Contents lists available atScienceDirect
Physics Letters A
www.elsevier.com/locate/pla
Laser wake field collider
NAPLIFE Collaboration
István Papp
a,b,∗, Larissa Bravina
c, Mária Csete
d, Igor N. Mishustin
e,f, Dénes Molnár
g, Anton Motornenko
e, Leonid M. Satarov
e, Horst Stöcker
e,h,i, Daniel D. Strottman
j, András Szenes
d, Dávid Vass
d, Tamás S. Biró
a, László P. Csernai
a,b,e, Norbert Kroó
a,kaWignerResearchCentreforPhysics,Budapest,Hungary
bDept.ofPhysicsandTechnology,UniversityofBergen,5007Bergen,Norway cDepartmentofPhysics,UniversityofOslo,Norway
dDept.ofOpticsandQuantumElectronics,Univ.ofSzeged,Hungary eFrankfurtInstituteforAdvancedStudies,60438Frankfurt/Main,Germany fNationalResearchCenter“KurchatovInstitute”Moscow,Russia gDept.ofPhysics,PurdueUniversity,WestLafayette,47907IN,USA
hInst.fürTheoretischePhysik,GoetheUniversitätFrankfurt,60438Frankfurt/Main,Germany iGSIHelmholtzzentrumfürSchwerionenforschungGmbH,64291Darmstadt,Germany jLosAlamosNationalLaboratory,LosAlamos,87545NM,USA
kHungarianAcademyofSciences,1051Budapest,Hungary
a rt i c l e i n f o a b s t r a c t
Articlehistory:
Received14November2020
Receivedinrevisedform11January2021 Accepted15January2021
Availableonline26February2021 CommunicatedbyA.Das
Keywords:
Laserwake-fieldacceleration Ionization
Inertialconfinementfusion NAPLIFE
RecentlyNAno-Plasmonic,LaserInertial FusionExperiments(NAPLIFE)wereproposed,as animproved way to achieve laser driven fusion. The improvement is the combination of two basic research discoveries:(i) thepossibility ofdetonationsonspace-time hyper-surfaceswith time-likenormal (i.e.
simultaneousdetonationinawholevolume) and (ii)to increasethisvolumeto thewholetarget,by regulatingthelaserlightabsorptionusingnanoshellsornanorodsasantennas.Theseprinciplescanbe realizedinaonedimensional configuration,inthesimplestwaywithtwoopposinglaserbeamsasin particlecolliders.Such,opposinglaserbeamexperimentswerealsoperformedrecently.Herewestudy theconsequencesoftheLaserWakeFieldAcceleration (LWFA)ifweexperience itinacollidinglaser beamset-up.Thesestudiescanbeappliedtolaserdrivenfusion,butalsotootherrapidphasetransition, combustion,orignitionstudiesinothermaterials.
©2021TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).
1. Introduction
In recent years the LaserWake FieldAcceleration (LWFA)be- cameawellknownconceptwithusefulapplications.Anintensive laserpulseimpingingonatargetcreatesahighdensityplasmaof 4x1019/cm3,andawakefield wavefollowsthepulse.This,non- linear wave indense plasma isformed ofthe EM-field,electrons and ions.A typical laser of 20mJ pulse energy, 7 fs length and λ wavelength cancreatea LaserWake Field(LWF)dense plasma waveofabout10λwavelength.
Thiswave is differentfromradiotransmission wavesinairor vacuum, wherethe materialisdilute, notorweakly ionized. Still thereareinterestingphenomenaifradiotransmissionwavescreate
*
Correspondingauthor.E-mailaddresses:papp.istvan@wigner.hu,steve.prst@gmail.com(I. Papp).
aninterference.Inthe1950sthisradiowaveinterferencewaswell knownduetoradiojamming(e.g.jammingtheRadioFreeEurope shortwaveAM49 mbandbroadcastinEasternEurope).Strong,un- modulatedjammingbroadcastonthesamecarrierfrequencycould lead to noiseless quiet sound, or it was white-noise modulated resultingin strongnoise. Interferenceof two original frequencies that are quite close can lead to a “beat frequency transmission”
with fbeat=(f1− f2)/2.This isoftentoolowto beperceived as anaudibletoneorpitch,instead,itisperceivedasaperiodicvari- ationin theamplitudeofthebroadcast. Weaimto study similar kindofvarietyofpossibilitiesincollidingLWFwaves.
Laser Wake Field Collider (LWFC) waves can be realized the simplest way by two opposing laser light on a target. This was recently suggestedin ref. [1,2] for laser driven fusion. Here two knowneffectswerecombined.First,thepossibilityofdetonations on space-time hyper-surfaces with time-like normal, so called https://doi.org/10.1016/j.physleta.2021.127245
0375-9601/©2021TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBY-NC-NDlicense (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Previous works alsoused colliding laser beams andLWFA for electronacceleration.Inref. [7] witha gas-jettarget,theprimary strongerbeamcreatedthe LWFbubbleandathreetimesweaker counter-propagatingbeaminjected electronsintothe bubble.The ultrashort laser pulseshad thesame central wavelengthand po- larization.Theelectronbeamsobtainedinthiswayarecollimated (5 mraddivergence),monoenergetic(withenergyspreadof10per cent),andelectronbunchdurationsshorterthan10fs.
Similar method is presented in ref. [8] for electron accelera- tion,alsoinasymmetricconfiguration,wheretheweakerinjection beamwasnotcollinearbutcounter-propagatingunderanangleof 150◦. Thesecolliding laser beamsdid not aim foranychange of thetargetandhavenotusednanoplasmonicsorsimultaneousvol- umetransition.
A different method for electron accelerator was presented in ref. [9] where two identical laser beams irradiated an array of nanoantennas, whichwere nanorods with long axis alignedpar- allel to thepolarization of thelaser light. Electronbuncheswere hitting thelayer ofthesenanoantennas fortheside alignedwith the directions of the nanorods. These bunches were then accel- eratedeach time passingananorod withtherightfrequencyand bunchperiodlength.Althoughthisproposalutilizednanoantennas, butforthelocalaccelerating electricfield toaccelerate electrons.
Thetargetwas astaticnanoantennaarray,changingitsphasedue totheincominglaserpulses.
Anotherexperimentusingcollidinglaserbeams[10] aimedfor achieving hightarget density fornuclear fusion, butdidnot uti- lize LWFwavesandnanoplasmonicsanddidnot attempttohave simultaneoustransitioninthetarget.
Thus,ourpresentaimdiffersfromthesepreviousworks.
2. Non-thermalignitionrate
InLaserWakeFieldCollider,thetargethastwosides,whichare initiallyacceleratedtowardseachother.
CarbonC6+ionsintherelativistic-inducedtransparencyaccel- eration(RITA) regime,havereachednearto1GeVenergyon300 nmtargetthickness[11].
Inref. [13] itwasshownthat intense laserpulseirradiatinga combinationtargetcan acceleratecarbonionstotheTeVlevelby thelaserplasmawakefield.
IfweconsiderLWFCwithadoublelayertarget1pre-compressed toiondensity,npc,andpre-acceleratedtoseveralGeV/nucleonen- ergy,(i.e.toaLaserWake(LW)velocityneartothespeedoflight, vLW ≈ c),thetwoLWFwavescaninter-penetrateandleadtoan ignitionreactionrateof
2
γ
2n2pccσ ,
(1)where
σ
istheion-ioncrosssection,andduetotheLorentzcon- traction, thetwo ion bunchesare compressedtoγ
npc. Thismay well exceedthethermal(th)rateperparticlenvthσ
.Iftheions are accelerated to 5 GeV/nucleon, thenγ
≈6, and if the pre- compression reaches a factor 8 (considerably less than at NIF,1 Theinitialtargetmaybetwolayers,e.g.DandT,withagapbetween.
TTones,likeinamixedDTtarget.
3. Laserandtargetparameters
Irradiatingadensetargetwithsuch beamscreatesLWFwaves, and we study what are the consequences. We used the EPOCH multi-component PIC code [12] to see first what kind of LWF wavesdevelop, ifwe irradiatea target witha laser beamhaving a wavelength of λ=1 μm, a Gaussian distribution in the trans- verse,[y,z]planeofhalfamplitudetimeδt=26 fs,andfullpulse lengtht=52 fs.
Thelaserfocusaveragediameteris2R=40 μm.Thelaserpulse energyin thepresent test is19.6J, andthe maximumintensity, inthe centerofthe transverse plane atthetop intensitytime is 3.0·1019W/cm2.
We studied the EM field and the target in a 3-dimensional box of 50 x 70 x 70 μm, divided into cubic cells of 100 nm (0.1 μm). The initial target consisted of H atoms. The H target consistedof two slabs with 24.5 μmthicknesswith a 1 μm gap betweenthem,andpre-acceleratedtowardseachotherwithamo- mentum of100 MeV/c.Due to the irradiation the target became mostlyionized, andprotons p andelectrons,e areformed.These componentswererepresentedby markerparticles.Therestnum- ber densityof H atoms inmarkerparticles in thiswork isnH= 2.13·1027atoms/m3=2.13·1021atoms/cm3,ornH=2.13·1025 atoms/m3=2.13·1019 atoms/cm3.Thisisneartothedensityof liquidhydrogen,whichis2.124·1022/cm3.Theinitialsizeofthese markerparticlesis0.0253·μm3=1.5625·10−5μm3.Forcompar- ison we also madea test with a two orders of magnitudemore dilute target. The different types of marker particles (mp) con- taineddifferentnumberofcomponents:
1emp
∝
1024e,
1pmp∝
1024p,
1Hmp∝
1024H.
Initially the H component marker particles were uniformly dis- tributedinthecalculationcells,sothateachcellcontained6Hmp. 4. Laserwakefieldwaves
As we can see in Fig. 1 at 100.2 fs the LWF wave length is λLW F ≈20 μm. Wecan alsoseethe pincheffect,that thetrans- verseextentofthebeamshrinks. At150fsthetransversesizeof thebeamisabout80%ofthesizeat50fs.
InFig.2weseetheeffectoftwoopposing laserbeamsonthe two target H atom slabs. The two beams hit the denser targets fromoppositesides,andastheirradiationisabsorbedtheHatoms areionized, protons andelectrons becomefree. By150 fs,the H atomtargetsare fullyionized, exceptattheoutsideedges where thepinchedirradiationbeamsdidnothitthetarget.
Electronswerecreatedduringtheirradiation. Hionsandelec- tronsweremovingduringthecalculationandcrossedovertoother cells.
InFig.3we canseethat ataround 125- 150fsatthislower targetdensity,thetwoLWFwavesconstructivelyinteractandthe EMfieldstrengthismaximal.Thismomentoftimewouldbeade- quateforashort,intensiveignitionpulse.
Fig. 1.(Coloronline)Theelectricfield,Ey(top)andmagneticfield,Bz (bottom)showtwoaLaserWakeField(LWF)wavesapproachingeachother(seeat100fs)formed byirradiationfromthe±x-direction.TherestnumberdensityoftheHtargetisnH=2.13·1025/m3=2.13·1019/cm3.Thelaserbeamwavelengthisλ=1 μm.TheLWF wavelengthisabout20λ.
Fig. 2.(Coloronline)Theionizationofthe HatomsinaLaserWakeField(LWF)waveduetotheirradiationfromboththe±x-directions,onaninitialtargetdensityof nH=2.13·1027atoms/m3=2.13·1021atoms/cm3.TheenergyoftheHatomsinJoule[J]permarkerparticleisshown.TheHatomsdisappearasprotonsandelectrons arecreated.DuetotheinitialmomentumofthecollidingHslabs,thetargetandprojectileslabsinterpenetrateeachotherandthisleadstodoubleenergydensity.Several time-stepsareshownat30fstimedifference.
Fig. 3.(Coloronline)ElectricField,EyinaLaserWakeField(LWF)waveformedbyirradiationfromboththe±x-directions.Thefieldstrengthsareshowninthemiddleof thetransverse,y,z,planealongthex-axis.Intheother,notshown,directionsthefieldsareweakerbyordersofmagnitude.TheinitialtargetdensityisnH=2.13·1019 atoms/cm3.Severaltime-stepsareshownat25,50,75,100,125and150fstimes.
Fig. 4.(Coloronline)ThesameasFig.3withtargetdensitynH=2.13·1021atoms/cm3.AtthishigherdensitytheenergyofEMradiationisabsorbedbytheionizationof thetarget.TheuppersetoffiguresshowtheElectricfieldinthewholetarget,whilethelowersetoffiguresshowtheE-fieldinthemiddleofthetarget.
The EM field strength for higherinitial target densities, nH= 1021/cm3, decreases strongly and becomes random. This is the consequenceofthestrongabsorptionbythedensertarget.Wecan seethesignsofincreasing randomnessinFig.4.Theamplitudeof both Ey andBzisreducedandrandomfluctuationsincrease.This can beseenalreadyinFig.4,whereat150fs,the penetrationof the Bz field intothe targetis delayedandreduced, andthecon- structiveinterferenceofthetwoopposing Bz fieldsisdelayed.
This can be attributedto the kinetic approach,where the in- teractions andpressure in the target are neglected andthus the dominant longitudinal momentum is transported to the kinetic motionofthetarget particles.Thesethencontribute tothepinch effectreducingtheEM-fieldstrengthandtargetbeamdirectedmo- mentum.
Themodelincludesakineticcollisionset-up,whichreproduces therelaxationtime approximation,so thatthe momentumdistri- bution converges towards the Maxwell-Boltzmann ideal thermal distribution. Thiscan then be characterized by atemperature. At thesametime thiseffectisdemonstratedforcollisionwithinthe sametypeofparticles.
Thusitismorerealisticforourmodelingtoconsiderthetarget andprojectileatomsandionsasseparateparticlespeciesanddif- ferent type ofmarker particles (simulation particles: Hp, Ht, pp, andpt,whiletheelectronsmayremaininasinglegroup,asthese aremorespreadoutinthespaceduetotheirsmallermass.
The LWF waves show increasing penetration into the target withincreasing laserbeamenergy.Thisisalsoreconfirmedbyre- cent experiments [14], showing that with increasing laser beam energythereflectionofthebeamdecreases,whiletheabsorption increasesto100%incaseof Autarget.
One shouldcheck actuallythe energydensitydistributionand itstimedependence,inthisdynamicalsituation.Uptonowinthe targetstudies[6] mainlystaticfinalstate configurationsweredis- cussed.
AsthepressureandtheEquationofState(EoS)doesnotappear in the EPOCH code, it is clearly solving the kinetic equations of
motionfortheelectronsandions.Relativisticthermaldistribution functionsareincludedintothecode.
Indensenuclearplasma,theEoSisalsovital,asatlower den- sitieswe havenuclearattraction whileathigher densitiesstrong nuclearrepulsion.Inidealgaskinetictheorytheseessentialeffects arenottakenintoaccount.Thiscouldplayasignificantroleincor- rectestimateoftheburningreactionrateofthetarget.
Anexperimentalreconfirmation oftheeffectofenergeticlaser beamswas done on a goldtarget [14], recently,andstrong light absorptions as well as the conversion effect to X-rays was ob- served.Thisexperimentactuallyconfirms earlier,originalideasin [4,2,1].
In[14], the conversionto X-rays radiationisparametrized by a “velocity”, attributing the frequency shift to a Doppler effect.
Nevertheless,thisvelocity is not connectedto any ofthe several possibleandabove mentioned processes,andthe authorsdo not elaboratewhatthisvelocityparameterwouldcharacterize.
5. Outlookfornanoantennas
The penetration of the LWF waves into the target was men- tioned earlier, and in colliding beam configuration this leads to substantialiondensityincrease. Therole ofnanoantennas inthis caseisthattheincreasedphotonabsorptionleadstoincreasedmo- mentum deposition in the target and higher density [1]. Finally thisresultsinfasterburningrate.
The nanoantennas have another effect too. Similarly to the golden (or depleted Uranium) hohlraum, which converts the in- cominglaserlight, to X-rays. Incaseofinternal nanoantennasin thetargetDTfuelwehavetwo maineffectsfor conversion ofthe visiblelaser light to higher X-ray frequencies:Bremsstrahlungin electroncollisions, andtransitionfromhighenergylevelelectron statestolowerones.
Thissecondeffectisespeciallystrongforresonantnanoanten- nas,whichleadtoperiodicextremehighelectrondensitiesatthe edgeof theantenna. As theelectrons are Fermions,at highden- sity they are forced to occupyhigh energylevels (at thecost of
Fig. 5.(Coloronline)Thedensityofelectronsin1/m3units.Theelectrondensityreachesne=3−5·1027electrons/m3,attheinitialHatomtargetdensityofnH=2.13·1021 atoms/cm3.
theincominglaserenergy)andthenasthedensityperiodicallyde- creasestheyemitthecorresponding X-rays.Thisprocessisspecific to nanoantennas. Due to momentum conservation the incoming laserlight momentumandtheemitted X-raymomentumarerel- ativelyaligned.
Arecentexperimentshows[14],thatevenwithoutnanoanten- nas,laserlightwithincreasingintensityongoldtargetleadstoin- creasingabsorption(andvanishingreflection).Furthermore,atthe sametimetheincreasingintensitylaserirradiationisaccompanied byincreasingx-rayconversion.Embeddedresonantnanoantennas areexpectedtoamplifytheseeffects.
Resonant nanoantennas have an electron density fluctuation parallel to the oscillation of the EM field of the laser irradia- tion.Significantchargeseparationaccompaniestheplasmonicres- onance, which leads to 108 C/m3 average charge density on the nanorod inlinear approximation atthe peakof a 26fs pulseal- readyat1.4·1012W/cm2thatwasreportedasathresholdresult- ing in permanent damage of similar gold antennas [15]. Further studiesareinprogresstodeterminethechargeseparationbytak- ing the nonlinear phenomena arising at high intensities into ac- count [6].Thisindicates thattheelectron densityincrease dueto nanoantennaswillsignificantlycontributetotheconversionto X- rays.
The Bremsstrahlung effect is always presentin electron colli- sions with, atoms,ions andother electrons(Fig. 5). Alsoelectron collisions onnanoparticlescanbetakenintoaccountasan addi- tionaleffectofnanoantennas.Moreimportantlyatthepointwhen all atomsare ionizedthe nanoantennas dobreakapart alsowith dynamical domains of highelectron density. Thesedomains lead toadditionalcollisionsandBremsstrahlung.Thustheinternalres- onant nanoantennashave an increasedconversionofvisiblelight to X-rays.
Theshortandmoreenergeticignitionlaser pulsemodifiesthe thermalequilibriumignitionscenario.Theretheaveragecrosssec- tion is calculated asthe thermalaverage of the constituentfuel ions(i),i.e.DandTions.Inthermalaveragethethermalenergies of differentcomponents areequal, Eki≈3/2·kT.Seee.g. [10,16].
Thus the average speed, the relative collision speed for heavier constituents is considerably smaller (e.g. for protons about 1800 times less than forelectrons). Consequently the thermal average collision rateis relatively small and increases around EkT hermal≈ 100−200 keV[16].
In contrast for colliding beams withLaser Wake Field waves, electrons andions move withthe same LaserWake (LW) speed, vLW.So,iftheprojectile andtarget interpenetrateeachother be- fore equilibration, the relative energy of ions is larger (e.g. for protons(p)andelectrons(e): Ekp≈1800Eke).Furthermore,therel- ative(r)kineticenergybetweenprojectileandtargetionsistwice asmuch(e.g.Erp≈3600Eke).Thisistheinitialignitionmechanism.
After3-4subsequentcollisionequilibrationisreached,andtherel- ative speed becomes the much smaller, isotropically distributed thermalspeed.However,incaseofanignitionlaserpulseof∼10
fs, there is no time for such equilibration,until the burning be- comes a dominant process. Forlonger, ns, laser pulses two step nuclearprocessesareconsidered[16],butfor∼10fspulsesthese arenegligible.
Thus, it is important to study experimentally, how the LWF wavesandthenanoantennadistributioncanachievethebesttime- likeignitioninmostofthewholetarget!
Interactionsofelectronsonthenanoplasmonicsurfaces,which caninteractwiththe surrounding H ions mayleadeventually to e(p,n)
ν
ereactionsincaseofhighelectrondensity.Thelowenergy neutronsthencanformDeuteriumions,H+(n,γ
)D+.See:https://www-nds.iaea.org/ngatlas2/.
Declarationofcompetinginterest
Theauthorsdeclarethattheyhavenoknowncompetingfinan- cialinterestsorpersonalrelationshipsthatcouldhaveappearedto influencetheworkreportedinthispaper.
Acknowledgements
Enlighteningdiscussions withAlex C. Hoffmann andOliver A.
Fekete are gratefully acknowledged. Horst Stöcker acknowledges the Judah M. Eisenberg Professor Laureatus chair at Fachbereich Physik of Goethe Universität Frankfurt. Dénes Molnár acknowl- edges support by the US Department of Energy, Office of Sci- ence,underAwardNo.DE-SC0016524.Wewouldliketothankthe WignerGPULaboratoryattheWignerResearchCenterforPhysics forprovidingsupportincomputationalresources.Thisworkissup- portedin part by the Institute of Advance Studies, K ˝oszeg, Hun- gary, the Frankfurt Institute for Advanced Studies, Germany, the Eötvös,Loránd ResearchNetworkofHungary,theResearchCoun- cil of Norway, grant no. 255253, and the National Research,De- velopment andInnovation Office of Hungary,projects: Nanoplas- monicLaserFusionResearchLaboratory(NKFIH-874-1/2020),Opti- mizednanoplasmonics(K116362),andUltrafastphysicalprocesses inatoms,molecules,nanostructuresandbiologicalsystems(EFOP- 3.6.2-16-2017-00005).
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