Monte Carlo simulations for the space radiation superconducting shield project (SR2S)

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Contents lists available atScienceDirect

Life

Sciences

in

Space

Research

www.elsevier.com/locate/lssr

Monte

Carlo

simulations

for

the

space

radiation

superconducting

shield

project

(SR2S)

M. Vuolo

a

,

b

,

∗

,

M. Giraudo

a

,

b

,

R. Musenich

c

,

V. Calvelli

c

,

F. Ambroglini

d

,

W.J. Burger

d

,

R. Battiston

e

a_Thales_Alenia_Space_Italia,_Strada_Antica_di_Collegno,₁₀₁₄₆_Torino,_Italy b_Politecnico_di_Torino,_Corso_Duca_degli_{Abruzzi 24,}₁₀₁₂₉_Torino,_Italy c_INFN-Genova,_Via_Dodecaneso_33,₁₆₁₄₆_Genova,_Italy

d_{INFN-Perugia,}_Via_Pascoli,₀₆₁₂₃_Perugia,_Italy

e_TIFPA-INFN_and_University_of_Trento,_via_{Sommarive 14,}₃₈₁₂₃_Trento_Italy

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received7May2015

Receivedinrevisedform4December2015 Accepted30December2015

Keywords:

Radiation

Superconductingshield MonteCarlosimulations Dose

Deepspacehumanmissions

Astronauts ondeep-spacelong-durationmissions willbeexposedforlongtimetogalacticcosmicrays (GCR)andSolarParticleEvents(SPE).Theexposuretospaceradiationcouldleadtobothacuteandlate effects inthe crewmembers and welldefined countermeasures do not exist nowadays.The simplest solution givenbyoptimized passiveshielding isnotabletoreducethedosedepositedbyGCRsbelow the actualdose limits, therefore othersolutions, suchas active shielding employingsuperconducting magnetic fields, are under study. In the framework of the EU FP7 SR2S Project – Space Radiation SuperconductingShield–atoroidalmagneticsystembasedonMgB2superconductorshasbeenanalyzed through detailedMonte Carlosimulationsusing Geant4interfaceGRAS.Spacecraft andmagnets were modeled together with a simplified mechanical structure supporting the coils. Radiation transport throughmagneticfieldsandmaterialswassimulatedforadeep-spacemissionscenario,consideringfor the firsttimetheeffectofsecondaryparticlesproducedinthepassage ofspaceradiationthroughthe activeshieldingandspacecraftstructures.Whenmodelingthestructuressupportingtheactiveshielding systemsandthehabitat,theradiationprotectionefficiencyofthemagneticfieldisseverelydecreasing comparedtotheonereportedinpreviousstudies,whenonlythemagneticfieldwasmodeledaroundthe crew.Thisisduetothelargeproductionofsecondaryradiationtakingplacein thematerialsurrounding thehabitat.

1. Introduction

Future manned missions to Mars and lunar outposts will re-quiretheevolutionoftechnologyandquitefascinatingengineering challenges.Amongthetechnicalproblemstodealwith,oneofthe most troubling is related to ionizing radiation (Durante and Cu-cinotta, 2011; Cucinotta,2013; Zeitlin etal., 2013). Reducingthe healthrisksassociatedwithspaceradiationisafundamental pre-rogativetoallowtheexecutionoflongdurationmanned interplan-etary missions. The solutions studied until todayinvolve theuse of passive andactive shielding (ECSS E-10-04; Spillantini, 2011). Theﬁrstisbasedonthelossofenergyduetotheinteractionsof

*

Correspondingauthor at:PolitecnicodiTorino, CorsoDucadegliAbruzzi 24, 10129Torino,Italy.

E-mailaddress:marco.vuolo@external.thalesaleniaspace.com(M. Vuolo).

particles withthe materials.Thelatterexploitsmagneticﬁeldsto deﬂectparticles.

The spaceradiationenvironment tobe counteractedis mainly producedbytwodifferentcomponents:SolarParticleEvents(SPE) andGalacticCosmicRays(GCR).

SPE are occasional events,with possible highﬂuence concen-trated in shortperiods (hoursordays). Due totheir relativelow energyparticles,theycanbestoppedbyapassiveshieldedshelter (Cucinotta,2013).

On the other hand GCR are very high energy particles arriv-ing isotropically fromoutside the solar system. The GCRs, if not shielded, produce the largest contribution to the total effective dose (

>

500 mSv/y)inalong-durationinterplanetarymissionand shieldingfromGCRisstillanopenchallengeduetotheir capabil-ity to producesecondary particles wheninteracting withmatter. Forthisreasonotheroptionsthanthepassiveshieldinghavebeen investigated during theyears and, amongthose, theuse of mag-neticﬁeldstodeﬂectradiationisoneofthemostinterestingones.

http://dx.doi.org/10.1016/j.lssr.2015.12.003

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Theuseoflargesuperconductingmagnetstogeneratea shield-ing field aroundthe spacecraft datesback to 1960andwas sub-sequentlyproposed inseveralconfigurations(Wilsonetal.,1997; Braun,1969).However,previousworksconsideredonlytheability ofthemagneticfieldindeflectingparticlesneglectinginthisway theoutcomesoftheinteractionof thechargedparticleswiththe magnetic materials necessary to generatethe field (Braun, 1969; Townsendetal.,1990; Hoffmanetal.,2005).

Thispaperdescribesatoroidalmagneticsystemstudiedinthe frameworkofEUFP7SR2SProject(SpaceRadiation Superconduct-ingShielding).MonteCarlosimulationshavebeenusedtoevaluate theeffectiveshield capabilityconsideringthecombinedeffectsof themagneticﬁeldandmaterialscomposingthemagnet,the space-craftsandarealisticsupportingstructure.

The aim of the work is not to provide the values cumulated byastronauts,buttocomparethedosereductionswithrespectto freespaceforseveralrealisticshieldingstructures.

2. Toroidalmagneticshield

2.1.Motionofchargedparticlesinatoroidalmagneticﬁeld

Aninitial trade-off between differentpossibleactive shielding structuresledtotheadoptionofatoroidalmagneticconfiguration (Battistonetal.,2013; Musenichetal.,2014).Thetoroidalfieldhas infactmanyadvantages,includingan isotropicprotectionaround the habitat anda very low fringe field inside the internal mod-ule.Clearlyatoroidsurroundingthespacecraftleavestheendcaps ofthehabitatmodulefree ofthefield (andthereforeprotection), soeventual solutions includingsmaller endcap toroidscould be consideredtoshield theside ofthehabitatnotattachedto other modules.Alternatively,passiveoracombinationofactiveand pas-siveendcap canbe used.Howeverthe treatmentofthisissueis beyondthescopeofthiswork.

Aschemeofthebasicideabehindatoroidalshieldisshownin

Fig. 1.Inthecaseofachargedparticlemovingradially,i.e.having zeroangular velocity, the motionequation inan inﬁnite toroidal magnetic ﬁeld can be analytically solved. It can also be demon-stratedthat a particlewithzeroangularspeed

˙θ =

0 isthe most penetratingoneandtherefore,asshowninBattistonetal. (2013)

theshieldingpowerofthetoroidcanbewrittenas:

Ξ

=

Re

Ri BϑdR

=

μ

0I 2

π

ln Re Ri (1)

where I is the total current ﬂowing in the toroid, Re the outer

radiusandRi theinnerradius.Theshieldingpowercanbewritten

alsoasafunctionoftheparticleproperties:

Ξ

=

m0

q c

γ

2

₋

₁

₍

₁

₋

_sin

_ϕ

₎

₍₂₎

wherem0,q and

γ

aretheparticlerestmass,chargeandLorentz factorrespectively.

ϕ

istheangleofincidenceshowninFig. 1.

Using(2)itisstraightforwardtocalculatethemaximumkinetic energyKη oftheparticlethatcanbedeﬂectedbythetoroidalﬁeld (Hoffmanetal.,2005): Kη

= −

m0c2

η

1

−

q m0c

Ξ

(

1

−

sin

ϕ

)

2

+

1

(3) where

η

isthenumberofnucleons,q thecharge.Iftheangleof in-cidence

ϕ

issetto

−

90◦(correspondingtoadirectionofaparticle enteringperpendicularlyinthemagneticﬁeldofthetoroid,being themagneticﬁeldclockwiseorientedasshowninFig. 1)thelatter

Fig. 1. SchematicviewofatoroidalSpaceRadiationSuperconductingShield. The trajectoriesoftwoparticleswithdifferentangleofincidenceϕareshown.

Fig. 2. Ideal“cutoff”kineticenergyKngivenasafunctionofthebendingpower forprotons,alphaandironnuclei.

equationdeﬁnestheshieldcut-offenergy.Undertheprevious hy-pothesistheidealtoroidalmagneticﬁeldwithbendingpower

Ξ

is abletodeﬂectalltheparticleshavingkineticenergylessthan Kη deﬁnedin(3).

Thisformulacanbeusefultoperformaﬁrstcheckonthe mag-neticﬁeldreproducedinthesimulationcode,while,however,the actual capabilitytoprotect thecrewmustbe evaluated including theinteractionofthecosmic rayswiththematerials surrounding theastronauts.

InFig. 2theideal“cutoff”kineticenergyKnisgivenasa

func-tionoftheBendingPower,forprotons,HeandFeions. 2.2. Magnetwindingandmechanicalstructure

TheSR2Ssuperconductingmagnetwasthoughtascomposedby severalracetrackcoilssupportedbyamechanicalstructure,whose goalistowithstandthemagneticforce.

Ina toroidalmagnet, itisnecessary tosupportboth intra-coil forces, which tend to enlarge each coil, and the radial, inward forces resultingfrom the interaction ofall the coils.As a conse-quence,thetoroid needsonemechanicalstructureto supportthe intra-coilforces,andaninneronefortheinwardforces.In princi-ple,underthehypothesisofperfectsystemsymmetry,themagnet wouldnotneedanymechanicalstructurebetweenthecoilsasno torquewouldbeexperienced bythe coils.However, small mispo-sitioningispossibleinarealmagnetthereforemetalfoamorlight honeycombwillbepresenttootospaceoutthecoils.

Different requirements with respect to an Earth based mag-net have been identiﬁed in the initial phase of the project. In particular,themassdensityoftheconductorandofall the mate-rialscomposingtheactiveshielding hastobeminimizedandthe

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mechanicalstructure should beoptimized inorder toreduce the wholemass;secondlythepowerconsumptionshouldbeaslowas possiblecompatiblewithaneffectiveshielding;inadditiona spe-cialattentionmust be paidto safetyandreliabilityissues (e.g.it ismandatory that theactive shieldingsystemmust bethermally, mechanicallyandelectromagneticallydecoupledfromthehabitat). Aftertherequirementsidentiﬁcation, apreliminarydesign has been studied for the magnet and for the mechanical structures supporting it where the toroidal ﬁeld is generated by a

super-conducting magnet wound by titanium clad, with a magnesium

diboride (MgB2) conductorwithpure aluminum strip inparallel. The magnet is supposed to operate in persistent mode at 10 K, cooled bycryocoolers. Adescriptionofthe magnetﬁrstdesignis reportedinBattistonetal. (2013).Furthermore,when developing the preliminary mechanical design (not described in this work), thenumberofcoilswas raisedto120to optimizethe stress dis-tribution.

Different choices of materials and structures have been eval-uated in the first 2 years of the project, and the configurations described in the present study are based on two different con-ceptsofmechanicalstructuresfora10mlongtoroidalmagnetfor two valuesofshielding power: 7.9and11.9Tm.These BL values resultedoutofan iterativetrade-offprocesswherethemain con-sideredcriteriaare the following: ideal fluxreduction (according to eq. (1) andat leastof 90%), compatibilitywith the SLSBlock IINASA launcher,maximummagnetic fieldoverconductorof4T (accordingtothe specificationofthe cableconsidered)and mod-ularity (possibility to subdivide the toroid in 4 and 6 segments;

Battistonetal.,2013).Inparticular,thesimulationresultsreported herearereferredto:

A. aﬁrststructurebasedonatitaniumalloycoilsupportwithtie rodsmadeofthesamematerial,wheretheinwardforcesare supportedbyanaluminum alloycylinder(Fig. 7) (A).

B. a second one, where the coil support is madeof aluminum

alloy andthe coil inner forcesare counteracted witharamid ﬁberswrappedaroundtheracetrack(Fig. 7) (B).Inwardforces aresupportedbyacylindermadeofaluminum–boroncarbide cermet, a composite material capable to support very high compressivestresses. Thisstructureis moreforward-thinking thantheﬁrstone, butalsolighter andinprinciple itis com-posedbymoreeffectivepassiveshieldingmaterials.

Themassofthesystemsandstructurescomposingthe conﬁg-urationAis315tonswhilefortheconﬁgurationBitisreducedto about100tons.

As regardsthe habitat usedin our simulations,the Columbus module of the International Space Station has been chosen as a reference.

Finally,ancillarysystems asthesolarshield andtheMeteorite andDebris Protection System (MDPS)have not been included in the simulation models because considered to have a low impact ontheradiationtransportthroughtheactiveshieldingsystems. 3. Simulationmodelsandmethods

Threedifferentsets ofsimulationsare presentedinthisstudy. Eachone was performedboth withactive shielding switchedon, i.e.consideringthemagneticfieldgeneratedbythemagnets,both consideringthestructurespresentintheconfigurationsbut with-outthemagneticfield,inordertodeterminetherelative contribu-tionofthemagneticfieldtothetotaldosereduction.

Detailsonthesetsofsimulationswillbegivenbelow.

Simulations on the different conﬁgurations were performed

using the GRASv3.3 code (Geant4 Radiation Analysis in Space)

(Santinetal., 2005), basedonthe MonteCarlosimulation toolkit Geant4.9.6(Agostinellietal.,2003).

Physical processes consideredin thisworkinclude: ionization, bremsstrahlung, photoelectric effect, Compton scattering, elastic and inelastic hadronic interaction, nuclear capture, and particle decay. In the simulations the physics list QBBC adopted also in SPENVIS1 was used. Thislisthas beenspeciﬁcally createdfor ra-diation biology, radiation protection and space applications and it includes combinations of selected interaction models to reach higher precision in a wide energy range. In particular QBBC in-cludes BIC (Binary Ion Cascade), BIC-Ion, BERT (Bertini), CHIPS (CHiralInvariantPhaseSpace),QGSP(Quark-GluonString

Precom-pound) and FTFP (Fritiof Precompound) models, Em opt3 was

ﬁnally used as electromagnetic model (Agostinelli et al., 2003; Ivantchenkoetal.,2012).

In apreliminary phaseofthe projecttheSR2S TAS-Italia sim-ulation framework was successfully tested against literature ex-perimentaldata onmonoenergetic protonandionbeamsin dif-ferent materials. Moreover,to test themagnetic ﬁeld models im-plemented inGRAS,magneticﬁeldvalueswere extrapolatedon a grid,matchingtheoneobtainedfromtheOPERAsoftware.2Finally initial simulations were run to check the particlespaths andthe maximumkinetic energyofthedeviatedparticlesresultswere in agreementwiththeformula(3).

Inthefollowingparagraphsthedeﬁnitionofparticletypesand energiesandthegeometrymodelingprocedurewillbedescribed. 3.1. Missionscenarioandenvironmentalmodel

Themissionscenariousedasreferenceforthisworkisadeep spacetripduringasolarminimum,characterizedbyahigherﬂux ofGCR.

BeingtheSPEeasilyshieldedbybothpassiveandactivemeans (Durante andCucinotta, 2011; Cucinotta, 2013),the focus ofthis

work was on the more problematic GCR population. The model

usedforthedescriptionoftheGCRenergyspectrawasthe

“stan-dard ISO15390 (ECCS 10-04 standard) model at solar minimum

without magnetic cut-off” (ECSS E-10-04), considering ions with atomicnumbers rangingfrom Z

=

1 to26.Thisleads to aworst case scenariofor a deep spacemission. Fig. 3showsthe spectra usedinthesimulationsforalimitedsubset ofions(1H,4He,12C, 14_N,16_O_and56_Fe)_and_{Fig. 4}_displays _{the relative}_contribution_to theeffectivedoseofeachion.Thesevalueswereobtained weight-ingtheISO15390GCRsﬂuenceswiththeICRP123“ﬂuencetodose conversion factors” (ICRP, 2013) considering the human body in deepspacewithoutanyshielding.

Thereferencesourcewasmodeledasashellwithradius9.5 m. GCRprotonsandionswere randomlygeneratedonits surface ac-cordingtotheISO15390spectra,andtheﬂuenceforeachdirection is proportionalto thecosineofthe anglebetweenthe source di-rectionandthelocalnormaltothespheresurface(cosinelawwith anglefrom0◦to 90◦).Theseparticleswerethentransportedinside themodeledvolumes.

Tobettercharacterizeandcomparetheshieldingperformances itwasthendecidedtofocustheattentiononlyonparticles cross-ing the magnetic ﬁeld, therefore, at this stage of the study, the contributionto thedose fromparticles comingfromtheEndCaps regionswasnotconsidered,beingitequivalentforeach conﬁgura-tion.

Todothis,particleswere generatedonlylaterallywithrespect totheaxial directionofthemodule,fromarestrictedareaofthe

1

SPENVIS is the online ESA’s Space Environment Information System:

www.spenvis.oma.be.

2 _The_OPERA_software_was_used_by_INFN_Genova_to_model_the_magnetic_ﬁeld,

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Fig. 3. Energyspectrashowedforalimitedsubsetofions(1_H,4_He,12_C,14_N,16_O

and56_Fe)_among_those_used_in_this_work_simulations.

Fig. 4. Relativecontributiontotheabsorbeddose,doseequivalentandabundanceof eachionafter5 g/cm2_of_aluminum._These_values_have_been_obtained_with_Geant4

andareinagreementwiththedatareportedinDuranteandCucinotta (2011).

referencesphericalsource,conﬁnedtoacylinder(9 mlong)placed outsidetheregionoccupiedbythetoroid(Barrelregion),asshown inFig. 5.

3.2.Geometricmodel

The complete geometric model used in the simulations was

built using the Geometry Description Markup Language (GDML),

whichallows the deﬁnitionof geometrydata inthe XML format (Chytraceketal.,2006).

Inthenextsectionsabriefdescriptionisgivenforeach ofthe modeledstructuresconsidered in thiswork.As alreadysaid, two differentcompleteconﬁgurationsweresimulated:

A. Aﬁrst one basedon titaniumstructuresto supportthe coils (totalmass315tons,thenparametricallyvaried).

B. Asecondonebasedonaramidﬁberssupportstructure reduc-ing the total mass to 104 tons and 147 tons for a bending powerof7.9and11.9Tmrespectively.

Thereasonforwhichtwodifferentstructureswere considered is that the initial approach of the project based on the use of the mostready technology, led to the adoption ofa heavy sup-portstructure mainlycomposed by titanium(A),butthe firstset ofsimulationsrevealedatoohighsecondaryparticles production, inparticularhigh-energyneutrons.Thisresulthighlightedthe ne-cessitytousealighter structurekeepingthesamebendingpower andthereforeledtothedevelopment ofthesecondconfiguration model(B),asan attempttoimprovethemagneticfieldefficiency

Fig. 5. SR2Sreferencesphericalsource,conﬁned toacylinder(9 mlong)placed outsidetheregionoccupiedbythetoroid(Barrelregion).

withtheaimofmakingthiskindoftechnologymoreattractivefor future developments.Twoversionsof the“B” conﬁgurationwere then designed(B1andB2)in ordertosupport twodifferent val-uesofbendingpower(7.9Tmand11.9Tm).Acompletegeometric descriptionofthemodelswillbeprovidedinthenext paragraphs andtheirmainpropertiescanbefoundinTable 1.

3.2.1. Referencehabitatmodule

As a courtesy ofThales Alenia SpaceItalia, itwas possibleto

use their geometrical models of the ISS Columbus module. The

structuresofthemagnetsandofthe mechanicalsupportsystems havethereforebeendesignedtobecompatiblewiththathabitat. 3.2.2. Magnetmodeling

FortheconﬁgurationA,themagnethasbeenmodeled with120 racetrackcoilsmadeofa homogeneousmaterialequivalent tothe windingpack,composedbytheconductor(Ti,Mg,B,Al),the insu-lation(C,O,H)andthecoilsupport(Ti)–seeFig. 6andFig. 7.To improvethecomputationalperformances,themodelwas properly simpliﬁed: as the titaniumrods are uniformlydistributed within each coil, it was decided to model them as a titanium cylinder withthesamemass,asshowninFig. 7.

Conﬁguration B1andB2 aremodeled ina moredetailedway. Thecoilsupportismadeofanaluminumalloyanditisconsidered asadifferentvolumefromtheconductorandtheinsulation(Fig. 6,

Fig. 7).Thecoilstierodsarereplacedbyanaramidﬁbersbandage wrapped around each racetrack structure, as shown inFig. 7 on theright.

Configuration B2 is built keeping the sameconceptual design andthesamematerialsofconfigurationB1butadaptingthemass, the shape and the size of each structure to support a magnetic fieldwithhigherbendingpower(11.9Tm).

The supporting structure between the coils and the habitat

needed to balance the inward magnetic forces arising in the

toroidal conﬁguration (Musenich etal., 2014; Calvelli,2013) was

heremodeled asa cylindermadeby aluminumalloy honeycomb

for conﬁguration A and by aluminum–boron carbide cermet for

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Table 1

Propertiesofthedifferentconﬁgurations.

ConfigurationA ConfigurationB1 ConfigurationB2

Total mass 315tons 104tons 147tons

Height 10m 10m 10m

Winding cable material 57%Al,9%MgB2,23%Ti,11%SiO2 57%Al,9%MgB2,23%Ti,11%SiO2 57%Al,9%MgB2,23%Ti,11%SiO2

Former Titanium Aluminum Aluminum

Struct. cylinder mat Alhoneycomb B4C/Al B4C/Al

Toroid int. radius 2.70m 2.80m 2.80m

Toroid ext. radius 6.30m 6.40m 8.75m

Bending power 7.9Tm 7.9Tm 11.9Tm

MC simulation Variabledensity:100%,75%,50%,25%,0% FieldONandOFF

RealdesigndensityﬁeldONandOFF RealdesigndensityﬁeldONandOFF

Asthe solarshieldandtheMDPShaveavery low mass com-paredtotheotherstructures,theywerenotmodeledinthe simu-lations.

Table 1listsalltherelevantdataforthesimulations. 3.3. Methods

Inthisparagraph an overviewofthe simulatedquantities, to-getherwiththecalculationhypothesesanduncertainties,isgiven. Afterthat the two main categories ofperformed simulations are deﬁned.

Theselectedquantitiesofinterestwerethedose(Gy/y)andthe effectivedose(Sv/y)receivedbythecrewinsidethehabitat.These quantities were obtainedconverting fluence values registered in-sidethehabitatintodose andeffectivedose usingthe“fluenceto dose conversion factors” provided by ICRP 123(ICRP, 2013). This procedureallowstoobtainequivalentdosesforeachorganand tis-sueofthe voxelizedICRPreferencephantoms (maleandfemale), computedusingtheICRPandtheNASA qualityfactors.Assuming thecrewmovementsduring themission asuniformlydistributed insidethespacecraft,ithasbeenbelievedagoodapproximationto calculatetheaverage fluences ofprimary andsecondaryparticles enteringthesurfaceofa2mdiametervirtualsphereplacedinside themodule.

The computation of particle ﬂuences and absorbed doses in

GRAS requiresa normalizationprocedure that takes intoaccount theparticlesourceproperties.Thepursuedphysicalquantity Qreal

(inthiscasetheparticleﬂuenceorthedepositeddose)isobtained with Equation(4):

Qreal

=

FN

·

QGRAS (4)

where QGRAS standsforthesimulatedquantity,normalizedtothe

incidentsimulatedevent,and FN isanormalizationfactor,which

canbecomputedwith Equation(5):

FN

= Φ

4π

π

R2

/

Np (5)

where R isthesourceradius,Np thenumberofprimaryparticles generatedand

Φ

4π isthesourceﬂuenceintegratedoverthesolid anglecomputedas:

Φ

4π

(

E

)

=

2π

0 d

ω

1

−1

Φ(

E

)

d

(

cos

ϑ)

=

4

π

Φ(

E

)

UncertaintieshereconsideredarerelatedonlytotheMonteCarlo code statistics. Epistemic uncertainties implied in the code, geo-metric model approximations (including compositions of materi-als), uncertainties in GCR ﬂuxes (ISO 15390) (ECSS E-10-04), in theICRPqualityfactors(ICRP,2013) andintheemployedphysical models(ECSSE-10-04;Agostinelli etal., 2003) arenotconsidered inthisanalysis.Sincethegoalofthisworkistoperforma compar-isonamongdifferentsolutionstheabove-mentioned uncertainties areassumedtobethesameforeachcase.

The relative error foreach energy bin,in theﬂuence analysis moduleofGRAS,iscomputedduringthesimulations.Then errors arepropagatedwhenapplyingtheICRP123qualityfactors. 3.4. Conﬁgurationsusedinthesimulations

Itfollowsadescriptionofthetwosetsofsimulationspresented inthiswork.

3.4.1. ConﬁgurationA.Parametricanalysisvaryingthemass

The first configuration used as input was the model relative to themechanicalstructure “A”,having atotal massof315tons. The goal of this first set of simulations was to understand how themassoftheactiveshield,influences theeffectivedose onthe crew inside the habitat, and so, the total shielding effectiveness. In particular, its impact on the capability to stop the incoming radiationandtogeneratesecondaryparticleswas evaluated vary-ing parametricallythemasswiththesamegeometricalmodelfor two cases:magneticfield onandmagneticfield off.Forthis pur-pose, starting from the geometric model of configuration A, the density values of coils andsupporting structures materials were virtually reducedinorderto decreasethetotal mass,leaving un-changed thedesignedrealistic massdistributionaround thecrew module.

This choice is not realistic and no mechanical stress analyses wereperformedwhenvaryingthedensity,neverthelessitwasvery usefulto understandthe contributionto thetotal dosereduction andtothesecondaryparticlesproductionoftheamountof mate-rialsplacedaroundthehabitat.

The followingrelative densities were takenintoconsideration, asapercentageoftherealone:

•

0%ofthetotal,withonlythecrewmodulemodeled

•

25%ofthetotalandthecrewmodulemodeled

•

3.4.2. ConfigurationB.Simulationofthemassoptimizedconfiguration Thissecondsetofsimulationswasperformedusingas geomet-ricalinputthemodelrelativetothemechanicalstructuresB1and B2.Whendesigningtheseconfigurationsthechallengewasto min-imizetheproductionofhighenergyneutrons whichhavea great impactonthedosewiththeirneutralchargeallowingthemnotto suffertheeffectoftheLorentzforceinsidethemagneticfield.

In a first partof the work (B1) a toroidal field with bending powerof7.9Tm,equaltotheoneusedintheconfigurationA sim-ulations,wasused,thenincreasedto11.9Tm(B2)tostudyhowa relevantgrowthofthisparameteraffectstheradiationtransport.

Sourcedimensions,normalizationfactorsandotherparameters arethesameasthoseused inthesimulationsdescribedpreviously.

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Fig. 6. SR2S geometrical models for conﬁgurations A and B1.

Fig. 7. SR2S geometrical models: details on the structure modeling assumptions (down).

4. Results

Inthe following paragraphs simulationresults are shown and discussed.Fig. 8,Fig. 9andTable 2reportforallthestudiedcases the simulation results in terms of sex averaged effective dose,

computed using the ICRP123 ﬂuence to dose conversion factors

obtainedthrough theICRPreferencehumanphantom.Sincea re-strictedlateral sourcewas usedfor thesimulations theobtained effectivedose for each caseisgiven asa percentageof the dose thatan astronaut wouldgetifindeep spacewithoutany shield-ing(thissituationis referredasthe“free space”case)andnotin terms ofabsolute effective dose in Sv. Results are initially given separatingthecontributiontotheeffectivedoseofGCRionswith atomicnumberZ

≤

2(1strowofFig. 8)fromtheoneofGCRions withZ

>

3 (2ndrowofFig. 8),giventhedifferentbehaviorofthe twogroups.ThenthetwocontributionsaresummedupinFig. 9.

ValuesreferredtotheColumbushabitatareobtainedwithboth magneticﬁeld offandon. In the lattercasethis means that the activeshieldingsystemmodelisnotpresentinthesimulation. 4.1.ConﬁgurationA

When analyzing the parametric analysis it is evident the im-pacttotheeffectivedose ofthesecondary particles(inparticular

neutrons) generated by the fragmentation of high-energy parti-cles and their nuclear reactions with the structural materials, is described in a ﬁrst approximation by the Bradt–Peters equation (Eq. (6)) (Durante and Cucinotta, 2011; Calvelli, 2013) for which theprobabilityoffragmentation(cross-section

σ

)is:

σ

=

π

r₀2c1

(

E

)

A1_P/3

+

A1_T/3

−

c2

(

E

)

2 (6)

where r0 is the nucleon radius (approximately 1.3 fm), c1 and c2 are semi-empirical terms, AP and AT the projectile and

tar-getatomicmassnumbers.Inorderto diminishtheproductionof thesecondary particles,itfollowsfrom(6) thattheactive shield-ingstructurearoundthehabitatshouldbedesignedwithmaterials havingtheatomicweight AT aslowaspossible.

TheﬁrstrowofFig. 8showsthat theEffectiveDoseforprotons and alpha particles initially increases when increasing the struc-turemassvaryingthematerialdensitytill50%,correspondingtoa structureofabout150tons.Suchaneffectisduetothesecondary particle production. For densities greater than 50% the stopping power of the structuresmaterials prevails on the secondary pro-ductionandEffectiveDosedecreasesreachingavalueclosetothe one found in freespace. The 100% density value corresponds to about315 tonsof materials and about100 g/cm2 of areicmass. Wheninsteadthemagneticﬁeld isoff,dosessubstantiallybehave withthesametrendsbuthavegreaterabsolutevalues.

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Fig. 8. Monte Carlo simulations results for the conﬁgurations A and B. Z≤2 in the ﬁrst row and Z>2 in the second row.

Fig. 9. Monte Carlo simulations results for the conﬁgurations A and B for Z=1–26.

Table 2

Sexaveragedeffectivedose[asapercentageofthe freespace dose,i.e.Effective Doseindeepspacewithoutshielding]resultingfromthe MonteCarlosimulations resultsfortheconﬁgurationsAand B.

Conf. type Field 0 Tm Field 7.9 Tm Field 11.9 Tm Columbus 88.0%±4.72% 59%±4% – Conf. A 25% 77.5%±4.19% 58%±2% – Conf. A 50% 78.5%±2.36% 61%±2% – Conf. A 75% 78.1%±1.93% 59%±1% – Conf. A 100% 69.4%±1.41% 55%±1% – Conf. B1 76.0%±0.90% 59%±1% – Conf. B2 77.4%±0.81% – 56%±1%

Simulationsshowthat theEffectiveDosedeliveredbytheHZE ions ( Z

=

3 to 26) is not evidently inﬂuenced by the magnetic ﬁeld presence when realistic values of mass are considered (see

Fig. 8,2nd row); this can be explained by the low range values forthemajorityofHZEattheenergies consideredinthe

simula-tions, namelyless than25 g cm−2.Even forthecase whereonly theColumbusmoduleissurroundedbya magneticﬁeld, itsmass is contributing in a major way into stopping the incoming ions. Increasingthestructuremass,dosesarethenreducedtosmall val-ues and the majority of HZE ions are stopped. As expected, for theseprimaryparticlesthepassiveshieldingcontributionprevails, however as the structure thickness increases (for density values greater than 50%), theeffective dose isreduced ina slowerway. This is dueto thesecondary particles produced by the HZE ions interactionswithmatter,whichcontinuetheirpathinthevolumes reachinggreaterdepths.

Fig. 9 showsthevaluesofthetotal EffectiveDose considering the contributionofboth light ions( Z

=

1 and2) andheavy ions ( Z

=

3 to 26).

Considering conﬁgurationA, with100% ofmass,the total lat-eraleffectivedose isreducedby afactorofabout2.Itshouldbe recalledthatthisvalueisobtainedconsideringonlyaﬁctitious lat-eralsource,addressingtheproblemofdealingwiththeendcapsto

(8)

thesecondpartofthestudy(Fig. 5)andwiththegoaltocompare theeﬃcienciesofdifferenttoroidalsolutions.

4.2.ConﬁgurationB

TheresultsfortheB1andB2conﬁgurationsareshowninFig. 7

nexttothepreviousonesobtainedintheparametricanalysis.The total effectivedose, for the field “on” case, is about 58.7% (B1– 7.9 Tm)and56.5%(B2–11.9Tm)of“freespace” dose,values com-parabletowhatobtainedforConfigurationAwiththe25%ofthe totaldensity(i.e.about80tons) whichwas 58.1%of“free space” dose.Thismeans thatConfiguration B1(104tons) isquite equiv-alentto Configuration A (25% density, 80 tons) from a radiation shieldingpointofview,keepingthesamemagneticbendingpower of 7.9 Tm. Configuration B2 reduces the effective dose of about 2.2%withrespecttotheB1casebutinspiteofanincrease ofthe bendingpowerofabout50%,from7.9to11.9Tm.

Itistonoticehow thedifferencesindosesbetweenthe “field on” and “fieldoff” cases for all the configurations (A – 100% of density,B1andB2)israngingfromabout14.7%of“thefreespace” effectivedosefortheconfigurationA,to17.3%forB1andto20.9% forB2(foratotaldosereductionof43.5%).Therefore,itwas pos-sibletoincrease thefieldeffectivenessbychoosingmaterials that optimizetheradiationshielding,pointingout howitisnecessary tocombinepassive andactive shielding trying toreach the

opti-mumsynergybetweenthem.

Therefore, given the fact that conﬁgurations B1 and B2 use

lower atomic mass number materials with respect to

conﬁgura-tion A,theirtotalweightislessthanconﬁgurationA,fora compa-rableradiationprotection. Itis alsoimportant tonote that while

conﬁguration B1 and B2 were designed taking into account the

mechanicalstrengthrequirementsresultingfromanassessmenton thearisingmagneticforces,beingthereforepotentiallyachievable inarealcase,forconﬁgurationA–25%(25%ofthetotaldensity) anadequatestressanalysiswasnotperformedbutvaluesof densi-tieswerevirtuallychangedtoobtainabetterunderstandingofthe massimpact on the physicalmechanisms determining the active shieldingperformances.

5. Conclusions

Thefuturehumanexplorationofthe SolarSystemdependson manytechnological challenges. Cosmicrays are one of the main showstoppersandtheSR2Sprojectaimstoassessthefeasibilityof aspaceradiationsuperconductingmagneticshield.

The performedanalyses with MonteCarlo simulations on the other handshowed forthe first time that in a realistic situation thesecondaryparticles,producedbytheinteractionofcosmicrays with the active shielding materials, are the major source of the crewradiationdose. Moreover alarge partof thesecondary par-ticlesare fastneutrons that cannot be deflectedby themagnetic field, therefore their production drastically reducesthe effective-nessoftheactiveshield.

Thefirstattempttodealwiththisissuewastodecreasethe to-tal structure massand to optimizethe material choice, resulting in thedesignofconfigurationB1. Thesecond attempt (configura-tion B2)consisted ofincreasing the shielding power to 11.9 Tm. Inboth cases the resultingeffective dose reduction of the active shieldwas not significantly improvedcompared to the“no-field” casewiththesamemass,reachingabout20%forconfigurationB2. Additionalsimulationshavebeenstartedmodifyingstructural ma-terialsto study theimpact on neutronproduction, andthey will thesubjectofadedicatedpublication.

An effort to reduce the amount of material is necessary too. Inthis sense,furtherdevelopmentsintheframeworkoftheSR2S

projectwillconcernnewconﬁgurationstoachievebetterdose

re-ductions. Open conﬁgurations which take advantage by a wide

strayfieldwereanalyzedbutresultedinefficient:theyrequirehuge magneticstructurestogeneratean effectiveshielding field.Other solutionsarepossible,includingnon-axialtoroidalgeometries,and willbeinvestigated.Furthermore,onceidentifiedthemost promis-ing active configuration,the efficiency of the magnetic field will be analyzed performing a comparisonwith an optimized passive shield,havingthesamemassperunitarea.

These results represent the estimated overall dose reduction basedonthe physicsmodel(Agostinellietal., 2003) available to-day,thatcouldsuffersofallepistemicuncertaintiesdescribed pre-viously. For futurestudy a reduction ofthe extrapolation energy rangefortheadoptedphysicsmodels,dependingonthe availabil-ityofthedata,willbedesirable.

Acknowledgements

ThisworkissupportedbyThalesAleniaSpaceItalia, INFNand co-fundedbytheEUFP7SR2SProject.

The SR2S consortium is funded by the EU 7th Framework

Programme (FP7, Grant agreement for collaborative project No. 313224)inthecontext ofthecalltitleSPA 20122.2.02,key tech-nology for in-space activities. The participants are the Italian In-stitute for Nuclear Physics (INFN), whichcoordinates the project, Thales Alenia SpaceItalia (Turin), CGS (Milan), Columbus Super-conductors(Genoa),CEA(Saclay),CERNandCarrCommunications (Dublin).

The authorswish tothankDr. E.Tracino, Prof. Dr.M.Durante and Dr. Maria Grazia Pia for the fruitful discussions and helpful suggestions.

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