CONICET Digital Nro.11513

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AnnalsofNuclearEnergy78(2015)10–14 ContentslistsavailableatScienceDirect Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene Feasibility study of a hybrid subcritical fission system driven by Plasma-Focus fusion neutrons Alejandro Claussea,⇑ , Leopoldo Sotob,c, Carlos Friedlib, Luis Altamiranod aCNEA-CONICETandUniversityofCentralBuenosAires,7000Tandil,Argentina bComisiónChilenadeEnergíaNuclear,Casilla188-D,Santiago,Chile cCenterforResearchandApplicationsinPlasmaPhysicsandPulsedPower,P4,Chile dDicontekLtda.,Santiago,Chile a r t i c l e i n f o a b s t r a c t Articlehistory: A feasibility analysis of a hybrid fusion–fission system consisting of a two-stage spherical subcritical Received13October2014 cascadedrivenbyaPlasmaFocusdeviceispresented.Theanalysisisbasedontheone-groupneutron Receivedinrevisedform24December2014 diffusionequation,whichwasappropriatelycasttoassesstheneutronicamplificationofasphericalcon- Accepted26December2014 figuration.Adesignchartwasproducedtoestimatetheoptimumdimensionsofthefissileshellsrequired toachievedifferentlevelsofneutronamplification.ItisfoundthatcascadesdrivenbyPlasmaFocusof tensofkJarefeasible.TheresultswerecorroboratedbymeansofMonteCarlocalculations. Keywords: (cid:2)2015ElsevierLtd.Allrightsreserved. Fusion–fissionhybrid PlasmaFocus Subcritical Breakeven Pulsedreactor 1.Introduction ADS(Nifeneckeretal.,2003).Inthelastdecadehasbeenarenewed interest in ADS systems, including experimental validations The concept of hybrid nuclear reactors combining fusion and (Shahbunder et al., 2010), comprehensive physical (Wang et al., fissionprocesseswasfirstproposedinthedecadeof1950(seeref- 2013) and economic analysis (Steer et al., 2012; Gulik and erencesinNifeneckeretal.,2003)andwasreactivatedlaterinthe Tkaczyk,2014).Veryrecentlythecommissioningofazeropower 70s(Bethe,1979).Afterthat,theinterestinthehybridideawaned, experimentalsubcriticalfacilityhasbeenreportedinIndia(Sinha not so much because of technical difficulties but for lack of etal.,2015).Also,basedonthetheoryofADSanisotopesourcedri- economic incentive. This remained so until the last two decades, vensubcriticalbatterywasproposed(WangandHe,2014). duringwhichtheinterestinhybridshasagainincreasedfortheir Itisgenerallyacceptedthatforsecurityandcontrolreasons,the possible application in energy production, either using Uranium effectivemultiplicationfactorofasubcriticaldrivensystemshould fuelorcombiningbreedersystemswithThoriumfuelcycles,and belimitedtoabout0.98forfast-neutronreactorsand0.95forther- also for the destruction of nuclear waste (Abalin et al., 1995; malreactors(Nifeneckeretal.,2003).Thislimitation,inprinciple, Gerstner, 2009; Freidberg and Kadak, 2009; Kotschenreuther imposes an upper bound to the amplification factor. In order to etal.,2009). increase the amplification without compromising the subcritical Thecentralconceptofhybridsistosurroundafusionsourceof condition,theconceptofcascadereactorswasintroducedasearly neutronswithfissilefuelconfiguredinsuchawaythatthewhole asthe50s(Borst,1957;Avery,1958;Dubovskii,1959)andreacti- systemissubcritical.Theneutronsinjectedbythesource,usually vated in the 90s by Daniel and Petrov (1996) and Barzilov et al. as a train of pulses, are then multiplied by fissions, generating a (1996).Recently,controlandsafetyissuesofspecificcascadecon- total energy that in principle should be larger than the input figurationswereanalyzedusingMonteCarlomethods,inspherical energyrequiredforthefusionprocess.Themostpopularneutron (Kolesov and Khoruzhii, 2003) and cylindrical geometries drivers that were proposed are spallation targets pumped by (Gulevich et al., 2007). Essentially a cascade or diode subcritical protonorelectronaccelerators,calledAcceleratorDrivenSystems, reactor consists of two multiplying sections (generally separated spatially)withasymmetriccoupling,insuchawaythatneutrons ⇑ produced in the first section easily penetrate the second while Correspondingauthor.Tel./fax:+542494385690. thoseproducedinthesecondhavelittleinfluenceoverthefirst. E-mailaddress:[email protected](A.Clausse). http://dx.doi.org/10.1016/j.anucene.2014.12.028 0306-4549/(cid:2)2015ElsevierLtd.Allrightsreserved.

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A.Clausseetal./AnnalsofNuclearEnergy78(2015)10–14 11 Ontheneutronsourceside,thealternativestoacceleratorsor @n (cid:2)Dmr2n¼(cid:2)R mnþtRmnþS ð1Þ laser induced neutrons are fusion neutron sources. For example, @t a f Moiseenkoetal.(2010)proposedastellarator-mirrordrivenreac- where nðx;tÞ is the neutron density, v is the average neutron tor.Theworkreportedhereisfocusedonassessingthefeasibility velocity, D is the diffusion constant, R and R are the absorption a f ofhybridfusion–fissionsystemsdrivenbyPlasmaFocus(PF)neu- andfissionmacroscopiccrosssections,tistheaveragenumberof tron sources. PF devices are special types of dense z-pinch dis- neutronsproducedperfission,andSisanexternalsource. chargesthatareveryefficient,bothtechnicallyandeconomically, Furthermore,letusassumethatthespatialdependenceofthe in producing neutron pulses within certain modest ranges, when neutronic density can be described by the Helmholtz equation operating with Deuterium or Deuterium–Tritium gases (Bernard (Hetrick,1971): et al., 1998; Moreno et al., 2002; Soto et al., 2008; Soto et al., 2010). Essentially, a PF is a high-voltage pulsed discharge in a r2nþB2n¼0 ð2Þ gasatlowpressureinducedbetweentwocoaxialcylindricalelec- where B2 is an effective geometrical buckling. This is a strong trodes separated by an insulator. The discharge starts over the assumptionthatshouldonlybetakenasanapproximationinorder insulator surface producing a plasma sheath that comes off and toproduceananalyticalexpressionoftheneutronicamplification isacceleratedaxiallybythemagneticfieldautogeneratedbythe intermsofgeometricparameters.Therefore,theresultswillneed current. After the current sheath runs over the upper end of the tobecorroboratedbyMonteCarlocalculations. central electrode, the plasma is compressed in a small region, Thetrainofperiodicpulsesinjectedbythesourceswillleadtoa calledfocusorpinch,wherepeaksofhighdensityandtemperature sustainedoscillatoryregimeofn.Ineachregion, substituting the areachieved.WhenthegasisDeuteriumormixturesofDeuterium spatial variation in the diffusion term in Eq. (1) according to Eq. and Tritium, fusion nuclear reactions are produced in the pinch (2), and then integrating over a temporal cycle with its periodic generatingneutronspulses.Theneutronyielddependsonseveral boundaryconditionsandoverthevolume,yields: design and operating parameters, namely, pinch current, filling ! pressure,geometricaldimensionsoftheelectrodes,amongothers. DB2þR ZZ a(cid:2)1 F¼ SdtdV ð3Þ Ingeneral terms,whenmostparametersare optimized,thepeak tR f neutronyieldisroughlyproportionaltothesquareoftheenergy stored in the capacitors. With Deuterium, the peak yield ranges where from104neutronspershotfortabletopdevicesoperatingattens ZZ of joules (Soto et al., 2008) to 1011 neutrons per shot for several F¼tR f mndtdV ð4Þ cubic-meter devices operating around 1MJ (Schdmidt et al., 2002). The neutron yield increases in two orders of magnitude isthenumberoffissionneutronsproducedintheregionduringthe using Deuterium–Tritium mixtures (Mather, 1971). There are a cycle. few studies that entertained the idea of using a PF device as the Notethatthetimederivativewouldgivevaluesoftheneutron seedof neutronsfor ahybridfusion–fissionsystem (Gribkovand densityatthebeginningandendofthecycle.However,theseare Tyagunov, 1983; Zoita and Lungu, 2001). Those studies analyzed identicalinthepermanentoscillatoryregimeandthereforecancel thesimplestarrayofasinglesubcriticalregionhostingaPFdevice, becausethereactorprocessisperiodic. concluding that, achieving break-even conditions would require Now, let us consider the special coupled case of a cascade, energiesashighas10MJcapableofdelivercurrentsof20MAin consisting of a core region 1 hosting an external neutron source, 1ls to produce pulses of 1018 neutrons. Alas, that sort of figure whichiscompletelysurroundedbyamultiplicativeblanketregion is out of the range of the current technology. In effect, although 2.Thecouplingisnotsymmetric,thatis,alltheneutronsleaking since their invention 50years ago several projects were carried fromregion1arriveinregion2,whereasonlyafractionofthose outtopushhighertheupperenergylimitofPFfacilities,theneu- produced in the latter penetrates the former. Then, for regions 1 tron production ceases to increase beyond 1MJ (Nukulin and and2,Eq.(3)boilsdownto: Polukhin,2007;Lee,2009). ! ! DB2þR DB2 Inthisarticle,thefeasibilityofhybridsystemsdrivenbyPFneu- a(cid:2)1 F (cid:2)c F ¼S ð5Þ tR 1 tR 2 tron pulses is revisited. The analysis starts from the model of a f f 1 2 two-stage cascade presented by Barzilov et al. (1996), which is ! ! herespecifiedforasphericalgeometry,derivingasetofequations DB2 DB2þR (cid:2) F þ a(cid:2)1 F ¼0 ð6Þ to assess the neutronic amplification in terms of the geometric tR 1 tR 2 f f parameters. The occurrence of optimum configurations is deter- 1 2 minedhere for two sphericalfissionblankets,varyingthe sizeof Note that the coupling coefficient c should ensure that the eachregionwhilekeepingconstantthetotalvolumeofthesystem. wholesystemissubcritical.Thetotaleffectivemultiplicationfactor Finallyasearchisconductedforan8%-enrichedUraniumcascade ofthesystem,k,canbedeterminedbymultiplyingthefissionterm bymeansofMonteCarlocalculations,determiningthefeasibility byafactor1/k(Zweifel,1973),thatis: rangeforhybridbreak-evenusingthecurrentPFtechnology. ! ! DB2þR 1 DB2 a(cid:2) F (cid:2)c F ¼0 ð7Þ tR k 1 tR 2 f f 1 2 2.Modelofsubcriticalfissioncascades ! ! DB2 DB2þR 1 Barzilov et al. (1996) showed that a multiplicative set of two (cid:2) tR F 1 þ tR a(cid:2) k F 2 ¼0 ð8Þ f f coupledsubcriticalregionsdrivenbyperiodicneutronpulsescan 1 2 be reasonably represented by the one-group neutron diffusion which has a non-trivial solution if the following condition is equation in each region. Accordingly, those authors wrote a set satisfied: of ordinary differential equations in terms of the multiplication ! ! ! ! factors of each region and the neutron transfer between regions. DB2þR a(cid:2) 1 DB2þR a(cid:2) 1 (cid:2)c DB2 DB2 ¼0 ð9Þ Letusrevisitthatsetofequationsstartingfromtheone-groupdif- tR f k tR f k tR f tR f 1 2 1 2 fusionequation,thatis:

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12 A.Clausseetal./AnnalsofNuclearEnergy78(2015)10–14 Eqs.(5)–(9)areequivalenttotheBarzilovetal.set,althoughthe approximationoftheleakagetermgivenbyEq.(2)providesamore direct mean to introduce the geometry of the system in the r 3 analysis. r 1 UsingEqs.(5,6and9),andtakingintoaccountthattheinfinite multiplicationfactorsofeachregioniaregivenby t(cid:2)R k ¼ i fi ð10Þ 1i R ai r andthattheno-leakageprobabilityforregioniisgivenby: 2 DB2 !(cid:2)1 p ¼ i i þ1 ð11Þ i R ai Fig.1. Diagramofasphericalcascadeconsistingofacentralmultiplicativecore thenthetotalnumberoffissionneutronsperneutroninsertedby surroundedbyasphericalmultiplicativeshell. the source,from now oncalled theamplificationfactorM, can be Thesymmetryoftheproblemisusefultoestimatethebuckling writtenas: parameterB ofeachregion.Fortheinnersphere(Reuss,2008): i F þF (cid:2) 1 1 1 (cid:3)1 p M¼ 1 2¼ þ (cid:2) (cid:2)1 ð12Þ B ¼ ð17Þ S p 2 k 12 p 1 k 11 k 11 D 1 r 1 where: andforthesphericalshell(Mattingly,2002): (cid:2) 1 (cid:3)(cid:2) 1 (cid:3) 1 p D¼ p 1 k 11 (cid:2)1 p 2 k 12 (cid:2)1 (cid:2)c k 11 B 2 ¼ r 3 (cid:2)r 2 ð18Þ 1 (cid:2)1 (cid:3)(cid:2)1 (cid:3) Theno-leakageprobabilities(Eq.(11))canbewrittenthenas: (cid:3) (cid:2)1 (cid:2)1 ð13Þ k p p 12 1 2 1 p ¼ ð19Þ and 1 1þR(cid:2)2 1 (cid:4) (cid:5)(cid:4) (cid:5) 1 (cid:2)k11 1 (cid:2)k12 1 c¼ p (cid:4) 1 1 (cid:2) k 1 (cid:5)(cid:4) p 1 2 (cid:2)1 k (cid:5) ð14Þ p 2 ¼ 1þðR 3 (cid:2)R 2 Þ(cid:2)2 ð20Þ p1 p2 whereR istheradiusr inunitsofthediffusionlengthtimesp,that i i is: 3.Subcriticalsphericalcascade r R i ¼ ppffi D ffi i ffiffi = ffiffi R ffiffiffiffiffiffi ð21Þ a Ingeneraltheconditionofperfectcascade,withnullfeedback from the blanket (region 2) to the central region (region 1), is Actually, if moderation effects are involved, the migration difficult to achieve. Two methods were proposed in accelerator- length would be more appropriate to apply, to account for the driven systems (Nifenecker et al., 2003), namely, by means of slowing down of the neutrons (Stacey, 2001). Nevertheless, even selective absorbers and by special geometric arrangements. The ifthematerialisthesame,thediffusionormigrationlengthscan first method is to produce a sort of neutronic greenhouse effect, differ from one region to the other, since the energy spectrum consisting of a central fast-neutron multiplier with strong ther- can be different. Alternatively, a few energy-groups model could mal-neutronabsorptionpropertiesandathermalblanketmedium. have being used from the start, but it would have obscured the Thefastneutronsgeneratedinmedium1thatreachmedium2are simplicityoftheanalysisthatisofferedforthepurposeofguidance then slowed down and multiplied, but the slow neutrons from inthesearchofoptimumconfigurationsusingMonteCarlocalcu- medium2couldnotreachmedium1withoutbeingimmediately lations.Forthesakeofsimplicityinthesearchfordesignpatterns, absorbedbythethermalabsorber.Inturn,thegeometricmethod allnuclearpropertieswillbeconsideredidenticalinbothregions takesadvantageofthedependenceoftheneutronleakageonthe inwhatfollows. relativegeometricalarrangementofthetworegions.Inthepresent Inordertodrawaconsistentpathtowardsfeasibledesignsof studythelattermethodwillbeapplied. subcriticalfissioncascadesdrivenbyPFsources,letusconsidera Letusconsideracentralspherewithradiusr surroundedbya system with total effective multiplicative factor k=0.95 and 1 sphericalmultiplicativeshellwithinternalradiusr 2 andexternal k 1 =1.18 in both regions as has been said in the last paragraph. radiusr (Fig.1).Fromanyleakagepointattheinnerwallofthe Thisvalueofk correspondsto8%-enrichedmetallicUranium,cal- 3 1 external shell, only those neutrons with directions contained in culated with the Monte Carlo code MCNP5 (Briesmeister, 2000). the cone tangent to the inner sphere with vertex in the leakage Using the geometric relations of the spherical configuration, the point reaches the core region 1 (Fig. 1). The solid angle defined amplification factor M of the cascade can be estimated in terms bythisconeisgivenby: oftheradiiR i .Assumingthenk 1 =1.18andk=0.95theamplifica- 0 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 tion factor is solely determined by only two geometrical dimen- r2(cid:2)r2 sions. This is due to the fact that the value of the effective X¼2p @1(cid:2) 2 r 1 A ð15Þ multiplication factor of the system, k, reduces in one degree of 2 freedomthesetofequations. Sincethetotalsolidangleofleakageis2p,thecouplingcoeffi- AninterestingdesignproblemisthevariationofMkeepingcon- cientcresults: stant the total volume V of the multiplicative regions, which in unitsofdiffusionlengthtimespisgivenby: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (cid:2)r (cid:3)2 c¼1(cid:2) 1(cid:2) r 1 2 ð16Þ V ¼ 4 3 p (cid:4) R3 1 (cid:2)R3 2 þR3 3 (cid:5) ð22Þ

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A.Clausseetal./AnnalsofNuclearEnergy78(2015)10–14 13 Fig. 2 shows the variation of the amplificationfactor withthe radiusoftheinnersphereforthreedifferentvolumesV.Itcanbe seenthatthereisanoptimumdistributionofthematerialwhich correspondstothecompetitionbetweenthemultiplicationpower of each region and the geometrical back coupling. It should be stressedthatinallcasestheeffectivemultiplicationfactorofthe system is kept at k=0.95 in order to ensure safe subcritical conditions. 4.MonteCarlocalculations In order to corroborate the results of the analytical model, Monte Carlo calculations were performed using the MNCP5 code (Briesmeister,2000).Asystemconsistingoftwosphericalconcen- Fig.3. DiagramoftheconfigurationofthesphericalcascadeusedintheMonte tric regions of 8%-enriched Uranium was tuned to maintain the Carlocalculations. total effective multiplication factor k=0.95. The inner core was modelled allowing a central void region to host a PF discharge chamber, which is simulated by a point neutron source of 14.1MeV(seeFig.3). Fig. 4 shows the amplification factor obtained following the sameprocedureasFig.2,thatis,keepingthetotalvolumeofUra- nium constant and the effective multiplication factor k=0.95. It can be seen that similar curves as the analytical approximation are obtained, with an optimum configuration for each volume. The reference length that makes the maxima of M of Figs. 2 and 4correspondtoeachothercanbeestimatedbyassuminganeffec- tive solid dimensionless radius R equal to the thickness of the 1 inner sphere of Fig. 3, which gives ppffi D ffiffiffi

ffiffiRffiffiffiffiffiffi (cid:4)14cm. Using this a value, the dimensionless volumes plotted for the analytical approximationinFig.2correspondstothevolumesoftheMonte CarlocalculationsshowninFig.4.Itcanbeseenthattheanalytical approximation gives a conservative assessment of the amplifica- Fig.4. MonteCarlocalculationsoftheamplificationfactorofthesphericalcascade tionfactor,whichinthiscaseisabout30%lowerthantheMCNP fordifferentvolumesof8%-enrichedUranium:4.2m3(j),11.3m3(d)and22.6m3 (s).Theeffectivemultiplicationfactorofthewholesystemisinallcasesk=0.95 predictions.Nevertheless,itisworthnotingthatthegeneraltrend andtheradiusofthecentralvoidregionforthelocationofthePlasma-Focussource ofincreasingoptimaisreproduced. isro=20cm. Theoptimum geometrical configurations for givenvolumes of fissilematerialthatgivesthemaximumamplificationfactorwere also calculated using MCNP. Fig. 5 shows the combinations of optimum radii corresponding to each material volume, together withthecorrespondingamplificationfactorM. 5.Energybalanceofafusion–fissionhybriddrivenbyPlasma- Focussources It is known that the optimum neutron yield of a PF operating with Deuterium is approximately given by 107kJ(cid:2)2 E 2, where PF Fig. 5. Optimum amplification factor, PF break-even energy, and geometrical parameters of the spherical cascade as functions of the volume of 8%-enriched Uranium,calculatedwithMCNP5. E is the stored energy in the capacitor (Bernard et al., 1998; PF Lee, 2009; Soto et al., 2010). For a mixture 50% Deuterium and 50%Tritium,giventhelargercrosssectionoftheD-Tfusionreac- tion, an increment in two orders of magnitude is expected (Mather, 1971). Thus, let us assume that the neutron source is a Fig.2. Amplificationfactorofthesphericalcascadefordifferentvolumesof8%- PFdeviceofchargingenergyE ,operatingwithagasmixtureof e b n y r E ic q h s e . d (1 U 2) r – a ( n 1 iu 4 m ).A ( l k l 1 di = m 1 e .1 n 8 si ) on ca s lc a u re la g te iv d en w i i n th u t n h i e ts a o n f a t l h y e tic d a if l fu a s p i p o r n ox le im ng a t t h io t n im g e iv s e p n . Deuterium and Tritium. Under PF optimum conditions, the neutron Theeffectivemultiplicationfactorofthewholesystemisinallcasesk=0.95. yieldofperpulseisgivenby:

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14 A.Clausseetal./AnnalsofNuclearEnergy78(2015)10–14 YðE Þffi109kJ(cid:2)2 E2 ð23Þ Bernard,A.,Bruzzone,H.,Choi,P.,Chuaqui,H.,Gribkov,V.,Herrera,J.,Hirano,K., PF PF Krejci,A.,Lee,S.,Luo,C.,Mezzetti,F.,Sadowski,M.,Schmidt,H.,Ware,K.,Wong, The number of fissions produced by Y is then ðM=tÞYðE Þ. C.S.,Zoita,V.,1998.ScientificstatusofPlasmaFocusresearch.J.MoscowPhys. PF ConsideringthatthefissilefuelisU235(193MeVffi310(cid:2)14kJper Soc.8,93–170. Bethe,H.,1979.Thefusionhybrid.Phys.Today32,44–51. fission,t(cid:2)ffi2:43),thefissionenergyproducedineachshotis: Borst,L.,1957.Theconvergatron:aneutronamplifier.Phys.Rev.107,905–906. Briesmeister, J., 2000. MCNP—a general Monte Carlo N particle transport code, E f ffi1:2310(cid:2)5kJ(cid:2)1 E2 PF M ð24Þ Version4C,LosAlamosNationalLaboratory,ReportLA-13709-M. Daniel, H., Petrov, Y., 1996. Subcritical fission reactor driven by the low power Now, only a small part of the energy of the capacitor bank is accelerator.Nucl.Instrum.Methods,A373,131. consumed in the pinch to produce the thermal conditions for Dubovskii,B.G.,1959.Sectionalizedreactorsystems.At.Energ.7,456–457. Freidberg,J.,Kadak,2009.Fusion–fissionhybridsrevisited.Nat.Phys.5,370. fusion reactions. A reasonable figure of this fraction is about 5% Gerstner,E.,2009.Nuclearenergy:thehybridreturns.Nature460,25–28. (Gonzálezetal.,2009).Inthatcase,thefusion–fissionbreak-even González,J.,Brollo,F.,Clausse,A.,2009.ModelingofthedynamicPlasmapinchin conditionsatisfies: Plasma-Focus discharges based in Von Karman approximations. IEEE Trans. PlasmaSci.37,2178–2185. 0:05E ffi1:2310(cid:2)5kJ(cid:2)1 E2 M ð25Þ Gribkov, V.A., Tyagunov, M.G., 1983. Possible applications of a hybrid PF PF thermonuclear energy source based in a DPF device in modern energy complexes.In:Bauer,G.S.,McDonalds,A.(Eds.),NuclearEnergyTechnologies Therefore,thePFenergyrequiredforhybridbreak-evenisgiven inaSustainablyEnergySystem.Springer,Verlag,pp.187–199. by: Gulevich, A.V., Zemskov, E.A., Komlev, O.G., Kukharchuk, O.F., Melnikov, K.G., Novikova, N.N., Fokina, O.G., Chekunov, V.V., 2007. Multipurpose electron 4000kJ E ffi ð26Þ acceleratordrivenelectronuclearsystembasedonasubcriticalcascadereactor. PF M At.Energ.102,108–114. Gulik,V.,Tkaczyk,A.H.,2014.CostoptimizationofADSdesign:comparativestudy Fig. 5 shows that the energy of the Plasma Focus required for of externally driven heterogeneous and homogeneous two-zone subcritical break-evenin the optimumspherical configurations for the range reactorsystems.Nucl.Eng.Des.270,133–142. Hetrick,D.,1971.DynamicsofNuclearReactors.UniversityofChicagoPress,p.5. of volumes considered in the MCNP calculations is about 50kJ, Kolesov,V.F.,Khoruzhii,V.K.,2003.Kineticsofaperiodiccascadeboosters:speedof which is within the range provided by the current technology. operationandsafety.At.Energ.94,61–70. Moreover,thereactorexternalradiusisabout2m,whichisalsoa Kotschenreuther,M.,Valanju,P.,Mahajan,S.,Schneider,E.,2009.Fusion–fission feasiblefigure. transmutationscheme—efficientdestructionofnuclearwaste.FusionEng.Des. 84,83–88. Lee,S.,2009.NeutronyieldsaturationinPlasmaFocus:afundamentalcause.Appl. 6.Conclusions Phys.Lett.95,151503. Mather,J.W.,1971.In:Lovberg,R.,Griem,H.(Eds.),DensePlasmaFocus,Methodsof ExperimentalPhysics,9B.AcademicPress,NewYorkandLondon,pp.187–248. Thefeasibilityofahybridfusion–fissionsystemconsistingofa Mattingly, J., 2002. Plutonium attribute estimation from passive NMIS two-stagesphericalsubcriticalcascadedrivenbyaDensePlasma measurementsatVNIIEF,ReportORNL/TM-2002/20. Moiseenko,V.E.,Noack,K.,Agren,O.,2010.Stellarator-mirrorbasedfusiondriven Focus was studied. An analytical model based on the one-group fissionreactor.J.FusionEnergy29,65–69. neutrondiffusionequationwasdevelopedtoestimatetheamplifi- Moreno,C.,Venere,M.,Barbuzza,R.,DelFresno,M.,Ramos,R.,Bruzzone,H.,Florido, cation achieved per source’s neutron knowing the neutronic P., González, J., Clausse, A., 2002. Industrial applications of plasma focus radiation.Brazilian.J.Phys.32,20–25. parameters of each region. The conditions for energy break-even Nifenecker,H.,Meplan,O.,David,S.,2003.AcceleratorDrivenSubcriticalReactors. for this hybrid concept were assessed. It was found that in InstituteofPhysicsPublishing,BristolandPhiladelphia. principle the concept is feasible given the current Plasma-Focus Nukulin,Y.,Polukhin,S.N.,2007.Saturationoftheneutronyieldfrommegajoule technology. The results were corroborated by means of Monte PlasmaFocusfacilities.PlasmaPhys.Rep.33,271–277. Reuss,P.,2008.NeutronPhysics,EDPSciences,LesUlisCedex,France,p.171. Carlo calculations and a design chart was produced for assessing Schdmidt,H.,Kasperczuk,A.,Paduch,M.,Pisarczyk,T.,Scholz,M.,Tomaszewski,K., the optimum configuration of the spherical cascade to achieve Szydlowsky, A., 2002. Review of recent experiments with the MJ PF-1000 differentlevelsofneutronamplification. PlasmaFocusdevice.Phys.Scr.66,168. Shahbunder, H., Pyeon, C.H., Misawa, T., Lim, J.Y., Shiroya, S., 2010. Subcritical The presentnovelanalysis ofPF-driven two-region reactorsis multiplicationfactorandsourceefficiencyinaccelerator-drivensystem.Ann. valuable regarding that the technology of PF neutron sources, in Nucl.Energy37,1214–1222. spiteofitslimitedneutronyield,iscurrentlymoreadvancedthan Sinha,A.,Roy,T.,Kashyap,Y.,Ray,N.,Shukla,M.,Patel,T.,Bajpai,S.,Sarkar,P.S., Bishnoi,P.,Adhikari,P.S.,2015.BRAHMMA:acompactexperimentalaccelerator theircounterpartsbasedininertialfusion.Theremainingchallenge drivensubcriticalfacilityusingD-T/D-Dneutronsource.Ann.Nucl.Energy75, istoincreasethedischargerateofPFdevicesoftensofkJinorder 590–594. toachievereasonablepoweroutputs. Soto, L., Silva, P., Moreno, J., Zambra, M., Kies, W., Mayer, R.E., Clausse, A., Altamirano,L.,Pavez,C.,Huerta,L.,2008.Demonstrationofneutronproduction inatabletoppinchPlasmaFocusdeviceoperatedatonlytensofjoules.J.Phys. Acknowledgement D:Appl.Phys.41,205215. Soto,L.,Pavez,C.,Tarifeño,A.,Moreno,J.,Veloso,F.,2010.Studiesonscalabilityand scalinglawsforthePlasmaFocus:similaritiesanddifferencesindevicesfrom The present work was supported by the Bilateral Chilean- 1MJto0.1J.PlasmaSourcesSci.Technol.19,055017. ArgentineprojectCONICYT-ACE01ANPCyT-PICT2697. Stacey,W.,2001.NuclearReactorPhysics.Wiley,NewYork,p.55. Steer, S.J., Cardin, M.A., Nuttalla, W.J., Parks, G.T., Gonçalves, L.V.N., 2012. References Minimising the economic cost and risk to accelerator-driven subcritical reactortechnology:thecaseofdesigningforflexibility.Nucl.Eng.Des.243, 135–147. Abalin, S., Alekseev, P., Ignatev, V., Kolyaskin, O., Menshikov, L., Mostovoi, V., Wang,S.,He,C.,2014.Designandanalysisofnuclearbatterydrivenbytheexternal Prusakov, V., Subbotin, S., Krasnykh, A., Popov, Y., Rudenko, V., Somov, L., neutronsource.Ann.Nucl.Energy72,455–460. 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