Affordable, manageable, practical, and scalable (AMPS) high-yield and high-gain inertial fusion AndrewAlexander1,LauraRobinBenedetti1,IndraniBhattacharyya1,JaredBowen1,JuneCabatu1,VirgilCacdac1, ChhaviChhavi1,ChiataiChen1,KarenChen1,DanClark1,JerryClark1,TylerCope1,WillDannemann1,Scott Davidson1,DavidDeHaan1,JohnDugan1,MindyEihusen1,C.LelandEllison1,CarlosEsquivel1,DavidEthridge1, BlakeFerguson1,BryanFerguson1,JonFry1,FernandoGarcia-Rubio1,TarunGoyal1,GaryGrim1,Justin Grodman1,BenHaid1,FredHowland1,VanHuynh1,VishalJohn1,PatrickKnapp1,IsaacKravitz1,EricS.Lander1, SamuelLangendorf1,KeithLeChien1,AnthonyLink1,NathanMeezan1,DouglasS.Miller1,NantasNardelli1, QueenelleOgirri1,JonHePeng1,AlexanderPinto1,RudolphPowser1,FritzRoyPuno1,KennyQuang1,Brett Rahn1,WillRegan1,KelseyReichenbach1,AdamReyes1,5,CourtneyRichardson1,DavidRose1,JosephSamaniego1, PaulF.Schmit1,VictorSilva1,NickSimon1,ShivaSitaraman1,HardeepSullan1,JamesTrebesch1,MinhTruong1, CarrieVonMuench1,CoryWaltz1,DougWilliams1,EchoWood1,SidWu1,andAlexB.Zylstra1 1PacificFusionCorporation,Fremont,CA,94538,USA High-yieldinertialfusionoffersatransformativepathtoaffordablecleanfirmpowerandadvanceddefense capabilities. Recentmilestonesatlargefacilities, particularlytheNationalIgnitionFacility(NIF),have demonstrated the feasibility of ignition but highlight the need for approaches that can deliver large amountsofenergytofusiontargetsatmuchhigherefficiencyandlowercost.Weproposethatpulser-driven inertial fusion energy (IFE), which uses high-current pulsed-power technology to compress targets to thermonuclearconditions,canachievethisgoal.Inthispaper,wedetailthephysicsbasisforpulserIFE, focusingonmagnetizedlinerinertialfusion(MagLIF),wherecylindricalmetallinerscompressDTfuel under strong magnetic fields and pre-heat. We discuss how the low implosion velocities, direct-drive efficiency,andscalablepulserarchitecturecanachieveignition-levelconditionsatlowcapitalcost. Our multi-dimensionalsimulations,benchmarkedagainstexperimentsattheZfacility,showthatscalingfrom 20MAto50–60MAofcurrentenablesnetfacilitygain. WethenintroduceourDemonstrationSystem (DS),apulsed-powerdriverdesignedtodelivermorethan60MAandstoreapproximately80MJofenergy. TheDSisdesignedtoachievea1000×increaseineffectiveperformancecomparedtotheNIF,delivering approximately 100× greater facility-level energy gain — and importantly, achieving net facility gain, or 𝑄 𝑓 >1—atjust1/10thecapitalcost.Wealsoexaminetheengineeringrequirementsforrepetitiveoperation, targetfabrication,andchambermaintenance,highlightingapracticalroadmaptocommercialpowerplants. 1 Introduction Growingglobaldemandforenergy,increasingurgencyforcleanpowersources,[1]andrecentscientificadvancesin fusion[2–4]havecatalyzedanationalconversationregardingthemostpromisingpathtocommercialfusionenergy.It iswidelyunderstoodthatapracticalfusionsystemwouldberevolutionaryfortheenergysupply,propellingeconomic growthandimprovingthefeasibilityofmeetingsocietaldecarbonizationgoals. Afusionreactioncombinestwolightnucleiintoaheaviernucleus,releasingenergy.Starsburnhydrogenintohelium undergravitationalconfinement. Terrestrially,themostreadilyaccessiblefusionreactionistofusetwohydrogen isotopes,deuterium(D)andtritium(T),intohelium.DTfusionrequiresreachingtemperaturesofseveralkeV(1keV ≈107K).Toextractenergyfromfusion,thetotalfusionenergyreleasedbythefuelmustexceedtheenergyinvestedin creatingandsustainingtheplasma(𝑄 fortheplasmaenergygainfactor).Thisleadstoacriterionontheproductof 𝑝 theplasmapressure(𝑃)andenergyconfinementtime(𝜏)byLawson[5],with𝑃𝜏requirementsof10’sofatm-s. Fusionhasbeenanactiveareaofbasicresearchforseveraldecadeswithinvestmentoverwhelminglyintotwoapproaches: (1)magneticfusionenergy(MFE),inwhichaplasma’schargedparticlesareconfinedbymagneticfieldsoverlong periodsoftime, and(2)inertialfusionenergy(IFE),inwhichatarget(smallcontainerholdingthefuel)israpidly implodedtohighpressureandhydrodynamicallyconfinedduringtheburnbyitsowninertia.Theconfinementtimes 2025-4-14 5202 rpA 41 ]hp-msalp.scisyhp[ 4621636/timbus:viXra Affordable,manageable,practical,andscalable(AMPS)high-yieldandhigh-gaininertialfusion ]rabM[ erusserp 107 laser-IFE 106 pulser-IFE 105 steady pulsed 104 intermediate-pulse state 103 (pulser-driven) 102 101 1 10-1 10-2 10-3 10-4 10-5 10-6 10-5 10-4 10-3 10-2 10-1 1 101 102 103 104 105 106 confinement time τ [μs] FIN IFE MFE MagLIF long-pulse magnetic long-pulse mass pulsed steady-state magnetic TFTR Figure1: Parameterspaceofpressure(𝑃)andconfinementtime(𝜏)forfusionapproaches,adaptedfromSciencefor America[6].Pulser-drivenfusioncanoperateintheregimesshowninpurple,includinginertialfusion(thefocusofthis paper)andintermediateconfinementtimes. forthesetwoapproachesdifferby8-12ordersofmagnitude:secondsandaboveforMFEvs.below10nsforIFE,with thepressuresvaryinginversely.Thefullparameterspaceforpressure(𝑃)andconfinementtime(𝜏)isshowninFig. 1.ItalsoincludesapproacheswithintermediatetimesandpressuresbetweenthoseforMFEandIFE[6–8].ForMFE, publicfundinghaspredominantlysupportedthetokamakapproachwithhistoricalinvestmentsintomajorfacilities includingJET[9]andTFTR[10]inthe1990s,andongoingsignificantinvestmentintotheconstructionofITER[11].For IFE,publicfundinghaspredominantlysupportedlaser-driveninertialconfinementfusion(ICF)—thatis,usinglasers toimplodeatarget.Majorfacilitieswithlaser-baseddrivershavebeenconstructed,includingtheNationalIgnition Facility(NIF)[12],OMEGA[13],LaserMegajoule[14],andothers. Thesciencebasisforinertialfusionhasadvancedsignificantlyinthelastfewyearswiththedemonstrationofignition andpropagatingburnontheNIF,whichwasthefirstcontrolledexperimenttoexceedLawson’scriterionforignition [3]andsubsequentlydemonstrate𝑄 >1[4].Whileagroundbreakingscientificdemonstration,theNIFisstillfar 𝑡𝑎𝑟𝑔𝑒𝑡 fromoverallnetfacilityenergygain(𝑄 > 1),definedasfusionenergyoutputexceedingtheenergystoredbythe 𝑓 driver;therecordfacility-levelgainachievedontheNIFis𝑄 ∼0.016,asdiscussedlater.Thisisdueinparttothelaser 𝑓 system’slowefficiency(∼0.7%)inconvertingstoredenergytolaserlightincidentonthetarget,andinpartfromthe inefficiencyofindirect-driveinconvertingincidentlaserlighttoheatingofthefuel(∼1%),atotalefficiencyof<0.01%. Amoreefficientandscalableapproachtoinertialfusionisneededforcommercialpowerproduction. Anyrealisticfusionenergysystemwillneedtobeaffordable,manageable,practical,andscalable(AMPS).Bythese termswemean: • Affordable.Theovernightcapitalcost(OCC)andoperatingcostsofafusionenergysystemmustbeeconomically competitivewithotherpowersources. • Manageable.Thereliability,availability,maintainability,andinspectability(RAMI)ofkeycomponentsmustbe sufficientlymanageabletoachievehighsystemup-time. • Practical. The system has a credible scientific and technological basis while being compatible with energy marketneeds. • Scalable.Thesystemisbaseduponmass-manufacturablecomponents,withnomajorsupplychainbottlenecks, sothatpowerplantscanbedeployedrapidly. 2 Affordable,manageable,practical,andscalable(AMPS)high-yieldandhigh-gaininertialfusion Figure2: Fusiontripleproduct(𝑛𝑇𝜏,equivalently𝑃𝜏)forvariousfusionapproachesversusyear.Figurederivedfrom Ref.16usingtheassociatedgeneratorathttps://github.com/swurzel/lawson-criterion-paper).Severalconcepts,suchas sphericaltokamaks,shearedflowz-pinch,andFRCshavenewerrecordsthathavenotyetbeenincorporatedintothis analysis.Foradescriptionofthisdatasetandassociateddefinitions,seeRef.[16]. ThispaperfocusesonanalternativetolaserIFE:pulserIFE,whichhasalsoseenmajorprogressinthepastfewyears. InpulserIFE,afastpulsedpowerdriver(risetime∼100ns)orpulser,magneticallyimplodesafusiontargettoreach fusionconditions(with𝜏 ≲ 1ns). TherangeofparametersforpulserIFEisoverlappingandadjacenttothosefor whichignitionwasdemonstratedontheNIFwithlasers(Fig. 1). (AsshowninFig. 1,thereareother(non-inertial) pulser-drivenapproachestofusionthatinvolvemuchlongerconfinementtimes;theseapproacheswillnotbediscussed here.) Asdiscussedinarecentcommunitywhitepaper[15]andelaboratedhere,pulserIFEisuniquelysuitedtoaddressthe AMPSrequirementsabove.ThedrivertechnologyforpulserIFEismoreefficientthanforlaserIFE:asdiscussedbelow, PacificFusion’spulserIFEDemonstrationSystem(DS)isapproximately200×asefficientatcouplingstoredenergy tofuelinternalenergycomparedtolaserindirect-driveontheNIF.Thisefficiencyadvantageisdueinparttorecent developmentsinpulsedpowerarchitecturesthatenablesystemsthatarehighlymodularandscalable,andthatcanbe designedformaintainabilityandpracticality. ThetechnicalbasisofpulserIFEstemsfromexperimentsdemonstratingvaluesof𝑃𝜏onparwiththoseobtainedby laserICFandtokamaks.RecentworkbyWurzelandHsu[16]documentedtheLawsonproduct𝑃𝜏achievedbyvarious fusionapproachesovertime.ForpulserICF,theleadingexperimentalprecedentwasestablishedontheZfacilityat SandiaNationalLaboratories[17],atwhichthemagnetizedlinerinertialfusion(MagLIF)targetconcept[18,19]isthe mostexploredinpublishedliterature.InFig.2,weadaptRef.16toincludemorerecentMagLIFexperimentsfromRef. 20;subsequentexperimentshaveexceededthesevalues[21]. Laser-drivenICFontheNIFhasdemonstratedthehighest𝑃𝜏experimentallyachievedtodatewithanyfusionconcept. MagLIFhasdemonstratedthesecond-highest𝑃𝜏, secondonlytolaser-drivenICFandexceedingeventhehighest tokamak𝑃𝜏todate. Notably,pulserICFachievedtheseresultswithasmallfractionoftheinvestmentdedicatedto tokamaksandlaserICF:accordingtothe2018JASONreportonProspectsforLowCostFusionDevelopment,thetotal fundingforpulserICFhasbeenapproximately1%ofthetotalfundingforlaserICFandMFE[7]. 3 Affordable,manageable,practical,andscalable(AMPS)high-yieldandhigh-gaininertialfusion 1.1 PacificFusion’sRoadmap Pacific Fusion is a privately-funded company founded in 2023 to develop and realize the commercial potential of pulser-driveninertialfusionenergy.Atahighlevel,ourimmediateobjectivesareto: 1. Demonstratefacilitygain(𝑄 >1),i.e.,generatemorefusionenergyoutputthanwasstoredinthecapacitors 𝑓 2. Resolvesignificanthurdlestobuildingfusionpowerplants Together,incollaborationwithourkeypartnersatU.S.NationalLaboratoriesandacademicinstitutions,ourgoalisto achievetheseobjectivesbytheendofthedecade.Thefirstgoalwillrepresentamajormilestoneinfusionengineering: whileinertialfusionhasexceededtargetgaingreaterthan1(NIF,𝑄 ∼2.4)andmagneticconfinementfusionplasma 𝑡𝑎𝑟𝑔𝑒𝑡 gainhasapproachedthisthreshold(JET,𝑄 ∼0.67),thetotalper-shotenergyinputofthesefacilitiesissignificantly 𝑝 greaterthantheenergycoupledtotheplasma,sothattheNIF’s𝑄 ∼0.016andJET’s𝑄 ∼0.03[22]. 𝑓 𝑓 Wewillaccomplishthisobjectivebyconstructinganinertialfusiondriverthatisordersofmagnitudemoreefficient thantheNIFatdeliveringenergytoatargetandtothefusionfuelitself(seeSection2.3)andisalsoconsistentwith theAMPSgoalsfordeliveringeconomicallycompetitivefusionpower(Section4). OurDSfacility(Section3)will demonstrate𝑄 >1andwillenableinnovationintargetphysicsanddesignoverthecurrentstateoftheart.DSwill 𝑓 deliver > 60 MA of current to a target in ∼ 100 ns, consistent with the established theoretical and computational basisforachievinghighgain(Section2). AnenablingtechnologyfortheDStoefficientlydeliverlargeamountsof currentatlowcostistheimpedance-matchedMarxgeneratorarchitecture[23],whichusescommoditycomponents andeliminatesenergy-inefficientpulseshapingstagesfromthepriorgenerationofpulsedpowerarchitectures. In paralleltoourfusiongainobjective,wewilladvancethetechnologicalreadinessofkeytechnologiesneededfora commercialpowergenerationsystem.Afterthesegoalsareachieved,acommercialpowergenerationsystemwillbe produced.Wewilldiscussengineeringconsiderationsforsuchcommercialsystemsinthispaper,andwillelaborateon technoeconomicsinsubsequentpapers. 2 Physicsbasisforhigh-gainpulser-driveninertialfusion 2.1 Physicsofpulser-driveninertialfusion Pulser-driveninertialfusionprovidesanopportunitytoachievefacilitygain𝑄 >1byleveragingthelessonslearned 𝑓 fromtheNIFtoaccessignitionandgainwhileusingadriverthatismoreefficientthanalaser.DTfusionschemesmust generateaplasmathatishotenoughtohavehighfusionreactivity(typically𝑇 ≳10keV)andisconfinedlongenough thatself-heatingbythe3.5MeValphaparticlesreleasedinthefusionreactionssurpassesallenergylossmechanisms. Intheinertialfusionregime,thehotfuel“ignites,”initiatingapropagatingwaveoffusionreactionsinwhichthefuel’s pressuresignificantlyincreaseswhilethefusionplasmaexpandsintoasurroundingreservoirofcooler,denserfuel[24]. Pulser-driveninertialfusionreliesonthedirectmagneticaccelerationandcompressionoftargets,typicallyelectrically conductingcylindricalshellsor“liners”filledwithDTfusionfuel.Linersareacceleratedtolowerimplosionvelocities (∼100km/s)thanlaser-driveninertialfusionschemes(≳350km/s[3])toaccommodatethetypicallylongerpulsed-power timescales(≳100ns)comparedtothatofhigh-powerlasers(∼10ns)whilemanaginghydrodynamicinstabilities. Externallysuppliedenergy(“preheat”)andthermally-insulatingmagneticfieldsareinjectedintothefuelcavityprior toimplosionorastheimplosionproceeds,conditioningthehotspottoreachhightemperaturesandigniteatlower stagnation(peak)pressures(∼10Gbar)thanlaser-drivenimplosions(∼100Gbar).TheabilityforpulserICFtoreach ignitionconditionsandnettargetgainatsubstantiallylowerpressuresandcorrespondinglyhighertargetmasses representsakeyadvantagerelativetolaserICF. OneexampleofthisapproachistheMagLIF(MagnetizedLinerInertialFusion)conceptdevelopedatSandiaNational Laboratories[18].TheMagLIFconceptprovidesanexcellentbaselineforscalingpulser-drivenICFtoignitionandhigh gainforfivereasons: • Soundtheoreticalbasis.Thereisasoundtheoreticalbasisforinertialfusionofmagnetizedfuel[25]. • Efficientenergydelivery.EnergycanbedeliveredtoMagLIFtargetswithhighefficiency. • High-fidelitysimulations.MagLIF-typeexperimentscanbestudiedwithhigh-fidelitysimulations. • Pathstoignitionandhighgain.Therearedocumentedscalingpathstoignitionandhighgain [19,26–28]. 4 Affordable,manageable,practical,andscalable(AMPS)high-yieldandhigh-gaininertialfusion • Experimentaldemonstration.Highfusionperformancehasbeenexperimentallydemonstrated,andthereisa demonstratedmethodtodetermineproximitytoignition[20]. Thesepointsarediscussedinturninthefollowingfivesections. 2.2 Theoreticalbasisforpulser-driveninertialfusion Aswithallinertialfusionconcepts,thecoreobjectiveistoassembleahotDTmassandconfineitlongenoughfor fusionreactionstoself-heatandignitetheDTfuel.AssumingacylindricalDTfuelarrangement,theevolutionofthe DTinternalenergy,𝐸̂ ,isgovernedbyanequationlike DT 𝑑𝐸̂ DT =𝑊̂ −𝑊̂ −𝑊̂ −𝑊̂ −𝑊̂ −𝑊̂ , (1) 𝑑𝑡 𝛼 𝑃𝑑𝑉 𝑟 𝑐𝑒 𝑐𝑖 end withnetheatingoftheDTfueloccurringwhen𝑑𝐸̂ /𝑑𝑡 > 0. Theenergiesandpowersintheaboveequationare DT expressedperunitlengthofthecylindricalfuelassembly,denotedbythehatnotation.Alpha-particleheatingofthe fuelscalesas 𝑊̂ ∝𝜂 (𝜌𝑅)2𝑠(𝑇), (2) 𝛼 𝛼 where𝜂 ≤ 1isalpha-particlecouplingefficiencytothefuelplasma,describedinRef.[29]. ThecharacteristicDT 𝛼 fuel mass density and radius at peak compression are given by 𝜌 and 𝑅, respectively. The term 𝑠(𝑇) captures the temperaturedependenceoftheMaxwell-averagedDTreactivity⟨𝜎𝑣⟩,whichcanbeapproximated𝑠(𝑇) ∝ 𝑇3 inthe 4-12keVrange.[27].TheremainingtermsontherighthandsideofEq.1representthedifferentmechanismschanneling energybetweenthehotDTfuelanditssurroundingenvironment,whichincludetheisentropicworkassociatedwith thefueldisplacingtheliner(𝑊̂ ),radiationlosses(𝑊̂ ),electronandionheatconductionlosses(𝑊̂ and𝑊̂ ),and 𝑃𝑑𝑉 𝑟 𝑐𝑒 𝑐𝑖 bulkflowsofhotfuelouttheopenend(s)oftheliner(𝑊̂ ).Forquantitativedescriptionsofthesetermswithrespect end totheunderlyingplasmaconditions,seeAppendixA. Self-heatingofDTfuelbyfusionreactionsoccurswhen𝑊̂ overcomesalltheenergytransportmechanismsrepresented 𝛼 inEq1.InMagLIF,insulatingmagneticfieldsareintroducedinthefueltoinhibitthermalconductionfromthehotDT plasmatothecoldlinerwallsprovidingtheinertialconfinement.[18]Thismagneticinsulationisessentialtosustaining theinternalenergyofthehotplasmaduringthe∼100nslinerimplosionstypicalofpulserICF. ThefuelenergybalanceconditionsrepresentedbyEq.1canbeintegratedintoanignitionproximitymetricbyaddition- allyconsideringthetimescaleduringwhichDTfusionoccursrelativetothetimescalethefuelishydrodynamically confined by the compressed liner. Following a canonical formulation of a “generalized Lawson criterion” (GLC) widelyusedbytheICFcommunity[30],wewriteageneralizedexpressionsuitableforanalysesofinertially-confined, magnetizedfusionplasmasas (𝑊̂ −𝑊̂ −𝑊̂ −𝑊̂ )𝜏 GLC′ ≐ 𝛼 𝑐𝑖 𝑐𝑒 𝑟 𝑇𝑁 𝑓. (3) ( 𝐸̂ ) DT Thenumericalparameter𝑓 ≈1.2hasbeencalibratedtoreproduceignitionthresholdfeaturesobservedinsimulations ofNIF-likeICFimplosions[30].Wemakeacommonsimplifyingassumptionthatthe𝑊̂ and𝑊 termsbecomesmall 𝑃𝑑𝑉 end astheliner“bounces”onthehigh-pressureDTfuelandexpandsafterpeakcompression.Simulationsprovideamore detailed,self-consistentpicturethatcontinuestoaccountfortheseenergytransportmechanisms.Theparameter𝜏 𝑇𝑁 representsthecharacteristicfusionburnduration,whichisgenerallyproportionaltothelinerarealdensityaccording to𝜏 ∝(𝜌𝛿𝑅)1/2,where𝜌 and𝛿𝑅 representthemeanlinermassdensityandthicknessatpeakcompression.Adeeper 𝑇𝑁 𝑙 𝑙 𝑙 discussionoftheseconceptsisprovidedinAppendixA.Inphysicalterms,theignitionthresholdconditionGLC′ ≈1 canbeinterpretedasthescenariowherethenetheatingoftheDTfuelbyfusionreactionsisenergeticallycomparable totheenergyofthecompressedfueljustpriortotheonsetoffusionburn. Figure3showsthebenefitsofmagnetizingfusionfuelbyplottingtheignitionthresholdcontoursofGLC′ =1asa functionoftheDTfuelarealdensity,(𝜌𝑅) (the‘DT’subscriptisaddedforclarity),andthemagneticfield-radius DT product,𝐵𝑅,atfusion-relevantplasmatemperaturesbetween5and8keV.ThesecurvesassumetheDTfuelisconfined byalong(highaspectratiowhencompressed)cylindricallinerwithtotalarealdensity(𝜌𝛿𝑅) =3g/cm2,implyingthe 𝑙 linerprovidesthemajorityoftheinertialconfinement.Thisisrepresentativeofthelinercompressionachievableby theDS,cf.Sec.2.5,andrepresentsaroughly3×increaseintheinertialtampingcharacteristicofpulserICFrelativeto 5 Affordable,manageable,practical,andscalable(AMPS)high-yieldandhigh-gaininertialfusion Figure 3: Contours of a generalized Lawson ignition threshold criterion GLC′ = 1 (Eq. 3) calculated for plasma temperaturesrangingfrom5to8keV.WeassumetheDTistampedbyalinerwitharealdensity(𝜌𝛿𝑅) =3g/cm2,a 𝑙 valueaccessibletotheDS.Plasmaconditionsaboveandtotherightofeachcurvearecapableofrobustself-heatingand ignition.Coloredrectanglesrepresenttheapproximateparameterregimesdistinguishingignition-scaleNIFimplosions, contemporaryMagLIFexperimentsonZ,andanticipatedfuelconditionsattainableonDS.MagnetizationwithDS-like targetscanconsiderablyreducefuelarealdensityrequiredforignition,easingdriverrequirementscomparedtowhatis requiredforNIF-liketargets. 6 Affordable,manageable,practical,andscalable(AMPS)high-yieldandhigh-gaininertialfusion ignition-scaleNIFexperiments,wherethetotalconfiningarealdensitiesarecloserto1g/cm2.[3,4]Whilelaser-driven schemestypicallyrequireheatingandablating≈90%oftheinitialcapsulemasstodrivehigh-velocityimplosions, leaving≈10%toconfinethehotspotatignitiontime[31],thecurrentdriveemployedinpulserICFacceleratesthe majorityofthelinermaterialinwardtoformthefinalcompressedfuel-linerassembly,leavingverylittletrailingmass behind. Ininertialfusionschemes,arealdensityissynonymouswithcompressionandpressure.Forcylindricalsystems,fuel massconservationimplies𝜌𝑅2 ≈ const,so(𝜌𝑅) = (𝜌𝑅) (𝑅 /𝑅) ≐ (𝜌𝑅) CR,whereCRisthefuelconvergenceratio. 0 0 0 IncreasingfuelcompressionrequiresincreasingtheCR,whichrequiresmoredrivepressureandcanincreasetherisk ofhydrodynamicinstabilities.Robustself-heatinginunmagnetizedDT,representedontheleftsideofFig.3,generally occursfor(𝜌𝑅) ≳0.2g/cm2.Thisisconsistentwiththehigh-pressure,high-compressiondesignspaceofNIFignition DT platforms,involvingstagnationpressures>300Gbar.[3,4] WhentheDTfuelismagnetized,self-heatingcanoccuratsubstantiallylowervaluesof(𝜌𝑅) .Figure3showsthat DT atsufficientlyhightemperatures,magnetizationreducesthefuelcompressionandassociatedpressuresneededby morethan10×. For𝐵𝑅values≳ 1.0MG⋅cm,thebenefitsofmagnetizationsaturatesas3.5MeValphaparticlesare largelyconfinedwithinthemagnetizedcylindricalfuelassembly.MagLIFexperimentsonZhavealreadydemonstrated 𝐵𝑅≈0.4-0.5MG⋅cm,[32–34]depictedschematicallybytheboxatthebottomofFig.3;scalingfromthe20MAZfacility to60MAontheDScouldleadtoanadditional2.6×increasein𝐵𝑅,[28]suchthatthebenefitsofmagnetizationarefully realized.Thetypicalhotspotarealdensityandmagneticfield-radiusproductsoccurringinsimulationsofMagLIF-like implosionsontheDSarealsoillustratedinFig.3,withexamplesshowninSec.2.5. 2.3 Efficientenergydeliverytotarget PulserICFprovidesapathtohighwall-plugefficiencyduetothesimplicityofthepulsertechnologyandthehigh efficiencyof(1)storedenergydeliveredtothetargetand(2)targetabsorbedenergycoupledtothefuelinternalenergy. Duetothehighcombinedefficiencyofbothofthesefactors,pulserICFoffersa200×increaseinoverallefficiency (storedenergycoupledtofuelinternalenergy)relativetolaserindirect-driveontheNIF. Forlaser-drivensystems,theconversionofelectricalenergyintocoherentlaserphotonstendstobeaninefficient process.Forexample,NIFstores330MJofelectricalenergyincapacitorbankstodeliver2.2MJofUVphotonstoa target,adriverefficiencyof𝜂 = 0.007. Modernlaserarchitecturesusingsolidstatepumpsinsteadofflashlamps D promiseefficienciesashighas𝜂 =0.1.PacificFusion’sDSstores80MJinthecapacitorsandtransfers≈90%ofthat D energytoanelectricalpulsewith100nsrisetime,ofwhich≈44MJisdeliveredtotheinsulatorstack(afunctionof machinedesignchoicesonly,independentoftheload)and≈ 8MJisultimatelydeliveredtothefusiontargetarea, a driverefficiency of 𝜂 = 0.1. The inherent efficiencyof theIMG drivertechnology, which eliminates inefficient D pulse-shapingstagesusedinlegacyarchitectures,providesclearadvantagesforenergydeliveryandfacilitysize.We note that a conventional Marx generator delivering a similar power pulse would require 6× the stored energy for comparableenergydeliveredtothetarget[15]. Theefficiencyofenergycoupledtothetargetisanadditionaladvantageofpulser-drivenICF.Thetarget,orload,is electricallyconnectedtothedriver,sotheamountofenergythedrivercandelivertothetargetdependsonitselectrical characteristics.Wedefinetheenergydeliveredtotheloadastheenergydeliveredtotheinitialvolumeofthefusion target[35].Asnotedabove,ofthe80MJofstoredenergy,approximately8MJisdeliveredtothefusiontargetvolume. Themetricofinterestfordefiningtheefficiencyofcouplingtoatargetistheworkdonetocompressandacceleratethe fusionfuellinerrelativetothetotalelectricalenergysuppliedbythedriver,oftenreferredtoasthehydrodynamicor implosionefficiency.PulserICFisa“directdrive”scheme,meaningthepulserdirectlymagneticallyacceleratesthe metallinerthatcontainsthefusionfueltocompressandheatthefuel.Weapproachthisfromacircuitperspective,as themotionofthelinerchangesitsinductance,whichfeedsbackonthedriver. Theworkdoneonthelinerischaracterizedbytheresponseofthecircuittothechanginginductanceofthetarget.As thelinerimplodes,itsinductancechanges,wheretheinductanceisdefinedusingtheexpressionforacoaxialsystemof conductors, 𝜇 ℎ 𝑟 𝐿= 𝑜 ln( 𝑐). (4) 2𝜋 𝑟 𝑙 Here𝑟 isthereturncurrentradius,assumedconstant,and𝑟 istheradiusofthefusiontargetliner,whichdecreaseswith 𝑐 𝑙 time.Theelectricalenergydeliveredtothelinervolumeispartitionedintotwochannels:abouthalfoftheenergygoes 7 Affordable,manageable,practical,andscalable(AMPS)high-yieldandhigh-gaininertialfusion intothemagneticfieldsurroundingtheliner,whichincreasesinmagnitudeandinvolumeastheenergyisdelivered. Theotherhalfoftheenergyismechanicalworkontheliner. Therefore,thepowerassociatedwiththemechanical workdoneonthelineris𝑃 = 1𝐼2 𝐿̇ [36],where mech 2 load load 𝜇 ℎ𝑟̇ 𝐿̇ =− 𝑜 𝓁 (5) 2𝜋 𝑟 𝓁 isthetimederivativeoftheloadinductance.Themechanicalworkdonetothetargetisthen 𝐸 = 1 𝑡𝑚𝑎𝑥 𝐼2 𝐿̇ 𝑑𝑡 =− 1 𝑡𝑚𝑎𝑥 𝐼2 𝜇 𝑜 ℎ𝑟̇ 𝓁𝑑𝑡. (6) mech 2 ∫ load load 2 ∫ load 2𝜋 𝑟 0 0 𝓁 Intheequationsabove,𝑡 isthetimewhichmaximizestheintegral,𝑟 isthelinerouterradiusand𝑟̇ itstimederivative. 𝑚𝑎𝑥 𝓁 𝓁 Powerisdeliveredtothelinerduringtherisingedgeofthedriverpowerpulse,andtheimplosiontimeismatchedtothe driverrisetime.Theimplosionefficiencyofthesystemisthendefinedas𝜂 =𝐸 /𝐸 .Aftertheimplosion,the imp mech driver drivercontinuesdeliveringpowertotheremnantsoftheload.Thismeansthatmuchofthe“inefficiency”inapulsed powerdriveriswrappedupinmagneticenergystoredinthevolumeofthetransmissionlinesaftertheimplosion stagnates. Inprinciple,thisenergycanbepartiallyrecapturedorusedtoenhanceconfinementlateintimewitha properlyengineeredimplosionscheme. Anaccuratecalculationoftheenergeticsofalinerimplosionrequiresamodelthatcouplesthelinerimplosiontoa circuitthatrepresentstheDS.Themodelshouldincludephysicalprocessessuchascompressionofthelinermaterial, ionization,ohmicheating,andotherprocesses.OneoptionistheSemi-AnalyticMagLIFModel(SAMM)[37],which capturesthephysicsofalinerimplosioninaseriesofordinarydifferentialequations.Anotheroptionisaradiation hydrodynamicscodethatusesaresistivemagnetohydrodynamicsmodel,suchastheFLASHsimulationsdescribedin Section2.4.In1DFLASHsimulations,themechanicalworkdoneonthetargetis≈4.5MJ,sothecouplingefficiency of driver stored energy to implosion energy is 𝜂 𝜂 = 5.6 %. At stagnation, some of the mechanical energy of D imp theimplodingshellisconvertedtointernalenergyofthefusionfuelshellandhot-spot,withefficiency𝜂 . In1D stag FLASHsimulations,theinternalenergyofthefusionfuelatstagnationis1MJ(ofwhichabouthalfisinthehotspot), correspondingto𝜂 ≈22%.Therefore,conversionefficiencyoftargetenergytofusionfuelinternalenergyis12%(1 stag MJfuelinternalenergycomparedto8MJdeliveredtothetarget),andthenetefficiencyofconvertingdriverstored energytofusionfuelinternalenergyis1.25%(1MJfuelinternalenergycomparedto80MJinitiallystored). Forlaserindirectdrive(LID)andlaserdirectdrive(LDD)ICFschemes,thereareseveralefficiencytermsthatmust beconsideredtoarriveatareasonablecomparison: thefractionofenergyabsorbedbythefuel-containingcapsule, theefficiencyofconvertingabsorbedenergytokineticenergyoftheimplodingshell,andthestagnationefficiency. InLID,mostofthelaserenergydeliveredtothetargetgoesintoheatingthehohlraumwallthatemitsandcontains thesoftx-raysthatdrivetheimplosion.Asmallfractionoftheenergydeliveredtothehohlraumtargetiscoupledto thefusion-containingcapsule: fortherecentNIFignitionexperiments,thiswas𝜂 ≈ 12%[38]. ForLDD,weare hohl concernedwiththecouplingefficiencyoftheUVlighttothecapsuleitself,whichistypically𝜂 ∼80%[39]. Both DD theLIDandLDDschemesacceleratethecapsuletohighimplosionvelocityviaablation, andmostofthecoupled energyisusedtoheatupandacceleratetheablatedmass,whichis∼90%oftheinitialmassofthesystem.Thismeans thatthemassoftheremaininglinerandfuelshellatpeakkineticenergyisquitesmallcomparedtotheinitialmass, andthekineticenergyissimilarlysmallcomparedtothetotalenergyabsorbedbythecapsule.Theefficiencyofthe “rocket”effectisgenerallyintherangeof7−15%.Duetothedeeperpenetrationofx-raysintotheablatormaterial comparedtolaserlight,LIDhashigherrocketefficiencythanLDD,whichpartiallycompensatesforthelowefficiency ofcouplingenergyfromthehohlraumtothecapsule.Ultimately,theimplosionefficiencyis𝜂 ≈2%forLID(LDDis imp higher,𝜂 ≈6%).Thetotalefficiencyofconvertingtargetabsorbedenergytofuelenergyis1%(>5×lowerthanfor imp pulser-drivenICFontheDS),andthenetefficiencyofconvertingstoredenergytofuelenergy𝜂 𝜂 𝜂 𝜂 ≈6×10−5, D hohl imp stag orabout200×lowerthananticipatedforDS.Alittlelessthanhalfoftheworkdoneonthefuelisconvertedtohot-spot internalenergy,whichleadstotheonsetofignitionandpropagatingfusionburn. In summary, pulser-driven ICFoffers atotal efficiency ofconverting stored energyto fuel energyof 𝜂 𝜂 𝜂 ≈ D imp stag 1.25×10−2,roughly200×higherthanLIDontheNIF.Asaresult,weanticipatethatDS,despitestoringabout4×less energythantheNIF,willdeliver50×moreenergytothefusionfuel;theimpactofthisonyieldandgainisdiscussedin thefollowingsections.TheseefficienciesarecomparedgraphicallyinFig.4.Finally,wenotethatevenifmodernsolid statelaserscanachievepromisedhighefficiencies,pulser-drivenICFalsoremainsmoreefficientthanLDD. 8 Affordable,manageable,practical,andscalable(AMPS)high-yieldandhigh-gaininertialfusion Figure4: Energyflowfromdriverenergystoragetofusionfuelinternalenergyforlaserindirect(hohlraum)drive (LID)ICFontheNIFandpulserdrivenICFontheDS.NIFnumbersarefrompublishedsimulations[38].DSnumbers arefromsimulationsdescribedbelowinSection2.4.Labelsrefertothevariousefficiencies𝜂describedinthetext. 2.4 Simulationcapabilityforignitionandhighgain Radiation hydrodynamics simulations have enabled ICF target design on today’s leading ICF facilities, including HYDRA’skeycontributionstoobtainingignitionontheNIF[38,40]andtheuseofHYDRA(e.g.,Ref.[28]),ALEGRA (e.g.Ref.[41]),andLASNEX(e.g.Ref.[42])fordesigningfusiontargetsatZ.Here,wedescribePacificFusion’starget designcode,presentabenchmarkagainstapublishedscalingstudytohigh-currentMagLIF,andshowsimulationsof high-gainfusiontargetsdrivenbyarepresentativecircuitmodelforourDS. For its target design simulation capabilities, Pacific Fusion is co-developing the FLASH radiation MHD code with thehostinstitutionforthecode,theFlashCenterattheUniversityofRochester.FLASH[43]isapublicly-available, massivelyparallel,multi-physics,adaptivemeshrefinement(AMR),finite-volumeEulerianhydrodynamicsandmagneto- hydrodynamics(MHD)code.FLASHhasaworld-wideuserbaseofmorethan4,600scientists,andmorethan1,300papers havebeenpublishedusingthecodetomodelproblemsinawiderangeofdisciplines,includingplasmaastrophysics [44,45],combustion,fluiddynamics,highenergydensityphysics(HEDP)[46,47],andfusionenergy.Overthepast decadeandundertheauspicesoftheU.S.DOENNSA,theFlashCenterhasaddedextensiveHighEnergyDensity Physics(HEDP)andextended-MHDcapabilitiestoFLASH[48],providinganexcellentfoundationforPacificFusion’s target simulation needs. Recent FLASH improvements include multiple state-of-the art hydrodynamic and MHD shock-capturingsolvers[49],three-temperatureextensions[48]withanisotropicthermalconductionandhigh-fidelity magnetizedheattransportcoefficients[50],electron-ionthermalequilibration,multi-groupradiationdiffusion,tabulated multi-speciesEOSandopacities,laserenergydeposition,circuitmodels,andnumeroussyntheticdiagnostics[51]. ToestablishconfidenceinFLASH’stargetdesigncapabilities,PacificFusionhasverifiedandvalidatedthecodeagainst analytictestproblemsanddatafromintegratedexperiments.Detailsofthiseffortarepresentedinaseparatearticle [52]. The experimental benchmarks include platforms for measuring hydrodynamic instability growth rates such as the magneto-Rayleigh-Taylor [42, 53] and Richtmyer-Meshkov [54] instabilities. We also benchmarked against a platform for measuring the inertial confinement time of a compressed liquid deuterium fuel [41] and precursor MagLIFexperimentsthatradiographedimplodingberylliumliners. Finally,webenchmarkedFLASHagainstfully integratedMagLIFexperiments,suchasZshot2977[34],andagainstthesimilarityscalingstudyforscalingMagLIFto highcurrents[28]. Resultsofthesebenchmarkscanbefoundintheupcomingpublication[52]. Inallcases,FLASH simulationshavebeenshowntoagreewellwiththeexperimentaldataandwiththepublishedsimulationresultsfrom thecodesusedtodesignthetargets,includingLASNEX,HYDRA,andALEGRA. Figure5showsanexampleofavalidationbenchmarkthatalsoillustratestheexcitingfusionregimeaccessibleathigh currents.ThefigurecomparesFLASHsimulationstopublishedHYDRAsimulationsofaMagLIFtargetscaledfrom15 MAto60MApeakcurrent[28].Thisscalingstudywasconservative,meaningitattemptedtomaintainthedynamics oftheimplosiondesignsonZbyconservingthevaluesofseveraldimensionlessparametersthatdescribethesystem, i.e.,similarityscaling.TheFLASHsimulationswereinitializedwithMagLIFtargetgeometriesdescribedinRef.[28] andcoupledtoalumped-elementexternalcircuitmodelrepresentingapulsedpowerdriver.NativeFLASHdoesnot possessmodelsforfusionreactionsofhydrogenicisotopes,sowehaveextendedourinternalversionofFLASHto 9 Affordable,manageable,practical,andscalable(AMPS)high-yieldandhigh-gaininertialfusion Figure5:Fusionyieldfrom2DFLASHsimulationsoftheMagLIFcurrent-scalingstudy,comparedwith2DHYDRA simulationsreportedinRef.28. Calculationsincludingalphaheating(“with𝛼”)areshownalongsidethosewithout alphaheating(“no𝛼”). includerelevantfusionreactionsandtocoupletheresultingenergytothematerialviaeitheralocal-depositionmodel oranalpha-energydiffusionmodel.Figure 5showsthatFLASHisabletoaccuratelymodelthefusionyieldofthese MagLIFtargets,representingtheculminationofmanyphysicalprocesses.Thescalingtrendiscapturedextremelywell, validatingthatFLASHissolvingtherelevantphysicalprocessestomatchthetheoryestablishedinRef.[28]andthe HYDRAsimulationsfromthesameReference.Moreover,thefusiongainfactorsandalphaamplificationfactorsare similartotheHYDRAsimulations,indicatingthatignitionoccursatsimilarvaluesofcurrentdriveinthetwocodes. Wenotethatthesesimulationswereinnoway“calibrated”totheHYDRAsimulationsbutweremerelyrunwiththe sameproblemdefinitionandtheinclusionoftherelevantphysicalprocesses.Athighcurrentswithalphadeposition on,HYDRAsimulationsindicateslightlyhigheryieldthanFLASH;thisdifferenceisanongoingareaofdevelopment. Figure5clearlyshowstheonsetofself-heatingandignitiondescribedinSection2.2:thesimulatedfusionyieldfrom calculationsthatincludealphaheating(“with𝛼”)divergefromcalculationswithoutalphaheating(“no𝛼”)at𝐼 ≥40 max MA,withyield𝑌 ≥60MJat𝐼 =60MA.ThemainresultofthesimilarityscalingstudyisthatMagLIFperformance 𝐷𝑇 𝑚𝑎𝑥 onZtodayscalesconservativelytoignition(asquantifiedbytheGeneralizedLawsonCriteron)atpeakdrivercurrent 𝐼 ≥50MA[28].Thesimilarity-scaleddesignsareconservativeinbothsensesoftheword:thescalingconservesthe max keydimensionlessparametersthatdescribethesystem,anditisbaselinedbyperformanceontheZfacilitytoday,with nomajorinnovationsintargetdesignandtechnologyassumed. TargetdesignscanbeimprovedbeyondsimilarityscaledversionsofMagLIFonZ,whichcanfurtherincreasegain andreducedrivercost.OnepromisingapproachinvolvesaddingacryogenicDTfuellinertotheinnersurfaceofthe implodingcylinder[19,26],asisdoneinsphericalNIFcapsules.TheDTicelinerservesmultiplepurposes:inaddition toshieldingthefuelhot-spotfromthemetallicliner,whichcouldmixintothefuelandincreaseradiationlosses,the fuelservesasareservoirofmassforthehot-spot,someofwhichissqueezedoutthetopandbottomofthecylindrical implosion.Theignitinghot-spotcandriveafusionburnwaveintothedensefuelliner,dramaticallyincreasingthe fusionyieldcomparedtogas-fuel-onlyMagLIFtargets. WepresentFLASHsimulationsofsuchaprototypecryogenictargetconceptdrivenbyacircuitmodeloftheDSpulser. Simulation-basedtargetdesignwillbeamajorongoingeffortatPacificFusion;hereweseektoshowaproof-of-concept illustration that the drive energy is sufficient for achieving ignition and facility gain with a target appropriately impedance-matchedtothedriver.IntheFLASHsimulationsoftheDS-driventargets,thecircuitmodelrepresentsthe voltagedriveprovidedbytheDSpulserandincludesimpedancesandlossesofthekeycomponentsofthesystem, includinglossesinthevacuumtransmissionlines.Thecircuitlossmodelsarecalibratedagainstparticle-in-cellkinetic simulations(describedinSection3.4). Figure6showsstreakplotsofdensityfortwoMagLIFtargetsdesignedtomatchtheDSpulser.Theberylliumliner design(Fig.6a)usesathinnerlinerthanthescaleddesignsfromFig.5,andisbasedonrecenthigh-performingMagLIF 10 Affordable,manageable,practical,andscalable(AMPS)high-yieldandhigh-gaininertialfusion Figure6:FLASHsimulationsof6mmtallMagLIFtargetsdesignedtomatchtheDSpulser.Thepulserdelivers𝐼 =56 𝑚𝑎𝑥 MAand𝐸 ≈8.3MJofelectricalenergytoeachdesign.Bothtargetshave300µmthickDTiceliners,𝐵 =15T,and 𝑙𝑖𝑛𝑒𝑟 𝑧 18kJpreheatenergy:(a)Berylliumlinerdesigngenerates109MJyield(b)Aluminumlinerdesigngenerates380MJ yield. 4 3 2 1 0 150 155 160 165 170 175 Time (ns) )2mc/g( R ytisned laerA Be liner 20 Al liner 15 10 5 a) 0 0.0 0.1 0.2 0.3 0.4 0.5 r (mm) )Vek( erutarepmet noI 400 Be liner 300 200 100 b) 0 )3mc/g( ytisned Be liner Al liner Figure7:CharacteristicplasmaconditionsofthedesignsshowninFig.6:(a)Linerarealdensity((𝜌𝛿𝑅))vs.time(b)Ion 𝑙 temperature(dash)andmassdensity(solid)vs.radiusatthetimeofpeak(𝜌𝛿𝑅).Thehigher(𝜌𝛿𝑅) ofthealuminum 𝑙 𝑙 linerdesignresultsinhighertemperature,density,andtotalyield. experimentsusingthinnerliners[55].Thealuminumlinerdesign(Fig.6b)isappropriatelyscaledfromtheberyllium design. Bothdesignsare6mmtallandaredrivento𝐼 = 56MA.Bothexampledesignsarepartofanextensive 𝑚𝑎𝑥 computationalstudyofMagLIFperformanceachievableontheDS.Theexamplesshownherehave300µmthickDT iceliners,𝐵 =15T,and18kJpreheatenergyandbothachievefacilitygain.Theberylliumlinergenerates109MJof 𝑧 fusionyieldforafacilitygainof𝑄 =1.36andthealuminumlinergenerates380MJforafacilitygainof𝑄 =4.75. 𝑓 𝑓 Insummary,PacificFusionhasahigh-fidelityradiationhydrodynamicssimulationcapabilitythathasbeenvalidated againstarangeofintegratedexperimentsatZ.ThiscodehasreproducedthekeyresultsoftheMagLIFcurrent-scaling studyofRef.[28],whichindicatesthatconservativelyscaledMagLIFtargetsarewellintotheignitionregimeatthe 60MAscale. PacificFusioniscurrentlyusingFLASHtodesignMagLIFtargetsfortheDSpulserthatcanachieve 𝑄 >1.Inthenextsection,weuseFLASHsimulationstodiscussscalingofMagLIFtofacilitygainandhowthisscaling 𝑓 comparestolaser-drivenICF. 2.5 Scalingtofacilitygain Intheinertialregime,therequirementstoheatandcompressfusionfueltoignitionconditionsareindependentof thecompressionscheme[56].IgnitionandtargetgainwereachievedontheNIFlaserbyacceleratingaDTfusionfuel 11 Affordable,manageable,practical,andscalable(AMPS)high-yieldandhigh-gaininertialfusion shelltohighvelocity(𝑣 ≥400km/s)whiletailoringthecompressibilityoftheimplosionandincreasingthesizeofthe implosionsystemtoprovidesufficientconfinement.Magnetically-driveninertialfusionsystemsaretypicallyscaled differentlyfromlaser-drivensystems.Itisinstructivetocomparehowthesetwodifferentsystemsscaletounderstand thetechnicalbasisforpursuingpulser-drivenICF. 2.5.1 Scalinglaser-drivenICF Hydro-equivalentorhydrodynamicscalingisoftenusedtoassesshowlaser-drivenfusionsystemsscaletolarger facilitydrivers[57].Inhydro-equivalentscaling,thefundamentalcharacteristicsoftheimplosionremainconstantas thesystemisenlarged.Theimplosionvelocityandablationpressureareheldconstant,leadingtoconstantvaluesof thestagnationpressure,density,andtemperature,intheabsenceofalpha-heating.Hydroequivalenceisachievedby scalinggeometricquantities(lengths)andtemporalquantities(timescales)together: 𝑟 =𝑠𝑟 0 𝑡 =𝑠𝑡 , 0 where𝑟 and𝑡 arethecharacteristiclength-andtime-scalesofthereferenceimplosion.Thus,geometricareasscaleas 0 0 𝑠2,andintensityonthecapsulesurfaceiskeptconstantbyscalingthelaserpower𝑃 bythesamefactor𝑠2.Thelaser 𝐿 energy𝐸 ,proportionalto𝑃 ×𝑡,scalesas𝐸 ∝ 𝑠3. Alternatively,thescalingcanbewrittenas𝑟 ∝ 𝐸1/3 . Density 𝐿 𝐿 𝑙𝑎𝑠𝑒𝑟 𝑙𝑎𝑠𝑒𝑟 isconstant, sothescaledsystemmassalsoincreasesby𝑠3. Ignoringtherelationshipbetween𝐸 andhohlraum 𝑙𝑎𝑠𝑒𝑟 efficiency,whichisrelativelyweakforNIF-sizeandlargerhohlraums,thisscalingappliestobothlaser-direct-driveand laser-indirect-driveschemes. Asanimplosiondesignishydrodynamicallyscaledtolargerdrivers,itpassesthroughthreeperformanceregimes:the pre-ignitionregimeatlowcapsuleabsorbedenergy𝐸 ,wheretheyieldscalesweaklywithenergy;theboot-strap 𝑐𝑎𝑝 regime,wheretheyieldrapidlyincreasesduetotheonsetofself-heating;andtherobustly-burningregime,wherethe yielddependsonlyontheDTfuelmassandtheinertialburn-upfraction𝜙,definedas 𝑌 =𝜙𝑚 𝑒 . (7) 𝐷𝑇 𝑓𝑢𝑒𝑙 𝐷𝑇 Here,𝑒 =3.4×1011J/gistheQ-valueoftheDTreaction(17.59MeV)permass.Theburn-upfractionforspherical 𝐷𝑇 inertialfusionsystemscanbederivedasafunctionoftheDTfuelarealdensity𝜌𝑅, 𝜌𝑅 𝜙= , 𝜌𝑅+6 where𝜌𝑅hasunitsofg/cm2[31].Sincehydro-equivalentscalingmaintainsaconstantdensity𝜌,thearealdensityscales onlyas𝑟,𝜌𝑅 ∝𝐸1/3,andfor𝜌𝑅 ≪6,𝜙∝𝐸1/3. Thismeansthatwhenhydrodynamicallyscalingarobustly-burning 𝐿 𝐿 design,theDTyieldandtargetgain𝑄 scaleas 𝑡𝑎𝑟𝑔𝑒𝑡 𝑌 ∝ 𝐸4/3 𝐷𝑇 𝐿 𝑌 𝑄 = 𝐷𝑇 ∝ 𝐸1/3 𝑡𝑎𝑟𝑔𝑒𝑡 𝐸 𝐿 𝐿 Thisunfavorablescalingasanimplosiontransitionsfromboot-strappingtorobustignitionmeans,forexample,that hydrodynamicallyscalingtherecentNIFexperimentswith𝑄 ≈2.4at𝐸 =2.05MJto𝑄 ≈10wouldrequire 𝑡𝑎𝑟𝑔𝑒𝑡 𝐿 𝑡𝑎𝑟𝑔𝑒𝑡 𝐸 ≈10MJ[58]. 𝐿 2.5.2 Scalingpulser-drivenICF InpulserICF,magnetically-drivenlinersarecontinuouslydriventhroughoutthepowerpulsebytheLorentzforce. Forcertaintargetdesigns,pre-heatenergyandmagneticfieldareinjectedintothefuelcavitybeforetheimplosion stagnates,preconditioningthehotspottoreachignitiontemperatures.IntheMagLIFconcept,forexample,thepre-heat energyisinjectedusingalaser,andthefuelismagnetizedbyexternalHelmholtzcoils.Thisapproachhasbeenstudied extensivelybutislimitedbythecapabilitiesoftheZFacilityatSandiaNationalLaboratories,notablythatZcannot drivemorethan∼20MAthroughaMagLIFtarget. 12 Affordable,manageable,practical,andscalable(AMPS)high-yieldandhigh-gaininertialfusion TosimplifytheengineeringofandachievelowcostsinfuturepulserIFEpowerplants,wearedevelopingtargetdesigns thateliminatetheneedforapreheatlaserandexternalHelmholtzcoils.Forexample,onecanpre-heatandmagnetize thefuelbyusingacurrentpre-pulsethatusesasmallfractionoftheenergyusedtocompressthetarget.Alternatively, higherpressureimplosionconceptscanreduceorentirelyeliminatetheneedforpre-heatand/ormagnetization[59]. PreviousstudieshaveinvestigatedsimilarityscalingofMagLIFtolarger(highercurrent)driversthanZ[27–29].When theamountofcurrentdeliveredtothetargetisincreasedwhilemaintainingthe≈100nsrisetimeofthecurrentpulse, thedrivepressureandstagnationpressurealsoincrease. Asaresult,thefusionyieldscalesas𝑌 ∝ 𝐼6 [28],even 𝐷𝑇 𝑚𝑎𝑥 beforeaccountingforplasmaself-heatingfromalphaparticles.Whenthetargetheightisheldconstantwith𝐼 ,the 𝑚𝑎𝑥 energydeliveredtothelinerscalesas𝐸 ∝𝐼2(seeEq.6).Thus,yieldandgainscaleas 𝑙𝑖𝑛𝑒𝑟 𝑌 ∝ 𝐸3 𝐷𝑇 𝑙𝑖𝑛𝑒𝑟 𝑌 𝑄 = 𝐷𝑇 ∝ 𝐸2 , 𝑡𝑎𝑟𝑔𝑒𝑡 𝐸 𝑙𝑖𝑛𝑒𝑟 𝑙𝑖𝑛𝑒𝑟 evenbeforeself-heatingistakenintoaccount.Thisgainscalingismuchmorefavorable—growingfasterwithenergy deliveredtoliner/target—thanthehydro-equivalentscalingthatappliestolaserICF.Combinedwiththelowcostand highefficiencyofpulsertechnology,thisscalingisamajorreasonPacificFusionisdevelopingpulserIFEonitsDS. 2.5.3 ComparingscalingontheNIFtoPacificFusion’sDS Combining our understanding of inertial fusion theory, driver efficiency, and scaling laws enables us to compare ourgoalof𝑄 >1onPacificFusion’sDStotherecentachievementofignitionontheNIF.Ignitionandtargetgain 𝑓 𝑄 > 1ontheNIFdemonstratethatfusiongainispossibleininertialsystems. Buildingasystemthatcanreach 𝑡𝑎𝑟𝑔𝑒𝑡 𝑄 >1requiresefficientlydrivinglargerfuelmassesthanthoseusedinNIFtargets.Pulser-drivenICFisideallysuited 𝑓 tomeetthischallenge,duetoitshighefficiencyandbecauseitcanachieve𝑄 >1bygeneratingfusionfuelconditions 𝑓 thathavealreadybeendemonstratedontheNIF,asdiscussedbelow. ThebasicsoffusionignitionandgainwereunderstooddecadesbeforetheyweredemonstratedontheNIF.Hydro- equivalentscalingwasusedtogenerateasetof“gaincurves”forlaser-indirect-driveICFbyMeadetal.,in1990[60]. Figure8showsthegaincurves(dashedgray)reproducedfromtheoriginalreport,withthex-axisconvertedfrom laser energy 𝐸 to capsule absorbed energy 𝐸 . These curves were generated by running the ICF design code 𝑙𝑎𝑠𝑒𝑟 𝑐𝑎𝑝 LASNEX[61] with various levels of degradation to the implosion. The curves are expressed as confidence bands, withhigherprobabilitiescorrespondingtomoredegradedimplosionsandlowerprobabilitiescorrespondingtomore optimalimplosions.Forexample,the5%confidencecurvecorrespondstonear-optimal,highlycompressed,perfectly symmetricalimplosionswithnomix.Theauthorsconcludedtherewasa5%probabilityofachievingthisperformance levelgiventhestateofICFknowledgein1990.ThecurvesclearlyshowthethreeperformanceregimesdescribedinSec. 2.5.1(pre-ignition,boot-strapping,androbustburn). Notethatthex-axisofFig. 8hasunitsofMJ,whereasthey-axisisdimensionless. Yield=gain×energy,solinesof constantfusionenergyoutputappearasstraightlines(withnegativeslope)ontheplot.ThesubsetofNIFimplosiondata showninFig.8revealstheprescienceofthe1990report:Earlyplastic(CH)shellimplosionsfromtheNationalIgnition Campaign(NIC,green)fallbelowthe95%confidenceband.Thismakessense,ascalculatingthepoorperformanceof theseimplosionsrequired3Dsimulationsthatincorporateddegradationsourcesthatwereunanticipatedin1990[62]. Improvingthehydrodynamicstabilityoftheseimplosionsledtoa≈10×improvementingain(magenta)[63].Switching todiamondcapsulesledtohigherperformancethanplasticatapproximatelythesamescale(blue)[64].Largerdiamond capsuledesigns(cyan),scaledupinsizefromthesmallerdiamonddesigns[65],achievedthelargestimprovementin performanceandgain,reachingignitionandtargetgain𝑄 >2[4,38].Theincreaseintargetperformanceatnearly 𝑡𝑎𝑟𝑔𝑒𝑡 constant𝐸 resultedfromimprovingtargetdesignandfabricationtoreducedegradationoftheimplosionbyablator 𝑐𝑎𝑝 mix. ThehighestperformingNIFshotto-date(darkcyanstarinFig. 8)liesonthe50%confidencegaincurve. Higher- performing,lower-confidencecurvescorrespondtoimplosionswithmorecompressionandlarger𝜌𝑅.Itremainstobe seeniffurtheradvancesintargetdesigncanleadtoadditionalperformancegainsorwhetherfutureNIFexperiments will“rollover”andfollowthe50%gaincurveintotherobustly-burningregime.Numerousdesignimprovementsare neededforexistingignitiondesignsontheNIFtoscalefavorablyto𝑄 >1onafuturelaserfacility[58]. 𝐹 InFig.9,wevisualizepulser-drivensystemsinthesamespaceasNIFimplosions.Forthispurpose,wetransformthe x-axisfromabsorbedenergy𝐸 toarealdensity𝜌𝑅.Specifically,weusetheharmonic-mean𝜌𝑅describedinEq.16of 𝑐𝑎𝑝 13 Affordable,manageable,practical,andscalable(AMPS)high-yieldandhigh-gaininertialfusion 103 102 101 100 10 1 10 2 10 3 10 4 10 5 10 3 10 2 10 1 100 101 Capsule absorbed energy (MJ) niag eluspaC 1000 MJ 100 MJ 10 MJ 1 MJ 2.2 MJ laser 5.4 MJ yield 0.1 MJ 0.01 MJ 5 % 16 % Scaled NOVA 50 % 84 % NIF ignition Gcap 20 95 % NIF large diamond NIF small diamond NIF CH alpha-heating NIF CH NIC NOVA data Figure 8: Ignition and gain scaling plot for laser-indirect-drive ICF, based on the 1990 study[60]. The gain curves (dashedgray)weregeneratedfromLASNEXsimulationswithmore(highconfidence)orfewer(lowconfidence)sources ofdegradation.ThebarsinthelowerleftrepresentunpublisheddeuteriumimplosionsfromtheNOVAlaserandthe samedatascaledupforDTfuel.CirclesareNIFDTimplosiondatafromvariouscapsuledesigns.Thedarkcyanstaris thetargetgain𝑄 ≈2(𝑌 ≈5MJ)resultfromFebruary2024. 𝑡𝑎𝑟𝑔𝑒𝑡 103 102 101 100 10 1 10 2 10 1 2×10 1 3×10 1 4×10 1 6×10 1 100 Harmonic mean areal density (g/cm2) niag renil ro eluspaC NIF ignition Gcap 20 NIF large diamond NIF small diamond 60 MA 65 MA NIF CH alpha-heating 56 MA Be NIF CH NIC 60,65 MA DS MagLIF Be + DT ice DS MagLIF Al + DT ice 56 MA 20 MA Figure9:Ignitionandgainscalingplotforlaser-drivenICFandpulser-drivenICF,plottedagainsttheharmonicmean √ arealdensity= 𝜌𝑅 (𝜌𝛿𝑅),animportanttermintheGeneralizedLawsonCriterion(Eq.16).Theredandblacklines 𝐻𝑆 𝑙 aretargetgainestimatesfromacurrent-scalingstudyofthetwoDTicelayerMagLIFdesignsdescribedinFig.6and Table1. Onlythe20MApointsareaccessibleonZtoday;largercurrentswillbeaccessedontheDS.Bothdesigns starttoigniteat𝐼 ≥50MA(thelast4pointsofeachline),wheretheMagLIFlinersachievesimilararealdensityto 𝑚𝑎𝑥 ignitingNIFcapsules. At𝐼 ≥ 60MA,theMagLIFdesignsreachlargertargetgain𝑄 andhigheroverallyield 𝑚𝑎𝑥 𝑡𝑎𝑟𝑔𝑒𝑡 thantheNIFignitionshot. 14 Affordable,manageable,practical,andscalable(AMPS)high-yieldandhigh-gaininertialfusion Table1:ComparisonofperformancemetricsforNIFignitionandsimulatedDStargets.TheBeDSandAlDStargets, drivenwithapeakcurrentof56MA,achieve𝑄 >1in1Dsimulations. 𝑓 Metric NIFIgnition BeDStarget AlDStarget Energystoredincapacitors 330MJ 80MJ 80MJ Energydeliveredtotarget 2.2MJ 8.3MJ 8.4MJ DTfuelmass 0.22mg ≈10.6mg ≈10.2mg Nuclearenergyyield 5.2MJ 109MJ 380MJ 𝑄 =𝑌 /𝐸 ≈2.4 ≈13 ≈45 𝑡𝑎𝑟𝑔𝑒𝑡 𝑇𝑁 𝑑𝑟𝑖𝑣𝑒𝑟 𝑄 =𝑌 /𝐸 ≈260 ≈100 ≈350 𝑓𝑢𝑒𝑙 𝑇𝑁 𝑖𝑛𝑡,𝐷𝑇 DTburn-upfraction𝜙 7% 3% 10% Facilitygain𝑄 0.016 1.36 4.75 𝑓 √ appendixA, 𝜌𝑅 (𝜌𝛿𝑅).Thisexpressionshowsthataninertialfusionassemblycanignitewhentheproductoffuel 𝐻𝑆 𝑙 arealdensityandlinerarealdensityissufficientlylarge.Sincetherequirementsforignitionandpropagatingburnare independentofthedriver,MagLIF-likeICFdesignscanbeplottedinthissamespacealongsideNIFdata.ForNIFpoints, weusepublishedvaluesof𝜌𝑅 and(𝜌𝛿𝑅) =𝜌𝑅 −𝜌𝑅 [38,66,67].Forexperimentswithoutpublisheddata,the 𝐻𝑆 𝑙 𝑡𝑜𝑡𝑎𝑙 𝐻𝑆 𝜌𝑅wasscaledas𝜌𝑅∝𝐸(1/3),perhydro-equivalentscaling.Therangeof𝜌𝑅spannedbytheNIFexperimentsisquite 𝑐𝑎𝑝 small,sotheuncertaintyintheestimated𝜌𝑅doesnotchangetheoverallconclusionsoftheplot. TheredandblacklinesarefromFLASHsimulationsofacurrent-scalingstudyofMagLIFtargetswithDTicelayers. ThesesimulationsarebasedonthetwoignitiondesignsdescribedinSection2.4andFigs.6-7.Thetwodesigns,with 𝐼 =56MA,weresimilarity-scaledtospanarangeofdrivecurrent𝐼 =20−65MAusingthescalingprescriptions 𝑚𝑎𝑥 𝑚√𝑎𝑥 presentedbyD.E.Ruiz[28,68]. The20MAZ-scalepointsgenerate 𝜌𝑅 (𝜌𝛿𝑅) ≈ 0.15g/cm3,farbelowwhatis 𝐻𝑆 𝑙 neededforignition.Asthedrivecurrentincreases,theMagLIFdesignsincreaseinarealdensityandgainslowly.From 𝐼 ≈50−65MA,thecurvesincreaserapidlyinarealdensityandtargetgain.The56MABe-linerdesignpointisjust 𝑚𝑎𝑥 totherightoftheNIFignitionstar,whereasthe56MAAl-linerpointreacheshigherarealdensityandgainatthesame current. WecancomparetheefficiencyoftheDSdriver/fuel-linedMagLIFcombinationtoarecentNIFignitionexperiment. Thereareseveralusefulmetricsforfusionsystemefficiency.Thetargetgain𝑄 andthefacilitygain𝑄 quantify 𝑡𝑎𝑟𝑔𝑒𝑡 𝑓 theoveralldriver-targetsystemefficiency,whereasthefuelgain𝑄 andburn-upfractionareusefulforassessingthe 𝑓𝑢𝑒𝑙 efficiencyoftheburnrequiredtogeneratelargefusionyields. For a recent igniting implosion on the NIF using 2.05 MJ of laser energy, the total work done on the DT fuel was approximately20kJ,or1%ofthelaserenergydeliveredtothehohlraum.Duetoincompleteconversionofkineticto internalenergyandotherlosses,8.2kJofthe20kJwereconvertedtofuelinternalenergy[38].Weextrapolatethisto 9-10kJfuelinternalenergyintheabsenceofalphaheatingfora2.2MJNIFshot.RecallfromEq.7thattheburn-up fraction𝜙istheratioofthetotalnuclearenergyoutputtotheoutputthatwouldbegeneratedbyreacting100%ofthe fuel.RecentNIFignitionshotsdrivenby2.05MJwithfuelmass0.22mgDTreleased3.2MJand3.9MJ,corresponding to𝜙=4.3%and𝜙=5.3%,respectively[58].Assumingthesamefuelmass,thehighestperformingNIFignitionshot, whichyielded5.2MJat2.2MJlaserenergy,burnedup𝜙≈7%ofitsDTfuel. Wecomparethistothe56MAMagLIF-liketargetdesignsfortheDSdescribedinSection2.4andFigs.6-7.Theelectrical energydeliveredtotheload(target),givenbyEq.6,dependsonboththepulserrise-timeandthetargetheightℎ,sowe wishtominimizebothtomaximize𝑄 ;thisiswhythedesignsinFig. 6are6mmtall. Table1comparessimulated 𝑓 performance metrics for these two DS targets to the highest performing NIF ignition experiment to-date. Table 1 showsthatreaching𝑄 > 1withMagLIFontheDSrequiresfuelgainandburn-upfractionlevelsthatarealready 𝑓 demonstratedonNIF.Facilitygain𝑄 >1isachievableontheDSduetothehighefficiencyofenergydeliverytothe 𝑓 targets,whichenablescompressionandheatingoffuelmassesnearly50×largerthanNIFignitiontargets. Insummary,theMagLIFICFconceptprovidesaconservativescalingpathto𝑄 >1.Withtheadditionofacryogenic 𝑡𝑎𝑟𝑔𝑒𝑡 DTfuellayer,MagLIFscalesto𝑄 >1onPacificFusion’sDSwithfuelgain𝑄 andburnupfraction𝜙comparable 𝑓 𝑓𝑢𝑒𝑙 tothosealreadyachievedontheNIF.Facilitygaincanbeincreasedfurtherbydrivingtolargerpeakcurrent. For example,A65MAaluminumlinertargetscaledfromthedesignshowninTable1andFig.9generates816MJofyield, correspondingtofacilitygain𝑄 ≳7,sufficientforafusionpowerplant.Inadditiontodrivingtohigherpeakcurrents, 𝑓 15 Affordable,manageable,practical,andscalable(AMPS)high-yieldandhigh-gaininertialfusion additionalimprovementstotargetdesigncanfurtherincreasegain. 2.6 Demonstratedperformancewiththermalfusionreactions Thehistoryofmagnetically-drivenpulsedfusionsystemscontainsexampleswherethepredominantmechanismof fusionproductionwasnon-thermalbeam-driven(thatis,highlyenergeticfuelionbeams,resultingfrominstabilities, thatdrovefusionbycollisionswithotherfuel)ratherthangeneratedbyathermaldistributionofions.Thiscanbeseen intheearlydaysofquasi-staticZ-pinches,wheresausage-andkink-modeinstabilitiestendedtobreakaparttheplasma column,producinglargetransientvoltagesacrossthecolumn[69],acceleratingionstohighenergy(∼1 MeV),resulting innon-thermalneutronproduction.SimilarbehaviorhasbeenobservedinavarietyofdynamicZ-pinchconfigurations, e.g.thedenseplasmafocus(DPF)[70–72]andgaspuffZ-pinch[73–78].Neutronsproducedbynon-thermalmeanstend tonotscalefavorablytoignitionandgain.Acommonfactorinallofthesesystemsisthatthedrivercurrentispresent withinthefuelitself.ThismeansthatfuelionswilldirectlyexperiencethetransientelectricfieldsresultingfromMHD andkineticinstabilities. Fortunately,pulserICFconceptssuchasMagLIFdonotsufferfromthisproblem.InMagLIFimplosions,athickmetal liner implosion is used to compress the fusion fuel, preventing the penetration of the driver current into the fuel andthecreationofenergeticionbeams. Allobservationsofdensity, temperature, andneutronspectrainMagLIF experimentsareconsistentwithfullythermalnuclearburnprocesses,exhibitingnoneofthesignaturesofnon-thermal ionpopulations,e.g.highenergyneutronsandanisotropicneutronemission[79].Gomezetal.showedthattheneutron spectraobservedalongtheaxialandradialdirectionswereroughlyequivalent[80–82].Whenfittingthecoreofthe spectrumwithathermalmodeloverawiderangeofexperiments,noexcessofneutronsinthehighenergytailwas observed. Anexcessofneutronsisobservedinthelowenergyportionofthespectrum,butthisisconsistentwith neutronscattering. Furthermore,theyieldsmeasuredalongdifferentdirectionsallagreewithinthemeasurement uncertainty[80].Inshort,theneutronemissionindicatesnoneedtoinvokeanon-thermalexplanationforanyofthe observablefeatures.AMaxwellianiondistributionisperfectlyadequatetoexplaintheobservedneutronsignatures. OtherevidencefromthewiderangeofexperimentsconductedatSandiaNationalLaboratoriessupportsthisclaim. Knappetal.demonstratedaBayesiandataassimilationapproachutilizingathermalplasmamodelthatisabletomatch allobservables(neutronandx-ray)simultaneouslyoverawiderangeofexperiments[20].Thespectralcharacteristicsof bothneutronsandx-raysareusedtofitmultiplediagnosticsignaturessimultaneously,assumingtheionsandelectrons areinthermalequilibrium.Gomezetal.showedthatthetargetyieldscaledasexpectedwithinferrediontemperature overarangeof∼ 1−3keV[83]. Furthermore,Knappetal. andHarvey-Thomsponetal. demonstratedthatmixof non-fuelmaterialintothestagnationcolumndegradesperformanceasonewouldexpectforathermalplasma[84,85]. Inabeam-targetconfiguration,mixatthefewpercentlevelwillonlydegradeperformanceinproportiontothedilution ofthetargetions.However,thetrendsinMagLIFdataareconsistentwiththereductioninperformanceexpecteddue totheenhancedradiationlossesandresultantcoolingofthefusionplasma.Theevidenceoverwhelminglypointsto thethermalnatureoffusionproductionintheMagLIFconfiguration,lendingstrongsupporttothescalingofthese conceptstoignitionandgain. 3 PulserDesign 3.1 DemonstrationSystem(DS)Overview PacificFusion’sDSisdesignedwiththegoalofdemonstratingfusionperformancerequiredforacommerciallyviable fusionenergysystem.TheDSstoresapproximately80megajoulesofelectricalenergyandwilldeliver>60MAover ∼100nanosecondtimescalestoafusiontarget.Figure10showsthelayoutoftheDSpulser,whichisbrokenupinto threesections:thepulsermodules,thewatertransmissionlines,andthetargetarea.TheDSconsistsofthreediscrete levelsofpulsermoduleswithanimpedance-matched-Marx-generator(IMG)architecture.Powerisdeliveredfromthe modulestothetargetareaviawater-insulatedcoaxialtransmissionlinesandtri-plateimpedancetransformers.The waterchambersurroundingthetargetchamberandthetri-plateswillbefilledwithdeionizedwaterprovidingthe necessaryneutronshielding–atleast5meters–toensurecaptureofallgeneratedradiation.Thetargetareaconsists ofawater-vacuuminsulatorstack,thetargetdiagnosticsuite,andavacuumareacontainingasetofmagnetically insulationtransmissionlines(MITLs),detailedinSection3.5,atriplepost-holeconvolutetocombinethelevels,and afinalinnerMITLthatdeliversthepowertoacassettecontainingthefusiontarget.Thetargetitselfconsistsofthe fusionfuelsurroundedbytheliner,andtheelectricalcurrentdeliveredthroughthetargetgeneratestheLorentzforce 16 Affordable,manageable,practical,andscalable(AMPS)high-yieldandhigh-gaininertialfusion Figure10: ConceptualschematiccrosssectionshowinghalfofPacificFusion’sDS.Thetotaldimensionsofthefull systemare∼73mx80m. thatrapidlycompressesthefuel. 3.2 PulserModules:IMGs TheDSpulserusesanIMGarchitecture[23,86].Figure11showsanIMGmoduleanditscomponents.Thebuilding blockofanIMGiscalledabrick,whichcontainstwocapacitorschargedatagivenvoltagedifferentialinserieswitha lowimpedancesparkgapswitch. Whentheswitchisclosed,theenergyfromthecapacitorsisdischargedintothe stage,whichconsistsofmultiplebricksdischargedsimultaneouslyinparallel.Thevoltageofagivenstageisthatofthe brickchargingvoltage,andtheenergydischargedisthesumofthestoredenergyinallcapacitors.Stagesareaddedin seriestocreateapulsermodule,withtheoutputvoltageofmodulebeingthesumofthestagevoltages.PacificFusion’s baselineIMGarchitectureconsistsof10bricksperstageand32stagespermodule.TheIMGhasabipolarconfiguration, witheachbrickchargedto+/-100kVinserieswithatriggeredsparkgapswitch.Withacapacitanceof160nF,the totalenergystoredpercapacitoris800J,resultinginatotalenergystorageof512kJpermodule. ThefullDSpulsershowninFigure10contains156modulesinparallel,storedincanistersfilledwithdielectricoil.The modulescollectivelystoreupto∼80MJofenergy,andthepulsercandeliver>350TWtothewatersection. 3.3 WaterTransmissionLines Current is delivered to the target chamber through the coaxial pulse tube and tri-plate transmission lines using deionizedwaterasthedielectric,asseeninFigure10.Thevacuumtargetchamberatthecenterofthepulsercontains themagneticallyinsulatedtransmissionlinesthatdeliversthecurrenttotheICFtarget.Duetothelowcapacitance andlowinductanceofthesystem,pulsecompressionisnotneededforpulsesasshortas100ns.Longerpulsescanbe createdbyvaryingthetriggeringtimesofthemodules. 3.4 TargetArea PacificFusionbreaksdowntheTargetAreaintofivesubsystems:vacuumpowerflowsystem,inner-MITL/cassette, chamber support systems, target diagnostics, and hardware used for blast management. The vacuum power flow 17 Affordable,manageable,practical,andscalable(AMPS)high-yieldandhigh-gaininertialfusion Figure11:IMGModuleandcomponents.Themodulediameterisapproximately1.9m. systemconsistsoftheinsulatorstack,theouter-MITLs,atriplepost-hole-convolute,andtheinner-MITL(iMITL), detailedmoreinSection3.5.Itisresponsiblefordeliveringenergyfromthewatertri-platesthroughthevacuumMITL levelsintoasingleiMITL.TheiMITLtransfersthecurrenttothetarget.Thecassetteisasmallportablechamberthat housesthefinalportionofiMITL,thetargetandsupportutilities,includingtheinterfacestothecryogenicsystem.The targetchamber,whichismadeupoftheinsulatorstackandthediagnosticspool,maintainsvacuumduringoperation. Thesupportsystemsareresponsibleformaintainingthetargetchambervacuum,provingthestructuralloadpath anddynamicresponse,andinstallationandalignmentofcomponentsintothesystemduringthebuild. Thetarget diagnosticsincludenuclear,x-rayandopticaldiagnosticsusedtoinformanditerateonourexperiments.Eachdiagnostic ismountedtoaportonthediagnosticspool,givingthediagnosticitsownlineofsighttothetarget.Diagnosticports include200mmdiameterequatoriallineofsightportsand400mmdiameter15deglineofsightports(Figure12). Thecassetteconceptisdesignedforflexibility,withthecassettereplacedaftereveryshot.ThisallowsPacificFusion toiterateandoptimizethetargetdesignovertime. Thecassetteisassembledofflinefromthemainsystem. During thebuildprocess,thetargetandiMITLsaremeticulouslymeasuredtoensureprecisionalignment.Oncethetargetis ready,thecassetteisbroughtdowntovacuumandthecryolayeringprocesscanbegin,ifdesired.Severalcassettes canbebuiltatatimetobereadyforshots. Thisallowsforhigh-temposhotoperations,includinghigh-yieldshots. Thecassettedesign,alongwithotherstrategicdesigndecisions,allowstheDStoachieveatleast1shotperdaywhile maintainingtheflexibilitytousesolidfuelandmultipletargettypes. AnotheradvantageoftheDSdesignisthewatertank.Thetargetchamberandtri-platesarecontainedbyawatertank with5mofwatersittingoverthevacuumtargetchamber.Thisprovidessufficientneutronshieldingtoensurethatthe desiredbackgroundradiationlevelsareachievedoutsidethesystem. 3.5 FullDSModeling TheentireDShasbeenmodeledusingthecircuitcodeCASTLE(CircuitAnalysisandSimulationwithTransmission-Line Emphasis)[87],andthemodelincludesallcomponentsdowntothemodulelevel. Everysubsystem(Figure13)has subsequentlybeenmodeledusing2D/3Dfullelectromagnetic-only(EM)orelectromagnetic-with-plasmasimulations usingtheParticle-In-CellcodeCHICAGO®[88]tovalidatethecircuitrepresentationsandtodeterminethetransport efficiencyofthevacuumsection.TheseCHICAGO®simulationsincludethefullcircuit,withindividualcomponents removedfromthecircuit.Theinput/outputsofremovedcomponentsarecoupledasboundaryconditionstothecircuit simulation.Thecircuitmodelisincorporatedinaproprietaryoptimizerthatbalancesmultipleconstraints,including thespecificcomponentdesignsandspatialconstraintssuchasthelayoutofthefacility. 18 Affordable,manageable,practical,andscalable(AMPS)high-yieldandhigh-gaininertialfusion Figure12:TargetAreaCrossSectionoftheDSTargetArea:ThedesignoftheouterMITL(oMITL)issimilartothat usedontheZmachinebutwith6conicaltransmissionlinesconsistingoffoursplitanodesandthreesolidcathodes leadingtotheconvolute.Forscale,theinsulatorstackhasaradiusof3.2m. Figure13:BlockdiagramofthefullDS:Thisshowsmajorsubsystemsrequiredforcircuitmodelingandelectromagnetic simulations. 19 Affordable,manageable,practical,andscalable(AMPS)high-yieldandhigh-gaininertialfusion 3.5.1 PowerDeliveryinVacuumSection ThevacuumsectionoftheDSissubjecttothehighestelectricandmagneticfieldsoriginatinginthepulser,soitis themostlikelyregionforcurrenttobedivertedenroutetothefusiontarget. Efficienttransportofcurrentinthis regimerequirestheuseofMagneticallyInsulatedTransmissionLines(MITLs)[89–95]tocarrythecurrentfromthe water-vacuuminterfacetotheload. IntheDS,thisisaccomplishedthroughsixouterMITLswhichareconnected togetherthroughatriple-post-hole-convolute.TheconvolutecombinesthecurrentsandsendsthemtotheinnerMITL, whichdeliverspowertothefusiontarget. Thewater-vacuuminterfaceisaninsulatorstackofdiscretedielectricringssimilartotheZdesign[96](butscaled toaradiusof3.2m)andhasbeensimulatedinfull-scaledynamicCHICAGO®EMsimulations. Thevacuumstack modelingincludesdetailedelectrodeshapingonthewatersideandthevacuumsidetocontroltheelectricfieldprofile acrossthestack,keepingaverageelectricfield(V/d)acrossanindividualinsulatorringtobelow160kV/cm.Thefull spatiotemporaldynamicsoftheappliedelectricfieldfromCHICAGO®simulationshavebeenusedinastatistical flashovermodel[97],predictingafullstackflashoverofanyvacuumlevelat<0.2%whenusingaconservative𝛾 [96]. 𝑆𝑀 Withafullchargevoltageonthemodules,thepulserwilldeliver≈310TWofpeakpowertotheinsulatorstack. Full EM, 2D/3D kinetic PIC simulations using CHICAGO ®were used to model the entire system, starting at the water-vacuuminterfaceandextendingtothelinersurface. Thevacuumsectionisspatiallytoolargetoefficiently modelinasinglesimulation,sothevacuumsectionwasbrokeninto3maincomponents:theinnerMITL,thetriple post-holeconvolute[98],andtheouterMITL/insulatorstack.Thesimulationsspatiallyoverlapsothattheconvolute simulationincludesthelast≈25%oftheouterMITLsandthefirst≈10%oftheinnerMITL,ensuringcontinuityof conditionsbetweensimulations.ThesimulationsoftheouterMITLsandconvoluteareresolvedto250µmspatially withtimestepsthatresolvetheelectroncyclotronfrequency.Theconvolutehasalargerradiusthansimplyscalingup fromthecurrentZdesign[99,100],tominimizeheatingoftheconvoluteandtoincreaseitssurvivability.Theincreased survivabilitycomesatacostofearly-timeinefficiencyrelativetoascaledZ,asthemagneticinsulationtakessometime tobeestablishedintheconvolute.Theconvoluteisintendedtoremaininplacebetweenshots,soitshouldbealow sourceofsurfacecontaminants,asitisnotregularlyexposedtoambientair. The convolute simulations use similar models and algorithmic approaches to prior state-of-art MITL simulations [88,99,101–105]andincludespace-charge-limitedemission[106]ofelectronsforelectricfieldstressesexceeding240 kV/cm,ionemission[107,108]forsurfacesheatedabove600K,and1Dtransportmodelsforparticleheating,thermal andmagneticdiffusionattachedtoeachelectrodesurfaceelement. TheouterMITLdesignissimilartotheZdesign[109]butwith6conicaltransmissionlines(Figure12)consistingof foursplit(hollow)anodesandthreesolidcathodesleadingtotheconvolute.Sincetheconvolutewillbeatarelatively largeradius,thesetransmissionlinescanmaintainconstantimpedanceuptothepost-holeregionintheconvolute andstillhavesufficientlylargeA-Kgapstominimizelosses.Inthecurrentdesign,theouterMITLshaveanaverage impedanceof≈2.3Ω. 3.5.2 Drivercouplingefficiency Theconvolutesimulationsareattachedtoalowinductance,lowmassinnerMITLsimulation. Thissimulationhas avariableresolutionfrom25𝜇mto125𝜇mspatiallywithanadaptivetime-stepsetto 8 ,where𝜔 istheelectron cyclotronfrequencyandusesanimplicitfieldsolver[88]tohandlehighmagneticfields 𝜔𝑐andplasma 𝑐 densities. The targetandinnerMITLarecontainedandreplacedwithanewcassetteeveryshot.Thetargetcassetteallowsmostof theMITLsystemtoremainundervacuumandfreeofcontaminants.Thesesimulationsincludethephysicspresentin priorconvolutesimulationsandadditionalelectrodeplasmasourcesfromthepresenceofsurfacecontaminants[101]. TheseplasmashavepreviouslybeenshowntobeabletocrosstheA-KgapviaaHall-likemechanism[99,110,111], leadingtothegenerationofadditionalcurrentpathwaysthatcandivertcurrentfromreachingthelinersurface.The innerMITLsimulationsalsoincludeelectronsandionsflowingfromtheconvoluteintotheinnerMITLregion. Figure14showsthenetcurrentdeliverytotheloadregion.Simulatedcurrentpulsesareshownfortheidealcircuit, withplasmasonlyintheouterMITLs;plasmasourcesinboththeouterMITLsandtheconvolute;andplasmasinthe entirevacuumsection.Inthesesimulations,theloadhasafixedimpedanceof27mΩ.Atearlytimes,lessthan60nsin Figure14,somecurrentisdivertedfromreachingtheloaduntilmagneticinsulationisestablishedineachlevel.Pulses onthetop,middle,andbottomlevelsarriveattheouterMITLatdifferenttimestotakeintoaccountthedifferences inthelengthoftheirrespectiveouterMITLs.Thedifferentlevelsmagneticallyinsulateatdifferentpointsalongthe 20 Affordable,manageable,practical,andscalable(AMPS)high-yieldandhigh-gaininertialfusion Figure14: Currentdeliveredtothelinersurfaceforcalculationswithincreasingvacuumcomponents. Zerotimeis takentobewhenthefirstkAarrivesfortheidealcircuitcase. currentpulse.Atpeakcurrent,theDSdeliversabout62.8MA,115TW,and10MJtotheloadregion,coupling96%of thecurrentdeliveredtotheinsulatorstacktothefinalload.Furtheroptimizationofthevacuumregionisunderwayto furtherincreasecurrentdelivery,throughacombinationofreducingthesysteminductanceandimprovingcurrent deliverythroughthefinalcomponents. DetailedinteractionsbetweentheinnerMITLregionandthetargetarealsoimportantconsiderationsandanactive areaofresearch. Physicsconsiderationsandmodelingmethodologiesforassessingthisinteractionareoutlinedin AppendixB. 3.6 PulseShaping ThemodulardesignoftheDS,alongwithwaterinsulatedtransmissionlines,allowsfortwolevelsofpulse-shaping. Theindividualmodulescanbeindependentlytriggeredandaretransit-timeisolatedbythepulsetubesatanindividual levelfor∼ 715nsfromtheoutermosttoinnermostsetofmodules. Thetop,middle,andbottomlevelsarefurther isolatedbyanadditional∼750ns. Longerpulsesoutsidethisrangecouldbegeneratedinamannersimilartohow longpulsesaregeneratedontheZ-Machine(seee.g.Ref.[17]),throughtheinsertionofwaterswitchesin-betweenthe moduleoutputsandthewaterimpedancetransformerforfurtherisolationwhenneeded.Panel(a)ofFig.15showsa comparisonbetweenthepulseshapesfromRef.[17]andequivalentpulseshapesachievableontheDS(inafullcircuit modelofthepulser)byonlyvaryingtheinitialchargevoltageandswitchtimeswhileutilizinglessthan∼30%ofthe totalstoredenergyavailable.Panel(b)ofFig.15showsthesesameprofileswithmanyofthemoduleschargedtofull voltage,leadingtoa2.75×increaseinpeakcurrent. 3.7 DiagnosticSuite TheprimarygoaloftheDSistoachievenetfacilitygain.Weexpectthatachievingthisgoalwillrequirerapidlyevolving thetargetdesignbaseduponunderstandingbuiltfromexperiments.ThisprocesswillrequirethateachDSexperiment beappropriatelydiagnosedtounderstanditsperformanceandtocharacterizethedegreetowhichtheexperimentsagree with,ordifferfrom,computationalmodels.Additionaldiagnosticswillberequiredfortargetedphysicsmeasurements ondedicatedexperiments,forexampletostudydriver-targetcouplingorhydrodynamicinstabilities.AsontheNIF, thisrequiredthedevelopmentofafullsuiteofdiagnostics[112]tomeasurekeyobservables. 21 Affordable,manageable,practical,andscalable(AMPS)high-yieldandhigh-gaininertialfusion Figure15:(a)ComparisonofpulseshapespresentedinRef.[17]fortheZmachine(dashedlines)andthoseachievable ontheDSwithonlychangingmoduletimingandchargevoltage(solidlines).(b)SameDSpulseshapeswhenutilizing asmuchofthestoredenergyaspossible. Linear Rail PROPRIETARY // C nT O o N F F _ ID 1 ENTIAL Manipulator PDV (Drop In) (90,0) ASTRA_1 Gate Valve (90,0) Scintillator RIDE CRAB VISAR Aperture (78,330) (90,15) (78,30) PMT @0.5m Camera MARS Collimator Target (90 6 , m 315) Cassette Mirrors Chamber Target FARAD VIRGO ENDOR_1 ENDOR_1 (90,285) (90,60) Aperture LOS nToF_4 (78,90) (88,90) (90,270) 3.1m ASTRA_2 ASTRA_4 12.9m ( n 9 T 0 o , F 9 _ 0 2 ) (90,90) (90,270) FARAD Injection (90,105) DIPPER (90,240) GALAXI CEKOV NGC (90,150) (90,120) (78,210) SPICE (90,195) ENDOR_2 Water Tank Aperture DIM(78,180) nToF_3 ASTRA_3 (90,180) (90,180) ENDOR_2 PROPRIETARY // CONFIDELNOTSIA (L88,180) Figure16:ConceptualplanfortheDSdiagnosticsuiteandlayout.DiagnosticsarenotedbytheirdistancefromTCC andangleinfacilitycoordinates(𝜃,𝜙)where𝜃isthepolarangleand𝜙istheazimuthal. 22 Affordable,manageable,practical,andscalable(AMPS)high-yieldandhigh-gaininertialfusion OurinitialbaselinediagnosticplanisshownschematicallyinFig.16.Thewaterchamberisontheorderof13meters inradius.Sixlongcollimatedlinesofsightareplannedfor6neutrontimeofflight(NTOF)and2EnergeticNeutron DetectorsObservingwithResolution(ENDOR)forneutronimaging;fouroftheNTOFsarearrangedintheequatorial planeandshowninFig.16.ThesearepositionedsothattheNTOFsarearrangedinopposingpairsthataremutually orthogonaltobestdiagnosespectralmoments(e.g. asin[113]). The2ENDORareorthogonaltooptimizefor3-D reconstruction[114].PositioningoftheseinstrumentsfarfromTargetChamberCenter(TCC),andthereforeoutsideof thewaterchamber,isnecessarytoachievethedesiredspectralresolutiononNTOFthroughthetimeofflightdispersion, andthedesiredspatialresolutionforENDOR.Allotherdiagnosticsareeitherwithinthewaterchamberorhaveoptical relaystoasidelaboratoryspace.Thisapproachmaximizestheinherentshieldingofthewaterchamber. CompletingthenucleardiagnosticsuiteareaDT𝛾-rayreactionhistorymeasuredbyaComptonElectroncherenKOV (CEKOV)detector[115],twoDDnuclearburnhistorymeasurementsbasedonaRecoilIonDEtector[116](RIDE)and on(n,𝛾)Cherenkovdetection(NGC),aMAgneticRecoilSpectrometer(MARS)[117]forneutronyieldandspectrometry, andActivationSamplesforThermonuclearReactionAnalysis(ASTRA)[118]intheequatorialNTOFlinesofsight. TheDSx-raydiagnosticsuitewillincludeanemittedpowermeasurementusingaCalibratedRadiometryandBolometry (CRAB)diagnosticcomposedofafilteredstreakcamera(e.g.similartotheSPIDERsystemonNIF[119]),whichprovides the highest temporal resolution, complemented by filtered diodes[120]; two equatorial orthogonal x-ray cameras forself-emissionimaging,GatedActiveLongAspectX-rayImager(GALAXI),andradiography,VersatileImaging forRadioGraphicObservations(VIRGO);andanx-raySPectroscopicInstrumentforCollisionalExcitation(SPICE), potentiallywithseveralcrystalsforkeyenergyranges.AlineofsightisreservedoppositeVIRGOforasource,the DynamicIrradiationwithPhotonsforProducingEnergeticRadiographs(DIPPER).Foropticaldiagnostics,weplanonan opticaltransmissionprobetoenableFAradayRotatationandDeflectometry(FARAD)inlow-densitynear-targetplasmas, alineVISAR[121]fordrivecharacterizationandmaterialsstudies, andfiber-coupledphotonDopplervelocimetry (PDV). WecontinuetoimproveuponthisconceptualdiagnosticplanforDS,andweareactivelydevelopingdetaileddesigns forindividualsystems,tobedetailedinfuturepublications.ThediagnosticsportsnotshowninFig.16areeitherused forchamberinfrastructureorareavailableasspares.Approximately10portsarepotentiallyavailableforadditional diagnostics;PacificFusionisactivelyevaluatingadditionalmeasurementsbeyondourbaselinesuite. Thebulkofthediagnosticsuiteisfocusedonthecoremissionofdemonstratingfacilitygain.Thisrequiresthatweare abletotracktheperformanceofavarietyofICFtargetsbyinferringtheGeneralizedLawsonCriterion(GLC)𝜒 foreach implosionexperimentaswellasobtainingenoughinformationtoascertaintherootcauseofobservedfailuremodes andperformancelimitingeffects.Thepotentialperformancelimitersarenumerous,includingsymmetry,endlosses, mix,andinefficientfluxcompression.Eachhasdifferentobservableconsequences.Wearedevelopingamodel-driven Bayesianapproachtoinferperformancefromtheensembleofdiagnosticobservables. Thismethodologyhasbeen demonstratedonMagLIFimplosionsontheZmachineusingastaticquasi-2Dmodeltoinferburn-averagedquantities and𝜒 acrossawiderangeofexperiments[20]. Additionalexamplesandextensionstothisapproacharediscussed inRef. [122]. Thisapproachallowsforthereconstructionofthetargetperformanceandextractionofunobserved dynamics,withuncertainties,fromtheunderlyingmodel.Thisformalismwillbeusedinthenear-termtoaidinthe designofthediagnosticsuitebyoptimizingparametersoftheindividualinstrumentstoobtainmaximallyinformative observations[123]. Thisquantitativeoptimizationenablesustoweightheconsequencesofdifferentdesignchoices forthediagnosticsinthecontextoftheentiresuiteofobservations,enablingtradeoffstobeconsideredthatcanhave dramaticimpactsoncost,schedule,andperformance. 3.8 Facilitycostcomparison Inprevioussections,wehavedescribedthedesignandparametersofPacificFusion’sDS.Here,webrieflydescribeits costrelativetotheNIF. Ourpresentdetailedestimateputsthecosttobuildthe80MJDSatslightlyover$6/𝐽,orapproximately$500𝑀.This estimateiscomparabletotheinflation-adjustedper-JoulecostoftheZRproject—whichcompletelyoverhauledand rebuilttheZfacilityintoitspresentstate—of$4/𝐽 in2006dollarsor$6.3/𝐽 in2025dollars[124].Thecapitalcostto buildtheNIFwasroughly$3.5𝐵in2012,inflation-adjustedtoabout$4.9𝐵in2025.Inshort,theDScosts∼10×lessto buildthantheNIF. 23 Affordable,manageable,practical,andscalable(AMPS)high-yieldandhigh-gaininertialfusion 4 Pathtocommercialpower ManyaspectsoftheDSwilltranslatedirectlytothepulserrequiredforsubsequentcommercialpowerplants,which willhave:asimilarsystemsizeandlayout;near-identicalmodulearchitecture;similarscalechambers;andthesame sortoftargets.TheDSmayachievefacilitygainswellbeyonditsdesigngoalof𝑄 >1.However,commercialpulser 𝑓 IFEsystemsdifferinseveralrespects;theymustlastfordecadesofcycling,becycledrapidly,andefficientlycapture fusionoutputandbreedtritium.Specifically,theyrequirethreeadditionaltechnicaldevelopments: • Componentlifetime.Developmentofpulsercomponentsthatallowforrepetitiveoperationwithlongcycle lifeandinfrequent,inexpensivemaintenance. • Fusionchamber.Developmentofafusionchamberthatallowsforhigh-gainshots,survivesrepetitivestresses arisingfromshots,andcanberapidlyclearedandpreparedforsubsequentshots. • Tritiumbreeding.Developmentofblanketsandfirstsolidwallsthatarecompatiblewithadurable,rep-ratable fusionchamberandthatpermitapracticaltritiumbreedingratioandefficientfusionenergycapture. Wewilldiscussthesetopicsinmoredepthinsubsequentpublications,butgiveanoverviewofthemainissueshere. 4.1 Componentlifetime OperatingapulserIFEpowerplantwillrequireshootingtargetsatrepetitionratesbetween0.1-10Hz,comparedtothe approximatelysingleshotperdayforcurrentleadingscientificfacilities(NIF,SandiaZmachine).Thepulsertherefore mustoperateatrepetitionrates104-106-foldhigherthanpresentlarge-scalefacilitiesatanaffordablecapitalcost,with componentlifetimesaveraging1billionshots. Currently,thetwocomponentswithintheIMGpulsermodulesthat donottypicallymeetthislifetimerequirementatoperatingparametersarethehigh-voltagecapacitorsandspark gap switches. Improving the lifetime of these key components can be achieved by two approaches: (1) reducing operatingconditions(e.g.,lowervoltageandstoredenergypercomponent)byusingmorecomponentsinparalleland (2)innovativecomponentdesign. Anexampleofthefirstapproachwouldbetoreduceoperatingvoltagesforcapacitorsby3-fold,from100kVto35kV, whichwouldbeexpectedtoincreasecapacitorlifetimefrom≈105shotsto≈109shots,attheexpenseof9×lessenergy storedpercapacitor[125].Thisresultsintheneedfor9-foldmorecapacitorstobeabletostoreanddischargethesame amountoftotalenergy. Lowervoltagesandcapacitancealsoreducethechargetransferredbytheswitches,which couldresultinasubstantialincreaseinswitchlifetime. Thesecondapproachwouldinvolvedevelopinginnovativedesignstoincreasethelifetimeofcapacitorsandhigh voltageswitches.Forcapacitors,forexample,thisincludesdevelopingdielectricpolymerswithimproveddielectric constantsandbreakdownstrengths,andcapacitordesignsthatreduceelectricfieldstressestodeceleratecapacitor aging. For switches, improved spark gap switch designs can reduce the charge transferred per unit area through increasedmulti-channeling,reducingablationandthereforeincreasingswitchlifetime;alternateswitchtechnologies (e.g.,solidstate)aswellasin-siturefurbishmentfortraditionalspark-gapswitchesareotheravenuesforincreasing switchlifetimes. Pacific Fusion is pursuing both above approaches to component improvement — using modern non-destructive evaluationmethods,acceleratedtesting,andparallelization—todevelopoptimizedcomponentsthatmeetcommercial requirementsandenableaffordable,firmfusionpower. 4.2 Fusionchamber ToachievehighpoweroutputinapulserIFEpowerplant,oneneedstorapidlycyclethefusionchamber,i.e. drive fusiontargetsinrapidsuccession,preparingthechamberaftereachshot.Todoso,onemustensurethatreplaceable electrodescanbeejectedwithoutdamagingthewalls,thatthepost-shotimpulsedoesnotdamagethewall,andthat highvacuumcanberapidlyrestored.Wediscusstheseissuesbelow. 4.2.1 Replaceableelectrodedisassembly InpastMagLIFandotherpulsedpowerexperiments,thedestructibletargetmasshasincludedlargereplaceableelectrodes (innerMITLs,oriMITLs)thatfracturefromtheshotblastandthemagneticpressurestemporarilyconstrainedbythem. Thisgeneratesaconsiderableamountofdebrisandrequiresalargeamountofmasstobeinsertedandevacuated.One 24 Affordable,manageable,practical,andscalable(AMPS)high-yieldandhigh-gaininertialfusion Figure 17: Low-mass inner MITLs are advantageous for low cost, high repetition systems. A 100𝜇m MITL with a 200𝜇m,1.25mmradiuswasherplacedonthetransmissionlinesisonepromisingsuchconfiguration.Thishasa2.49nH inductanceusinga100nslinearrampto60MA,13.7%greaterthanlarge-mass,theoreticallyimmovableMITLs.[36]. optionwearepursuingislow-massiMITLsthatminimizetheamountofmaterialconsumedandrecycled.Thecriteria forasuccessfuliMITLarethatitmustcarrythesurfacecurrentsuppliedbythepulsedpowersystemandmustnot deformsignificantlyduringtheshotastonotimposetoolargeofanimpedancepenaltyonthesystem[126].Theskin depthofcopperisjustunder50𝜇mduringthesetimescales,settingasmallminimumthicknessnecessaryforcarrying thecurrent.OnepromisingiMITLoptionisshownFig.17. 4.2.2 Post-shotvacuumchamberimpulseresponse PulserICFsystemsrequireextremetemperaturesandpressuresoveraveryshortperiodoftime.Themagneticenergy drivingthefusiontargetsystemisreleasedastheimplodingtarget“bounces”andexpands.Thealphaparticleenergy fromanignitinghigh-gaintarget,whichcanbemanytimesthedrivingenergy,isabsorbedbythetargetandnear- targetmaterialoverafewnanoseconds.Theresultingrapidenergyreleaseandmaterialexpansionimpartsloadson target-facingstructures. Theseloadsarebroadlythesameasotherinertialconfinementfusionfacilitiesandcanbe categorizedasthehydrodynamicblast,theradiativex-rayemissionsandresultingablativeshocks,neutrondamage,and anydebrisorshrapnel[127–129].Weareusingacombinationoflarge-scale,late-timeradiationmagnetohydrodynamic simulationsandhighstrainrate,shockEOS,structuraldynamicssimulationstopredicttheloadsonthestructureand analyzetheshorttermeffects.Weareextendingthisouttoimplicitdynamicsandfatiguesimulationstodetermine thelong-termeffectsonthestructure.Theflexibilityofourapproachallowsustoselectivelysteeranydebrisand/or locallyprotectanysolidmaterialsthatcouldfacedamage. Forexample,magneticpressurepushesourtargetlinerinwardbutalsopushestheiMITLsaxiallyduringtheimplosion. Theresidualmagneticfieldresiststheradialexpansionofthereboundinglinerandtheresultisthattheradialmomentum isminimizedandthetargetprimarilyexpandsaxially,orthogonaltothedrivinghardware.Themass,momentum,and kineticenergydistributionforthehydrodynamicblastcanbeseenin(Fig.18).Forthefewpiecesofhardwarethatare exposedtodamagingshocks,wearedevelopingconsumableshieldingstrategiestomitigatetheeffects. 4.2.3 Chamberpumpingandreloading Whilemanychallengesforacommercialfusionsystemaresharedamongpulsedfusionconcepts,considerationsthat areuniquetopulser-drivenICFsystemsinclude∼1HzrepetitiveinjectionofinnerMITLsectionsinamannerthatis compatiblewithMITLsurfaceconditionandvacuumrequirementsforcurrentdelivery,blanketneutronicsandtritium breedingcharacteristics,energyrecoveryandheatexchange,andradiationshieldingofcriticalsystemcomponentsand theoverallfacilityshieldingenvelope.Foreachcycle,thechambermustbepreparedforthenextshot.Thisincludes insertinganewtarget,insertingnewiMITLs,andre-establishingthevacuumstateinbetweentheMITLs.TheiMITLs aresplitbetween(i)low-massconsumabletransmissionline(CTL)[126]orrecyclabletransmissionline(RTL)[130,131] sectionsand(ii)permanentMITLsthatareshieldedbythetritiumbreedingmaterialandaremeanttolastforalarge numberofshots. ThetargetandconsumableiMITLinsertioncanbeperformedmechanicallyviatargetexchange hardware.Thiscanbedoneinaflexiblewaygiventhefactthattheenergyistransmittedalongthegapbetweenthe MITLsanddoesn’thaveanysignificantline-of-sightrequirements.ThevolumebetweentheMITLsmustberapidly pumpeddowntoahighvacuuminpreparationforthenextshot.Severalstrategiesarebeingpursuedtodoso,suchas sweepingthechamberwithagetteraftereachshot;moredetailswillbesharedinsubsequentpublications. 25 Affordable,manageable,practical,andscalable(AMPS)high-yieldandhigh-gaininertialfusion Figure18:Late-timeradiationmagnetohydrodynamicsimulationswiththeresultingdistributionofmass,momentum, andenergyejectedfromtheexplosion.Thesimulationsshownranto2.4𝜇spastthefusionignitiontimeandtracked materialleavingthesimulationboundaries.Zerodegreesisatthenorthpoleand180degreesatthesouthpoleshowing 93%ofthemass,85%ofthemomentum,and55%ofthekineticenergytravelingwithin25degreesofthepoles. 4.3 Tritiumbreeding Achievementofatritiumbreedingratioappreciablyexceedingunitywithinastabletargetchamberfirstwallisa necessaryconditionforafeasiblefusionpowerplant.Apulsed-power-MITL-drivensystemiscompatiblewithlithium- containingblanketandshieldingtechnologiesthatmeetthisrequirementvianeutronreactionswithlithium-6,using configurationssimilartothoseshownintheHYLIFE[132–134]andZ-IFE[135–138]reactordesignstudies,(cf.Fig.19 andreference136).NeutronicsanalysisinMCNPfornotional1Dtargetchamberandblanketconfigurationsconfirms thatsufficienttritiumbreedingratiocanbeachievedwithappropriateradialthicknessofaFLiBemoltensaltblanket, c.f.Fig.20.Otherblanketmaterials(e.g.,PbLi)andconfigurationsarecompatiblewithourapproachaswell. Incontrasttolaser-basedIFEconcepts—whichrequirelineofsightbetweenthefinalopticsandtarget–thepulsed powerMITL-basedenergycouplingislessconstrainingforblanketconfigurations.Forexample,powermaybedelivered viaasteppedconicalfeedtoinjectedtargetsinsuchawaythatradiationlineofsightfromthetargetisfullyoccluded. Thusthetargetcanbeeffectivelyfullysurroundedbyblanketmaterial,moderatingwater,andstructural/shielding materialsatthetimeoftherepetitivefusionenergyrelease.Thesurface-conformalenergydeliveryoftheMITLsis alsoadvantageousforapproachestothemitigationofmanyfirstwallissues,allowingfortheprotectionofthetarget chamberfirstwallfromdynamicblastloading[139]andpromptx-rayandgammarayemissionsviathickinjected liquidblanketmaterialand/oraerosol/gascushions,andshieldingofchamberstructuralsteelstowithinmaterialDPA limitsforthelifetimeofthesystem. MoredetailsofapulserIFEpowerplant,buildingupontheschematicinFig19,willbediscussedinfuturepublications. 5 Utilitytothebroaderfusioncommunity Inaggregate,thehighscientificmaturity,highefficiency,andrelativelylowcostofpulserICFmakesPacificFusion’s DSavaluablecomplementtotheotherflagshipfusionfacilitiesintheUS’sstrategicpathtocommercializingfusion energy.TheNationalAcademyofSciencesreportBringingFusiontotheU.S.Grid recommended(i)pursuingaFusion PilotPlantinthe2035-2040timeframeand(ii)investinginconcept-agnosticfusiontechnologydevelopments[140]. TheDScontributessignificantlytobothoftheseobjectives.TheschedulefordeliveringtheDSandachievingfacility gainwouldallowpilot-plantscalefacilitiestobedevelopedwellbeforethistargetedtimeframe. As discussed in this paper, we believe pulser IFE has substantial prospects for innovations and cost reductions in deliveringfusionpower.Intermsoftechnologydevelopments,therearemanycommunity-widebenefitstopursuing theseobjectives,includingimprovedpulsedpowertechnology,thedevelopmentofhighfluxneutronsources,improved 26 Affordable,manageable,practical,andscalable(AMPS)high-yieldandhigh-gaininertialfusion Figure19:Pulser-drivenIFEsystemschematic,illustratingincorporationofinjectedtargets,recyclabletransmission lines,andliquidorsolidfirstwall/breederblanket. plasmadiagnostics,improvedsimulationcapabilities,andimprovedunderstandingofburningplasmadynamicsin MHDregimes. TheDSalsoadvancesthefeasibilityofhigh-yieldfusionfornationaldefense.High-yield(>100MJ)inertialfusionis acriticalnationaldefensetoolbecauseitistheonlywaytocreatetheextremeconditionsessentialforensuringthe effectivenessandsurvivabilityofkeydefensecapabilities.AlthoughtheNationalIgnitionFacility’srecentachievement of∼ 5MJwasamajormilestone,itfallswellshortoftheyieldsneededtoreplicatethreat-levelenvironmentsand obtainthedatarequiredforcomprehensivevalidationofthesesystems.Meanwhile,adversariesareracingtoachieve 100+MJfusionby2030,potentiallytwodecadesbeforethecurrentU.S.goalof2050[141].Pulser-driveninertialfusion offerstheUnitedStatesatimelyopportunitytomaintainitsleadershipinadvanceddefensetechnologies. TheDSdeliversalow-costcapabilitythatcancouple∼10MJtothefusiontargettogeneratemanytensorhundredsof MJoffusionenergyinadjacentparameterregimestothoseaccessedbylaser-drivenICF.High-gainfusionplatforms fieldedattheDScanthereforeadvancetheNNSA’smission,andcollaborationsonplasmadiagnostics,targetdesign, simulations,andfundamentalplasmaphysicscanbenefitallparticipants. Oneeffectivewaytoadvancesucheffortsisthroughthepublic-privatepartnershipmodel.Public-privatepartnerships arebecomingincreasinglyimportanttotheUS’sfusionstrategy,andwerehighlightedasakeyrecommendationinthe NationalAcademyofSciencesreport[140].TheUSDOEhaslaunchedseveralfundingprogramsfocusedonprivate companies,includingtheINFUSEnetworkandtheMilestone-BasedFusionDevelopmentProgram.Ithasalsopublished formalRequestsforInformationonCost-SharingPartnershipswiththePrivateSectorinFusionEnergyand,recently,on PulsedPowerPublic/PrivatePartnerships.PacificFusionhasalreadyprocuredsignificantprivatefundingforbuildingits DS,creatinganopportunityforUSDOEtoleveragetheseinvestmentsbypartneringtofurtheradvancethebroader fusioncommunity’sobjectives. 6 Conclusion Pulser-driven inertial fusion can enable affordable, abundant commercial fusion power and also close the gap to high-yield(>100MJ)capabilities.BydirectlydeliveringtensofMJofelectricalenergytomagnetizedfusiontargets athighefficiency, pulserICFoffersanear-termpathtoachieving𝑄 > 1—anachievementthatwouldmarkthe 𝑓 decisiveturningpointinfusionenergydevelopment. PacificFusion’sDS,capableofexceeding60MA,showshow newpulsed-powertechnologiescanbescaledandoptimizedforaffordable,manageable,practical,andscalable(AMPS) fusion.Critically,itrepresentsa1000×increaseinfusioncapabilitiesbyproducing100×thefacility-levelgainatabout 1/10thecostoftheNationalIgnitionFacility,acceleratingprogresstowardbothcommercialpowerandhigh-yield fusionreadiness. 27 Affordable,manageable,practical,andscalable(AMPS)high-yieldandhigh-gaininertialfusion 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.1 0.2 0.3 0.4 0.5 0.6 FLiBe thickness (m) oitar gnideerb muitirT MCNP OpenMC Figure20:RadiationMonte-Carlocalculationofpulser-IFE-relevantchamberneutronics,blanketthickness,andtritium breedingratio 7 Acknowledgments The authors would like to thank the following individuals for their contributions: Andrew Benson, Kurt Boehm, JonathanCarroll-Nellenback,PhilipDatte,MichaelFarrell,EdwardC.Hansen,AmberHennessy,YannickdeJong,Ian Scott,PetrosTzeferacos,DaanvanVugt,andDaleWelch. ThefollowingarticlehasbeensubmittedtoPhys.Plasmas.Afteritispublished,itwillbefoundat: https://publishing.aip.org/resources/librarians/products/journals/ Appendix A AnignitionmetricforpulserICF Inthissection,weillustratethecoreconceptsbehindourgeneralizedLawsoncriterion(GLC’)suitableforassessingthe proximityofpulser-drivenICFconceptstoignition,cf.Eq.3.Beginningwiththehotspotenergybalanceexpression givenbyEq.1,thepowertermsontherighthandsidescalewiththecompressedfusionfuelconditionsas:[27] (alphadeposition)→𝑊̂ ∝𝜂 (𝜌𝑅)2𝑠(𝑇), (8) 𝛼 𝛼 (compression/expansion)→𝑊̂ ∝(𝜌𝑅)𝑇𝑈 , (9) 𝑃𝑑𝑉 liner (bremsstrahlungradiation)→𝑊̂ ∝(𝜌𝑅)2𝑇1/2, (10) 𝑟 (electronconduction)→𝑊̂ ∝𝑇7/2𝑔 (𝑥 ), (11) 𝑐𝑒 𝑒 𝑒 (ionconduction)→𝑊̂ ∝𝑇7/2𝑔(𝑥), (12) 𝑐𝑖 𝑖 𝑖 (endlosses)→𝑊̂ ∝𝑇3/2𝜌𝑅2/ℎ∝𝑇3/2(𝜌𝑅)(𝑅/ℎ). (13) end Theenergiesandpowersintheaboveequationsareexpressedperunitlengthofthecylindricalfuelassembly,denoted bythehatnotation.Thehotspotmassdensityis𝜌,thelinervelocityis𝑈 (wherenegativevaluescorrespondtofuel liner compression),andtheradiusandlengthoftheDTcylinderare𝑅andℎ,respectively.Weassumeelectronsandionsare inthermalequilibrium(𝑇 =𝑇 ≐𝑇). 𝑒 𝑖 Thedegreeofmagneticinhibitionofthermalconductionfromthehotfueltothecoolerlinerwalliscapturedbythe 28 Affordable,manageable,practical,andscalable(AMPS)high-yieldandhigh-gaininertialfusion functions𝑔 𝑒,𝑖 (𝑥 𝑒,𝑖 ),wheretheelectronandionmagnetizationarerepresentedbytheHallparameters𝑥 𝑒,𝑖 ∝ 𝑇3/2𝐵/𝜌. Inthestronglymagnetizedlimit,𝑔(𝑥) ∝ 1/𝑥2. When𝐵 → 0,𝑔 → 1. Intheintermediateregimewhereaspeciesis marginallymagnetized,i.e.,𝑥 ∼(1),thetransportregimeis“Bohm-like”and𝑔 ∝1/𝑥.InMagLIF,wherethemagnetic fieldentrainedinthefuelissufficienttostronglysuppresselectronheatconductionbutweakenoughthattheplasma thermalpressureexceedsthelocalmagneticpressure,theionsareofteninthisBohm-likeregime. Figure21illustratestheexpandedspaceofself-heatingconditionsaffordedbypulserICFwhentheDTfuelismagnetized. Here,weplotcontoursofneutralpowerbalancewithintheDTfuel𝑊̂ =𝑊̂ +𝑊̂ +𝑊̂ atpeakcompression(stagnation), 𝛼 𝑐𝑒 𝑐𝑖 𝑟 wherewemakethecommonsimplifyingassumptionsthat𝑊̂ and𝑊̂ aremomentarilyignorable.Weassumeafuel 𝑃𝑑𝑉 end radiusof100𝜇m,theapproximatescaleatpeakcompressionofsimulatedMagLIF-likeimplosionsmatchedtotheDS. Eachdashedcontourcorrespondstoadifferentamountofaxialmagneticfluxentrainedinthefuel,expressedintermsof themagnetic-field-radiusproduct,𝐵𝑅,whichisproportionaltotheratioofthefuelradiustothe3.5MeValpha-particle gyroradiusandthusquantifiesthedegreeofconfinementofthealphaparticles.Thevalue𝐵𝑅≈0.5MG⋅cmcorresponds tothecasewherethealphagyroradiusequalsthefuelradiusandalphasaremarginallyconfinedwithintheDTcolumn [33].Combinationsof𝑇 and(𝜌𝑅) aboveandtotherightofthesolidcontoursarecapableofself-heating.Thedashed DT linesinFig.21demonstratethatincreasing𝐵𝑅enablesself-heatingatdecreasinglysmallfuelarealdensities,withthe impactsaturatingfor𝐵𝑅>1MG⋅cm. Inadditiontoachievingnetfusion-drivenself-heating,anignitingtargetmustalsoremainconfinedlongenoughforthe cumulativeeffectofself-heatingtosignificantlyincreasetheinternalenergyoftheDTfuel.Thisignitionrequirement iscapturedinthegeneralizedLawsoncriterion,orGLC.WeadopttheversionusedinRef.[30],Eq.(9): 𝐸̂ /𝜏 𝐸̂ 𝑌̂ /5 𝑌̂ 𝑚 GLC≐ 𝛼 𝑇𝑁 = 𝛼 𝑓 = DT 𝑓 = DT 𝑝 𝑓 (14) 𝐸̂ DT /𝜏 𝐸 (𝐸̂ DT ) ( 𝐸̂ DT ) (𝑀̂ DT )(6𝑘 𝐵 𝑇 DT ) Here,𝐸̂ isthealphaparticleenergygeneratedbyfusion,whichis1/5thetotalDTyield,𝑌̂ .(Thisexpressionassumes 𝛼 DT 100%ofthealpha-particleenergyisdepositedinthehotspot,thoughwerevisethisassumptioninourmodifiedGLC below.)Thecharacteristicburndurationandenergyconfinementtimesaregivenby𝜏 and𝜏 ,respectively.Usingthe 𝑇𝑁 𝐸 value𝑓 =1.2fortheratioofthetwoconfinementtimesreproducestheignitionthresholdbehaviorseeninsimulations ofNIF-likeICFimplosionswhenGLC≈1.0[30]. WefindfromtheGLCgivenbyEq.14thatignitioninthelower-(𝜌𝑅) pulserICFdesignspacerequiresalargeareal DT densityoftheconfiningliner,(𝜌𝛿𝑅).FollowingRef.[142],werepresentthelinerasathincylindricalshelloflinear 𝑙 massdensity𝑀̂ ,whoseinteractionwiththehotDTfuelcanbeapproximatedbytheequationofmotion, 𝑙 𝑀̂ 𝑅̈ =2𝜋𝑅𝑃 . (15) 𝑙 𝑙 𝑙 DT InEq.15,theexternaldrivepressureisignoredrelativetothemuchlargerfuelpressure𝑃 nearstagnation.Bydimen- DT sionalanalysis,thehydrodynamicconfinementtime𝜏 iswellapproximatedby𝜏 ≈(𝑀̂ /2𝜋𝑃 )1/2 ≈[(𝜌𝑅𝛿𝑅)/𝑃 ]1/2, 𝐸 𝐸 𝑙 DT 𝑙 DT wherethelinerdensity𝜌,radius𝑅 (assumedequaltothefuelouterradius𝑅 =𝑅),andthickness𝛿𝑅 areevaluated 𝑙 𝑙 DT 𝑙 atstagnation.FromEqs.2and14,wefind𝑌̂ ≈𝑊̂ 𝜏 =𝑊̂ 𝜏 /𝑓,whiletheDTlinearmassdensity𝑀̂ =𝜋𝑅2𝜌 . DT 𝛼 𝑇𝑁 𝛼 𝐸 DT DT InsertingtheserelationshipsintoEq.14leadstoanimportantscalingrelationapplicabletoallinertialfusionapproaches: 𝑠(𝑇) GLC∝ [(𝜌𝑅) (𝜌𝛿𝑅)]1/2 (16) [𝑇3/2] DT 𝑙 InEq.16,theGLCisproportionaltotheharmonicmeanofthefuel(hot-spot)andlinerarealdensities;thus,toignite atlow(𝜌𝑅) ,thelinerarealdensity(𝜌𝛿𝑅) mustbeincreasedaccordingly. Fortunately,pulserICFisideallysuited DT 𝑙 to compressing liners to large values of (𝜌𝛿𝑅). MagLIF experiments on the Z facility have already demonstrated 𝑙 (𝜌𝛿𝑅) ≈1g/cm2[20]. Thelinerarealdensityincreasesapproximatelylinearlywithpeakcurrent,[27]soscalingup 𝑙 present-dayMagLIFexperimentsfrom𝐼 ≈20MAto𝐼 ≈60MAshouldtriple(𝜌𝛿𝑅),puttingsuchdesignsina 𝑚𝑎𝑥 𝑚𝑎𝑥 𝑙 favorableignitionspace. InFigs.3and21,weplotavariationoftheGLCrepresentingthenet heatingoftheDTfuelbyaccountingformanyof thesourcesandsinksdescribedbyEq.1. Specifically,wereplace𝐸̂ ≐𝑊̂ 𝜏 with𝐸̂ ≐(𝑊̂ −𝑊̂ −𝑊̂ −𝑊̂ )𝜏 , 𝛼 𝛼 𝑇𝑁 net 𝛼 𝑐𝑖 𝑐𝑒 𝑟 𝑇𝑁 suchthat (𝑊̂ −𝑊̂ −𝑊̂ −𝑊̂ )𝜏 GLC′ ≐ 𝛼 𝑐𝑖 𝑐𝑒 𝑟 𝑇𝑁 𝑓. (17) ( 𝐸̂ ) DT 29 Affordable,manageable,practical,andscalable(AMPS)high-yieldandhigh-gaininertialfusion Figure21:Self-heatingthresholdcontours(dashedlines)formagnetizedDTplasmaspanningmagnetic-field-radius products𝐵𝑅from0(darkest)to1.0MG⋅cm(lightest)in0.2MG⋅cmincrements.Allplasmaconfigurationswith(𝜌𝑅) DT and𝑇 residingaboveandtotherightoftherespectivedashedcontourundergoinstantaneouspositiveDTheatingin DT theabsenceofplasmacompressionorexpansion,i.e.,atstagnation.SolidlinesarecontoursofageneralizedLawson ignitionthresholdcriterionGLC′ =1(Eq.3)spanningthesamerangeof𝐵𝑅values,assumingtheDTistampedbya linerwitharealdensity(𝜌𝛿𝑅) =3g/cm2,conditionsaccessibletotheDS.NotethatwhiletheLawsonthresholdto 𝑙 igniteismorestringentthanthethresholdforinstantaneousself-heating,alphaheatingcanhelptheassemblycross overtheignitionthreshold. 30 Affordable,manageable,practical,andscalable(AMPS)high-yieldandhigh-gaininertialfusion This expression combines the self-heating and confinement requirements for ignition and can only be positive in regionswhereinstantaneousnetself-heatingoccursatstagnation.Weplotcontoursrepresentingtheignitionthreshold criterionGLC′ =1assolidlinesinFigs.3and21forthespecificcase(𝜌𝛿𝑅) =3g/cm2,demonstratingthelargedesign 𝑙 spaceopenedupbyfuelmagnetization. Notethatforboundarycasesabovethedashedcurvesbutbelowthesolid GLC′ ≈1curvesinFig.21,self-heatingcanpushthefuelabovetheignitionboundary. B Pulser-targetcouplingphysics AccuratemodelingoftheevolutionofplasmawithintheinnerMITLandloadregionrequiresinclusionofphysics beyondthatusuallyincludedinradiationMHDmodels(PICorHallphysicsasjustdiscussed);however,somesimple MHDconceptsareoftenusefulinunderstandinghowtheevolvedplasmainfluencescurrentdeliverytoorwithinthe target.TheMHD-likepicturecancapturegrossfeaturesoftheplasmaflowwhentheparticledynamicsaredominated by𝐸×𝐵drift.Thisapplieswhenbothionsandelectronsarestronglymagnetized,i.e,gyro-radiiforbothspeciesare smallcomparedtotheAKgapandthe𝐸×𝐵driftdominatesoverpolarizationdrift(whenthegyro-periodisshort compared to the rate of change of the flow) as well as gradient B and curvature drifts (again in the limit of small gyro-orbits).TheseconditionstypicallyapplywithintheinnerMITLandtargetregionduringthemaincurrentrisebut areviolatedearlyintime. If the conductivity of the plasma is sufficient (above a few eV in electron temperature) then the MHD concept of “frozenflux”isuseful:theconceptthatmagneticfieldandplasmaareapproximately“tied”together.Inasystemwitha purelyazimuthalfield,ignoringthecomparativelyweakaxialfieldthatmightbeusedtomagnetizeaMagLIFtarget, the magnetic field and plasma can be treated as a collection of magnetic flux loops of infinitesimal area 𝛿A, with magneticfieldstrengthB,andmagneticfluxB𝛿A.Theplasmamassentrainedwithintheloopis2𝜋𝑅𝜌𝛿𝐴,whereRis thecylindricalradius.Ifthemagneticfluxandmassaretiedtogether,thentheflux/massoftheloopisproportional to𝐵/(𝜌𝑅),whichisaconstantofthemotionfortheMHD-likeflow.Sincethemagneticfield,ignoringsmallcurrent losses,variesas𝑅−1,thisindicatesthattheinward(target-directed)plasmaflowwilltendtoconcentratethedensityas 𝑅−2.Thesimplefluxlooppictureoffersanotherinsight:IftheplasmaintheinnerMITLisacceleratedtowardthetarget duetoitsincreasinginductanceandassociatedelectricfieldincrease,thenthefluxloopsmustincreasetheirkinetic energy.Itmightbeexpectedthatthechangeinkineticenergyoftheloopswouldbelimitedbytheavailablemagnetic energyintheloops,i.e. 𝑀𝑣2/2 < 𝐵2/2𝜇 ⋅𝑉,where𝑣isthe𝐸×𝐵velocityandVisthevolumeoftheloop=2𝜋𝑅𝛿𝐴. 0 Thisconditionisequivalentto𝑣 <𝑣 Alfven ,where𝑣 Alfven = √ 𝜇 𝐵 0𝜌 istheclassicAlfvénvelocityforwavepropagationin magnetizedplasmas.Since𝐵variesas𝑅−1and𝜌variesas𝑅−2thereisatendencyforthepowerflowregiontohavea characteristic(time-dependent)Alfvénvelocity.Inpractice,thepresenceofplasmawheretheincreaseinflowvelocity ismorethanafewpercentoftheAlfvénvelocityleadstonoticeablemagneticenergyloss,whichmanifestsascurrent losstotheload. Anidealizedversionofloadandplasmaevolutionhelpstounderstandthiseffect.Ifweimagineaninitialstatewitha staticcylindricallinerandaplasma-filledMITLwithdensityvaryingas𝑅−2andmagneticfieldvaryingas𝑅−1,i.e.,a constantAlfvénvelocity,thenoncethelinerbeginstomove,ararefactionwaveislaunchedoutwardintotheMITL plasma.Inalowbeta(beta=plasmapressure/magneticpressure)magnetizedplasma,thespeedofthemagneto-acoustic rarefactionis𝑣 . Themagneticfieldandmagneticpressureatthesurfaceofthelinerarelessthanthevacuum Alfven valuesduetotherarefaction,implyinglessthan100percentcurrentdeliverytotheload. OntheZaccelerator,the magnitudeoftheseeffectsdependsonthenatureoftheloadandtheconditionofelectrodesurfacesthatcontribute plasmaintotheMITL.LowvelocityloadssuchasMagLIFmayhavelesssensitivitythanhighvelocitylikegaspuffs orwirearrays,althoughhighinductanceloadscanhaveahighMITLelectricfieldand𝐸×𝐵velocitysince𝑑𝐿/𝑑𝑡 is proportionaltoboththelinervelocityandtargetheight.Inanycase,attentiontovacuumconditioningandelectrode contaminantsthatcontributetoMITLplasmaareimportantconsiderations,althoughtheseeffectscanbecaptured inthePICmodelsoftheMITL.TheeffectofplasmaonthetargetitselfisusuallyincludedinradiationMHDtarget simulationsasaboundaryconditionordensityfloor.Theplasmacancausecurrentredistributionwithinthetarget volumeaswellastheMITL.Atthetargetscale,theMHDmodelisusuallyabetterapproximationthanintheMITL. 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