fuel dis-charged from a light-water reactor typically containseveral kilograms of fissile transuranium elementslike plutonium and Minor Actinides (MA): neptu-nium, americium and curium [14]. Up to 99.9% ofplutonium can be extracted and then further usedin nuclear reactors [15]. However, other radioactiveelements, MA and long-lived fission products, arestill very hazardous due to their high radiotoxicity,and their release to environment has to be avoided.There are plans to confine them in very robust vit-rified blocks stored in deep geological repositories.Alternatively, MA contained in spent nuclear fuelcan be separated and recycled in a dedicated facilityoperating with fast neutrons (as thermal neutronsare not efficient). As demonstrated by many ded-icated studies, see e.g. [14], the extracted MA canbe efficiently transmuted into short-lived or stablefission products in fast reactors or in accelerator-driven reactor cores.Certainly, more theoretical and experimentalstudies are needed to design an intense fast-neutronsource or a spallation target containing fissionableor fissile materials. For many years experimen-tal studies of transmutation of long-lived radiotoxicnuclides have been carried out at the Joint Insti-tute for Nuclear Research in Dubna, Russia, in theframework of an international collaboration [16].In particular, Np and
Am were transmutedinto short-lived or stable nuclides by neutrons pro-duced by protons in a thick lead target. Within theproject called “Energy plus Transmutation” beamsof protons and deutrons were used, and the flux offast neutrons was amplified by a massive uraniumsleeve surrounding a non-fissile target [10, 17, 18].Detailed theoretical modeling of ADS prototypesshould precede their construction and operation.Therefore, a reliable computational tool based on modern software is necessary to foster studies inthe field of the accelerator-driven transmutation.A number of Monte Carlo codes have been used tosimulate neutron production and transport in spal-lation targets of ADS: PHITS [19], SHIELD [20],MCNPX [21] and others. However, to the best ofour knowledge, spallation targets containing Amwere not studied with these codes so far. In thepresent work we further develop our Geant4-basedcode MCADS (Monte Carlo model for Accelera-tor Driven Systems) [13, 22] in order to apply itfor fissile spallation targets containing U and Am.Modeling spallation targets containing americiumis motivated by the following two reasons [14].First, americium is the most abundant MA in spentnuclear fuel and its transmutation into relativelyshort-lived fission products can reduce the radiotox-icity of radioactive waste by an order of magnitude.Second, the operation of fast reactors with a highcontent of MA causes certain safety concerns. Al-ternatively, a subcritical system driven by an accel-erator could be a promising option to burn ameri-cium extracted from spent nuclear fuel.
2. Modeling of americium transmutation byslow and energetic nucleons
As demonstrated in our previous works [13, 22],all physics processes relevant to neutron generationand transport in conventional non-fissile and alsoin fissionable uranium targets can be successfullysimulated with the Geant4 toolkit [23, 24, 25]. Inparticular, these processes include spallation andfission reactions induced by primary protons andsecondary nucleons. Usually specific Geant4 simu-lations are performed with a set of physical modelsknown as a Physics List.All present calculations were performed withGeant4 of version 9.4 with patch 01 as in ourprevious works [13,22]. In this version of thetoolkit the following models are available for sim-ulating p -nucleus interactions: Bertini Cascade,Binary Cascade and Intra-Nuclear Cascade Li`egecoupled with the fission-evaporation model ABLA.These models are included in the QGSP BERT HP,QGSP BIC HP and QGSP INCL ABLA PhysicsLists, respectively. The prefix QGSP indicates thatquark-gluon string model is used for high-energyinteractions. All three Physics Lists employ HighPrecision (HP) model for neutron interactions be-low 20 MeV which use evaluated nuclear data li-braries described below. The ionization energy loss2f charged particles was simulated with StandardElectromagnetic Physics package of Geant4. Thephysics models used in Geant4 are described in de-tail in Geant4 Physics Manual [26].In Ref. [13] we have evaluated the performance ofthe above-mentioned physics models for tungstenand uranium targets irradiated by protons. Fis-sion cross sections and multiplicities of neutronsproduced in thin uranium targets by protons withenergies of 27, 63 and 1000 MeV were calculatedand compared with experimental data [27, 28]. Itwas demonstrated, that the INCL ABLA [29, 30]better describes the data as compared with othermodels. In particular, only INCL ABLA predictsthe fission cross section and the neutron multiplic-ity for 1000 MeV protons very close to data, withinthe uncertainty of the measurements. However,one can note that all the considered cascade mod-els become less accurate for proton energies below100 MeV [13].The average numbers of neutrons produced inextended tungsten and uranium targets irradi-ated by 400-1500 MeV protons were also calcu-lated and compared with experimental data, seeRef. [13]. As shown, also in this case the com-bination of INCL ABLA and NeutronHP mod-els provides the most accurate results, which dif-fer by less than 10% from the experimental data.The Bertini Cascade model mostly overestimates,while the Binary Cascade model underestimatesthe neutron yields. Therefore, we conclude thatthe QGSP INCL ABLA HP Physics List is the bestchoice among other options for simulating nuclearreactions in uranium and tungsten targets. Theaforementioned lack of accuracy for nucleons withenergies below 100 MeV does not affect significantlythe results, as such nucleons do not dominate in theconsidered spallation targets.In order to perform simulations with mate-rials containing americium several extensions ofthe Geant4 toolkit have been introduced in [31].This made possible the simulations of proton- andneutron-induced nuclear reactions and elastic scat-tering of nucleons on Am and other transuraniumnuclei. In our recent publication [32] the (p,f), (n,f)and (n, γ ) cross sections as well as mass distribu-tions of fission fragments, average number of neu-trons per fission event and secondary neutron spec-tra were calculated with MCADS for Am and
Am, and good agreement with experimental datawas obtained. This justifies using MCADS to simu-late extended targets containing
Am and
Am. The physics of transmutation of
Am and
Am nuclei by neutron irradiation can be wellunderstood from Fig. 1. Depending on the neu-tron energy both nuclei can either undergo fissionor be transformed via (n, γ ) reaction into A+1 iso-topes Am and
Am. After β − -decay with half-life times 16 h and 10 h these nuclei change finallyinto long-lived Cm and
Cm, respectively. Asharp rise of the fission cross section at incidentneutron energy of ∼ . Am and
Am over the neu-tron capture above 1 MeV. Therefore, fast neutronsproduced in primary spallation reactions and subse-quent neutron-induced fission reactions can be usedto burn
Am and
Am very efficiently. C r o ss S e c t i on ( ba r n ) Neutron energy (keV) Am (n, γ ) MCADS(n, γ ) ENDF/B-VII.1(n, γ ) Weston’85(n,f) MCADS(n,f) ENDF/B-VII.1(n,f) Laptev’04 0.01 0.1 1 10 100 C r o ss S e c t i on ( ba r n ) Am (n, γ ) MCADS(n, γ ) ENDF/B-VII.1(n, γ ) Jandel’08(n,f) MCADS(n,f) ENDF/B-VII.1(n,f) Alexandrov’83 Figure 1: Radiative neutron capture cross section (n, γ ),shown in red, and neutron-induced fission cross section (n,f),shown in blue, for Am (top) and
Am (bottom) nu-clei. MCADS results are represented by solid lines, crosssections from ENDF/B-VII.1 evaluated nuclear data library– by dashed lines. Measured cross sections, (n, γ ) for Amand
Am from Refs. [33, 34] are shown by triangles, and(n,f) cross section from Refs. [35, 36] – by squares.
The radiative neutron capture (n, γ ) and fission(n,f) cross sections calculated by MCADS by means3f the Monte Carlo modeling of neutron interactionswith a thin layer of Am or
Am are plotted inFig. 1 together with the corresponding experimen-tal data [33, 34, 35, 36]. Nuclear reactions inducedby neutrons with energy below 20 MeV are sim-ulated by MCADS on the basis of the evaluatednuclear data library JENDL-4.0 [37] converted intoa format readable by Geant4 [38]. It was found thatthe Geant4-compatible nuclear data files based onJENDL-4.0 provide the most accurate descriptionof the energy spectra of secondary neutrons with re-spect to other nuclear data libraries. The MCADSresults below 20 MeV can be compared to the crosssections extracted from ENDF/B-VII.1 [39], whichare also shown in Fig. 1. As seen from this figure, avery good agreement is obtained between MCADS,experimental data and ENDF/B-VII.1 data.
3. MCADS calculations of neutron multipli-cation in fissile materials
The key issue in designing a spallation target con-taining fissile materials is the calculation of the neu-tron multiplication factor to ensure that the targetoperates in a safe subcritical regime. Neutron mul-tiplication factor k is calculated with MCADS asthe ratio between the numbers of neutrons in thepresent and previous generations of neutrons aver-aged over many simulated events. The obvious con-dition is to keep k <
1, i.e. strictly in the subcriticalmode. The number of neutrons in the target is de-termined by the balance between their production,absorption and leakage through the target surface.In order to validate the MCADS model with re-spect to generation of fission neutrons and theirabsorption in (n, γ ) and (n,f) processes, we haveperformed simulations of neutron multiplication inbare (unreflected) spheres made of several fissilematerials listed in Table 1. The radius of eachsphere made of specific material was gradually in-creased until k asymptotically exceeded 1, and themass of such a sphere was defined as the criti-cal mass for the given material, see Table 1. Thecritical mass data published by the European Nu-clear Society [40] and Monte Carlo simulation re-sults obtained with JENDL-3.2 library for Npand
Am in Refs. [41] and [42] are also presentedin Table 1. The results of calculations with MCADSfor , U, Np and
Pu agree within 2–8%with the published data [40], but diverge by ∼ Am. We attribute this deviations to uncer-tainties of the nuclear data for
Am. As dis- cussed in Ref. [41], the calculated critical mass of
Am sphere is very sensitive to the cross sectionsof neutron-induced reactions tabulated in evaluatednuclear data libraries. The critical mass varies from55 to 106 kg depending on the nuclear data libraryused in simulations, while the results obtained withthe same library (JENDL-3.2), but with differentcodes (Polina [41] and MCNP [42]) agree quite well,see Table 1. New measurements and new evalu-ations of nuclear data for
Am are required toreduce these discrepancies. Presently, the lowestestimate of the critical mass of
Am ( ∼
55 kg)should be considered as a conservative safety limit.Much higher values of the critical mass are reportedfor
Am: from 155.7 to 548.6 kg [41] and from 143to 284 kg [42], again depending on the data libraryused in simulations. This indicates the degree ofuncertainties in nuclear data available for
Am.Following the validation of MCADS results forthe critical mass of the
Am sphere without ex-ternal irradiation, we investigated the criticalityissues for a cylindrical spallation target made ofpure
Am and irradiated by a proton beam. Thelength of the target was fixed at 150 mm to en-sure that all beam protons are stopped in the tar-get material, while the target radii were varied from40 mm to 110 mm. It was assumed that the tar-get was irradiated by a 600 MeV proton beam withthe transverse beam profile of 20 mm FWHM. InFig. 2 we show the time dependence of the aver-age number of neutrons inside the targets with thetarget radii of 40, 60, 80, 100, 106 and 110 mm.One can see that the average number of neutronsin the targets with radii 40–100 mm decreases atlate time because less neutrons are produced insidethe target volume than escape it or lost in nuclearinteractions. The number of neutrons saturates inthe target of 106 mm radius (with the weight of72.4 kg) just 30 ns after the impact of a beam pro-ton. This case is very close to the critical regimewith k = 0 . k = 1 . Am targets with typical radiiof ∼
50 mm and length of 150 mm irradiated by600 MeV protons will operate in a deep subcrit-ical regime with k ∼ .
7. This suggests that anequivalent amount of
Am can be used to build afissile spallation target. All geometrical configura-4 able 1: Calculated critical masses (kilograms) of bare spheres made of , U, Np,
Pu and
Am. Data from EuropeanNuclear Society [40] and Monte Carlo modeling results by Polina [41] and MCNP [42] codes both based on JENDL-3.2 libraryare given for comparison.
Material MCADS results data [40] calculations [41] calculations [42]
U 16.1 15.8
U 48.4 46.7
Np 62.4 63.6 75.0
Pu 10.8 10.0
Am 66.7 57.6 71.8 73.7
Time (ns) N u m b e r o f n e u t r on s i n t h e t a r g e t p (600 MeV) + Am241150x40 mm, k=0.64150x60 mm, k=0.82150x80 mm, k=0.90150x100 mm, k=0.979150x106 mm, k=0.999150x110 mm, k=1.013 Figure 2: Number of neutrons as a function of time inthe cylindrical targets made of
Am with the length of150 mm and various radii and irradiated by 600 MeV pro-tons. The neutron number is normalized per beam particle.The steady-state behavior (horizontal line) corresponds toapproaching critical regime with k = 0 . tions of spallation targets containing Am consid-ered below are also designed to operate in a deep-subcritical mode with k < .
4. Comparison of targets containing ura-nium and americium
The operation of spallation targets containinguranium can be simulated with confidence, as thenuclear data for nat
U and all its most abundantisotopes are reliable in all versions of nuclear datalibraries. The simulations of pure uranium tar-gets are very instructive for further comparisonwith U+Am and pure Am targets. Moreover, theneutrons from U fission can be used for the Amtransmutation. Therefore, we have performed sim-ulations of cylindrical targets made of nat
U, pure
Am, a mixture of
Am and
Am (57% and 43%, respectively) and americium oxide Am O with the same isotopic composition of Am. Thechoice of Am O is motivated by the fact thatamericium is usually extracted from spent nuclearfuel in the form of americium oxide. Each targethas the radius of 40 mm and length of 120 mm.All these targets have masses well below the criti-cal mass given in Sec. 3. It was assumed that thetargets were irradiated by the proton beam withthe FWHM of 20 mm and the energy of 600 MeV.The spatial distributions of neutron flux calcu-lated with MCADS for the considered four tar-gets are shown in Fig. 3. Although the resultsare given for the proton current of 10 mA, theycan be easily rescaled to the actual beam current.The average neutron flux in the americium target(1 . · n/s/cm ) is higher than in the uraniumone (1 . · n/s/cm ) due to a higher fissioncross section for Am. Since the fission cross sec-tion on Am is almost 3 times higher than on U,one could expect even a larger difference in favorof
Am. However, other reactions, like (n,2n),(n,3n), (n,4n), are much more probable on uraniumnuclei. As the result, the difference in the averageneutron flux between U and Am targets is reduced.As one can see from Fig. 3, the results for pure
Am and mixed
Am+
Am targets are verysimilar.Calculated spatial distributions of heat deposi-tion inside the considered targets are presented inFig. 4. As expected, in fissile spallation targetsa significant energy is deposited due to fission re-actions [22]. The difference between fission crosssection on Am and U leads to significantly largerenergy deposition in the americium targets (11.9–16.1 MW, depending on the isotope composition)compared to the uranium target (7.7 MW). There-fore, designing a cooling system for the Am targetmay cause a serious problem.The values of the average neutron flux (1 . · (cm) R ( c m ) × Average flux, n/s/cm2: 1.217328e+16Maximal flux, n/s/cm2: 4.973289e+16
U; beam FWHM: 20 mm nat p(600 MeV) + n/s/cm Z (cm) R ( c m ) × Average flux, n/s/cm2: 1.557999e+16Maximal flux, n/s/cm2: 4.747965e+16
Am; beam FWHM: 20 mm p(600 MeV) + n/s/cm Z (cm) R ( c m ) × Average flux, n/s/cm2: 1.441741e+16Maximal flux, n/s/cm2: 4.573794e+16
Am); beam FWHM: 20 mm
Am+ p(600 MeV) + ( n/s/cm Z (cm) R ( c m ) × Average flux, n/s/cm2: 1.058857e+16Maximal flux, n/s/cm2: 3.515257e+16 ; beam FWHM: 20 mm O + Amp(600 MeV) n/s/cm Figure 3: Distribution of the neutron flux inside cylindrical targets made of nat U, Am, mixture of
Am and
Am andAm O , all of the same dimensions specified in Table 2. The targets are irradiated by a 10 mA 600 MeV proton beam. (cm) R ( c m ) Total power, MW: 7.664180
U; beam FWHM: 20 mm nat p(600 MeV) + kW/cm Z (cm) R ( c m ) Total power, MW: 16.083296
Am; beam FWHM: 20 mm p(600 MeV) + kW/cm Z (cm) R ( c m ) Total power, MW: 14.045476
Am); beam FWHM: 20 mm
Am+ p(600 MeV) + ( kW/cm Z (cm) R ( c m ) Total power, MW: 9.307320 ; beam FWHM: 20 mm O + Amp(600 MeV) kW/cm Figure 4: Distribution of heat deposition inside cylindrical targets made of nat U, Am, mixture of
Am and
Am andAm O , all of the same dimensions specified in Table 2. The targets are irradiated by 600 MeV proton beam with current of10 mA. n/s/cm ) and heat deposition (11.9 MW) cal-culated for a pure Am target are lower comparedto a pure
Am target. This is explained by a lowerfission cross section of
Am compared to
Am,see Fig. 1. The corresponding values for the targetmade of the mixture of isotopes,
Am+
Am,are intermediate (1 . · n/s/cm and 14 MW)with respect to the monoisotopic targets.It is expected that an increased number of fis-sion reactions in a spallation target makes possibleto boost the transmutation rate of americium con-tained in the target. However, due to the additionalenergy released in fission events the heat depositionin the target rises too. As seen from Fig. 4, theenergy deposition in U and Am targets in thehottest region located close to the target axis ex-ceeds 100 kW/cm , which looks very problematicfrom technical point of view. Therefore, more so-phisticated target systems with a reduced energydeposition per fissioned Am nucleus are needed.By this reason we extended our calculations fortwo U targets containing Am as proposed in [13]and a pure
Am target mentioned above. Twotargets containing
Am considered in [13] wereschematically designed as following. In the firstcase
Am was uniformly mixed with U with 10%mass concentration and in the second case a cylin-drical core ( V = 200 cm ) of Am is placed inthe hottest region of the uranium target. In bothcases the target has the radius of 10 cm and lengthof 20 cm. The heat deposition values per burnedAm nucleus in these targets are several times higherthan the corresponding values for the pure ameri-cium targets because of additional fission events ofuranium nuclei which also produce neutrons.The numbers of Am fission events per beam par-ticle N fis are listed in Table 2 for the six targetscontaining Am and also for the nat U target takenas a reference case, where, accordingly, U fissionevents are counted. As seen from the table, de-pending on isotope composition 2 to 3 times morefission events per beam proton are estimated for thepure Am targets compared to the uranium target.Calculated energy deposition per fissioned Am nu-cleus,
Q/N fis , is also given in Table 2. For the pureAm target this value (203 MeV) is by 30% lowerthan for the uranium one (279 MeV). As expected,much more energy is deposited per Am fission eventin two U+Am targets (
Q/N fis = 901 MeV and739 MeV), because only a part of fission events cor-respond to Am and most of them to U, accordingto their concentration in the targets. Since Am O target contains less Am nuclei thanthe pure Am target, this leads to a lower numberof fission events and results, correspondingly, in alower neutron flux (1 . · n/s/cm ) and lowerenergy deposition (9.3 MW). The heat depositionper fission event Q/N fis = 229 MeV calculated forAm O target is close to the Q/N fis value for thepure
Am+
Am target.Finally, burning rates of Am calculated for 10 mAproton beam are presented in Table 2. It was as-sumed that the burning rates are proportional tothe number of Am fission events N fis in a corre-sponding target. As found, more than 0.5 kg of Am can be transmuted per month in the spal-lation target containing exclusively this isotope.Lower burning rates are estimated for other con-sidered geometry and material options, mostly dueto a lower Am content. The amount of americiumtransmuted during the first month of operationdm / dt(t = 0) can be used to calculate the amountof Am burned during the first year. In this estima-tion it is assumed that the amount of Am m ( t ) de-creases exponentially, m ( t ) = m exp( − t/τ ), fromits initial amount m with the characteristic time τ = m / (dm / dt(t = 0)). The corresponding re-sults are listed in the last column of Table 2 whichgives the minimum annual consumption of Am inthe considered spallation targets. Indeed, a possi-bility to upload additional quantities of Am to thetarget (e.g. on the regular monthly basis) can beconsidered, thus substantially increasing the trans-mutation capability of the ADS system. One canconclude, that Am can be more efficiently burned inthe spallation targets made of pure Am (more than4 kg of Am per year) compared to mixed U+Amtargets. However, the use of larger amounts of pureAm is restricted due to criticality issues.As shown in our previous publication [13], inthe spallation targets made of nat U the neutronproduction is significantly enhanced with respectto the tungsten targets of the same size due toadditional contribution of neutron-induced fissionof uranium nuclei. In the present study we havefound that even more neutrons are produced by fis-sion reactions in targets made of pure
Am and
Am. This follows from Table 3, where the num-bers of neutrons produced or absorbed in variousnuclear reactions are given per beam particle for nat U, Am and
Am targets of the same size.This means that even small Am targets are highlyefficient in incinerating Am in fission reactions. Thenumber of neutrons which escape from the targets8 able 2: Initial amount of Am, number of fission reactions on Am per beam proton, N fis , heat deposition per fissioned Amnucleus, Q/N fis , the burning rate of Am at the beginning of operation and the amount of Am transmuted in the first year ofoperation for various target options.
Material Length Radius Initial N fis Q/N fis dm / dt(t = 0) Burned in(cm) (cm) Am mass Burning rate first year(kg) (MeV) (g/month) (kg) nat U 12 4 0 2.74 * * — —U+ Am (10%) 20 10 11.7 1.84 901 120 1.4U+
Am (core) 20 10 2.68 2.25 739 147 1.6Pure
Am 12 4 8.24 7.91 203 514 4.3Pure
Am 12 4 8.24 5.49 216 357 3.4
Am+
Am 12 4 8.24 6.74 208 438 3.9Am O
12 4 6.46 4.07 229 265 2.5 * Number of fission reactions on U nuclei per beam proton. For all other target options N fis corresponds exclusively to Am fission events.are also presented in Table 3. Obviously, the num-ber of leaking neutrons is equal to the differencebetween the number of produced and absorbed neu-trons. The calculations show that about 45% moreneutrons are produced in Am target than in nat
Uone. This means that
Am target can serve as anintensive neutron source which can be used for var-ious applications.When dealing with spallation targets made of fis-sile materials one should consider also an additionalheat produced in fission reactions. The total heatdeposition Q and heat per leaked neutron are pre-sented in Table 4 for the same targets as before.One can see that about twice as much heat is gen-erated in the Am target as compared with nat
Uone. This means that a sophisticated cooling sys-tem is required for its operation.
5. Spallation targets made of Am with Ubooster and Be reflector
Several advanced geometry options of the spalla-tion target can be considered to increase the burn-ing rate of Am by enhancing the neutron flux insidethe target. Two such options are considered be-low. The first target option ( b ) consists of an Amcylinder covered by a 2 cm thick nat
U booster. Thesecond option ( c ) is additionally covered by a Bereflector which is 10 cm thick. The core of the bothtarget options consist of a
Am cylinder (rod)with the length of 150 mm and radius of 20 mm,which is also used alone as a reference target op-tion ( a ) for comparison. All three target options Table 3: Average contributions to neutron production andabsorption from different reaction channels and the numberof leaking neutrons for nat U, Am and
Am targets withthe length of 12 cm and radius of 4 cm. All numbers are givenper beam proton. nat U Am Amp + A 11.77 9.01 9.34(n,2n) 0.44 0.04 0.11(n,3n) 0.15 0.01 0.02(n,4n) 0.09 0.06 0.06(n, > * γ ) -0.45 -1.45 -1.00leak 20.12 29.14 24.40 * Only from neutron-induced fission below20 MeV.are schematically shown in Fig. 5 and their param-eters are listed in Table 5.Initially all the three targets contain four timesless
Am (2.58 kg) compared to the pure
Amtarget considered in Sec. 4. However, the numberof fission events per beam proton N fis in the target(c) is only twice as low as in the target of Sec. 4.This means that Am is burned more efficiently inthe presence of the booster, or with both boosterand reflector. At the same time Q/N fis calculatedin the Am core for option (c) is comparable to thesame parameter for the pure
Am target consid-9 able 5: Initial amount of Am, number of fission events on Am per beam proton, N fis , heat deposition per fissioned Amnucleus, Q/N fis , the burning rate of Am at the beginning of operation and the amount of Am transmuted in the first year ofoperation for various target options.
Material Initial N fis Q/N fis dm / dt(t = 0) Burned inAm mass Burning rate first year(kg) (MeV) (g/month) (kg) Am ( a ) 2.58 3.00 241 194 1.53 Am + U booster ( b ) 2.58 3.79 229 245 1.76 Am + U booster 2.58 3.95 228 256 1.79+ Be reflector ( c ) Table 4: Average heat deposition Q and heat depositionper leaked neutron Q/N calculated with MCADS for nat U, Am and
Am targets with the length of 12 cm andradius of 4 cm. All values are given per beam proton. nat U Am Am Q (MeV) 766 1608 1185 Q/N (MeV) 38.1 55.2 48.6
Figure 5: Geometry options: bare
Am cylinder (option a ), Am cylinder covered by a U booster (option b ) and Am cylinder covered by a nat
U booster and a Be reflector(option c ). The arrows indicate direction of the proton beam. ered in Sec. 4. The total power deposition in Amvolume calculated for options (b) and (c) (8.67 and8.98 MW, respectively) is much less than for thepure Am target (16.08 MW). This indicates theadvantages of more complicated target geometries(b) and (c) with respect to simple geometry, sinceadditional neutrons are produced in the U booster.We should also note that no essential improvement in the target performance was achieved by the ad-dition of the Be reflector.The absolute Am burning rates are smaller( ∼
200 g/month) than for the simple target ( ∼
500 g/month). However, the relative burning ratesare higher for the advanced options. Indeed, about42% of the initial Am mass is burned in the firstyear of ADS operation in the simple pure
Amtarget, as compared with 69% in the advanced tar-get (c).The distributions of the neutron flux and en-ergy deposition for the options (a)–(c) are shown inFigs. 6 and 7. As seen in these figures, the distri-butions are more uniform both along the axis of thetarget and its radius. One can see that adding thebooster and the reflector leads to increased averageneutron flux by about 50% and 90%, respectively.The highest neutron flux of 4 . · n/s/cm isreached locally in the target (c) with its averagevalue of 2 . · n/s/cm . The highest volumetricenergy deposition is below 70 kW/cm for the op-tions (b)–(c), which is twice as low as the value of140 kW/cm calculated for the simple Am tar-get.
6. Conclusions
In this paper we have applied the MCADS modelbased on the Geant4 toolkit for calculating neutronfields and heat deposition in spallation targets con-taining uranium and americium. We have investi-gated the criticality of such targets using the MonteCarlo method. We have demonstrated that the crit-ical mass of extended spallation targets containing
Am can be evaluated with MCADS by calculat-ing the corresponding neutron multiplication factoras a function of time elapsed since the impact of abeam proton. The MCADS results for the critical-ity of targets made of
Am provide a guide-line10 (cm) R ( c m ) × Average flux, n/s/cm2: 1.397831e+16Maximal flux, n/s/cm2: 3.728471e+16
Am rod; beam FWHM: 20 mm p(600 MeV) + n/s/cm Z (cm) R ( c m ) × Average flux, n/s/cm2: 2.155456e+16Maximal flux, n/s/cm2: 4.502735e+16
Am rod+Booster; beam FWHM: 20 mm p(600 MeV) + n/s/cm Z (cm) R ( c m ) × Average flux, n/s/cm2: 2.604993e+16Maximal flux, n/s/cm2: 4.894165e+16
Am rod+Booster+Reflector; beam FWHM: 20 mm p(600 MeV) + n/s/cm Figure 6: Distribution of neutron flux inside
Am cylindrical target (option a ), Am cylinder covered by a nat
U booster(option b ) and Am cylinder covered by the nat
U booster and a Be reflector (option c ). The distributions are calculated forthe targets irradiated by 600 MeV proton beam of 10 mA. (cm) R ( c m ) Total power, MW: 7.216660
Am rod; beam FWHM: 20 mm p(600 MeV) + kW/cm Z (cm) R ( c m ) Total power, MW: 8.666207
Am rod+Booster; beam FWHM: 20 mm p(600 MeV) + kW/cm Z (cm) R ( c m ) Total power, MW: 8.983042
Am rod+Booster+Reflector; beam FWHM: 20 mm p(600 MeV) + kW/cm Figure 7: Distribution of heat deposition inside
Am cylindrical target (option a ), Am cylinder covered by a nat
U booster(option b ) and Am cylinder covered by the nat
U booster and a Be reflector (option c ). The distributions are calculated forthe targets irradiated by 600 MeV proton beam of 10 mA. Am,
Am, their mixture orAm O ), 2.5–4.3 kg of Am can be transmuted intoshort-lived or stable fission fragments per year ofoperation in the spallation target of the ADS facil-ity irradiated by 600 MeV proton beam of 10 mA.The results of simulations with targets of differentmaterial composition show that the highest rate ofamericium incineration is achieved in the targetsmade of pure americium. As demonstrated by sim-ulations, when Am cylinder is covered by the Ubooster and shielded by the Be reflector, the rel-ative annual incineration rate of Am increases upto 69%. The burning rate may be increased by ∼
50% if uploading of additional quantities of Amto the spallation target is made on a regular ba-sis. Higher incineration rates can be obtained byincreasing the neutron multiplication factor up to k ∼ .
8. However, a high energy deposition in thesetargets creates serious challenges to their coolingsystems. Additional studies of technological issuesrelated to the high heat deposition and also to theradiation damage of target materials due to a veryhigh neutron flux predicted in the target are neededto prove the viability of the proposed concept.In the uranium targets with small admixture ofAm long-lived isotope
Np is produced followingthe capture of two neutrons by
U and the subse-quent beta-decay. However, our estimations showthat the amount of
Np produced after a yearof irradiation does not exceed 100 grams, which ismuch less than the mass of transmuted MA. Theneutron capture on Am nuclei leading to the pro-duction of heavier long-lived MA does not changethe total amount of MA in the target.In this paper we did not discuss a well-known so-lution where a spallation target of a full-scale ADSfacility is surrounded by an extended subcritical re-actor core [43, 44]. In this case one could not onlyuse neutrons escaped from the spallation target, butalso use additional neutrons produced in the reac-tor core to burn MA placed there. This may sig-nificantly, by a factor of 10 or more, increase theamount of burned MA [43] as compared with burn-ing only in the spallation target. Several such ADSfacilities can solve the problem of utilization of MAproduced in thermal reactors. The thermal energyproduced in the spallation target and reactor corecan be converted to electricity in order to cover (atleast partially) the energy consumed by the accel- erator.Finally, one can note that the highest neutronflux (4 . · n/s/cm ) is reached in the target withthe booster and reflector, and the average neutronflux (2 . · n/s/cm ) is also high in this tar-get. Therefore, the ADS facilities can be used tostudy the properties of materials under the impactof intense irradiation by fast neutrons, as well asfor basic research. Acknowledgments
Our calculations were performed at the Centerfor Scientific Computing (CSC) of the Goethe Uni-versity, Frankfurt am Main. We are grateful tothe staff of the Center for support. We thank toE. Mendoza and D. Cano-Ott (CIEMAT, Madrid)for providing the evaluated neutron data in Geant4-format. We are also thankful to Siemens AG forfinancial support.
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