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ELI Summer School, 29.8.2019

Plasma P hysics and Laser-Plasma Interaction C. Riconda LULI, Sorbonne Université , Paris, FRANCE. ELI Summer School, 29.8.2019. Plasma in a nutshell Lasers interacting with plasma /matter Simulation of laser-plasma interaction (LPI)

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ELI Summer School, 29.8.2019

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  1. Plasma Physics and Laser-Plasma InteractionC. RicondaLULI, Sorbonne Université, Paris, FRANCE ELI Summer School, 29.8.2019

  2. Plasma in a nutshell • Lasers interacting with plasma/matter • Simulation of laser-plasma interaction (LPI) • Collective effects – parametricinstabilities (PI) • Twoexampleswhere PI play a role • LPI for InertialConfinement Fusion (ICF) • Plasma Optics – Plasma Amplification • Conclusion/outlook Outline of the talk

  3. Plasma in a nutshell

  4. The 4th state of matter • Ionized gas: positive & negative charges are in some sense «free» particles: • cold plasma neverreally « cold » (1eV = 11605 K) • Πλάσμα (plasma) isthemost abundant form of matter in theuniverse: 99,999% • "In thebeginningthere was plasma. The otherstuffcamelater.“ (Rogoff, Coalitionfor Plasma Science) • Introducedby Langmuir & Tonks in 1929.

  5. The ubiquitousplasma (The 1st state of matter)

  6. Defining a plasma: somebasicparameters  All functions of density ne [in cm-3] andtemperatureTe [in eV] N.B. ne=ni , mi>>me • (electron) plasma frequency: ωpe= (4πnee2/me)1/2 = 5.64 x 104ne1/2 [Hz} • (shielding) Debyelength: λD= (kTe/4πne2)1/2 = 7.43 x 102Te1/2 n−1/2[cm] • (electron-ion) collision frequency: νe = 2.91 x10−6ne ln Λ Te−3/2 [Hz] • (electron) thermal velocity: vTe= (kTe/me)1/2= 4.19 x 107Te1/2 [cm/sec] • average distance: do = ne -1/3 • average potential energy for binary interaction: Epot = e2/do = e2 ne1/3 • average (electron) kinetic energy: Ekin = mevTe2 = k Te

  7. Somederivedparameterstocharacterize a plasma • onedefinitelyneeds for typicalscales: L >> λD & t >> 1/ωpe , 1/ωo • an importantparameteristhenumber of particles in a Debye sphere: • ND≡ (4π/3) ne λD3 >>> 1 • Freeness: Ekin >> Epot  Te >> e2/do=e2ne1/3  ne2/3 Te / e2ne = ND2/3 •  ND >> 1 • Collisionlessness: νe / ωpe ~ 1/ND << 1 • Aplasmaisveryoftendominatedbycollectiveeffects! • Definition of a classicalplasma: fields due to Coulomb binaryinteraction ≈ 0 on average, but collectivemotionandabilitytogeneratemacroscopicfieldsimportant. • ND>>1 canbesatisfiedforwiderange in neandTe

  8. A comment on relativisticandquantumplasmas • relativisticplasmas: Te ~ mec2 ~ 500 keV • quantumeffects: verydense, low-temperatureplasmas, e.g. WDM studies, or • veryintenselaserfields, QED effects • uncertitude in spatialcoordinate: • δr~ ne-1/3 --> δp ne-1/3~ ħ/δr = ħ ne1/3 • For classic descriptionrequire: • δp << <p> ~ (meTe)1/2  • ne << (meTe)3/2/ħ3  ne ≪ 1023Te2/3 • with ne [cm-3] andTe [eV]

  9. Lasers interacting with plasma/matter

  10. Plasma creation & heatingbylaser In a quasi-staticfield • Initial ionization • H-atom: Eion = 13.6 eV • λ = 1 μm Ephoton= 1.2 eV • Electricfield E • Keldyshparameterγ = ωo (2meEion)1/2/eEdistinguishesbetweentunnel (γ << 1) • and multi-photon (γ >> 1) ionization • depends on intensity& wavelength of laserandionizationstage/potential of atom • seedelectronsoscillate in thelaserfield  gain energy  collisionalionization  avalancheprocess  create a plasma

  11. Plasmas interactwithlaserelectromagneticfields • plasmaisensemble of chargedparticleswhicharesubjecttotheoscillating • electromagneticfield of thelaser: • Lorentz-force(field-lineeffect): dp/dt= -e [ E(r,t) + v x B(r,t) ] • becauseofthemassratio, ionmouvementcanbeneglected • First-order approximation collectivequivervelocity of electrons: vosc= eE0/(meω0) , • i.e. neglecting v x B = O(v/c) • Coherentmotion of thelaserinducescoherentmotionofelectrons, enslaved, • e.g. plane wave, linear polarizationparticlesoscillateupand down following E. • Dispersion relationandvphofthewavemodified : onlywaveswithcanpropagate . • Oscillatingelectronscollide with ions & lose orderedenergy (inverse Bremsstrahlung) •  wavseabsorptionandplasmaheating voscII E ωo>ωpe N.B. Relativisticeffects,O(v2/c2),  drift parallel topropagation + figure8 motionforintensitiesabove ~1018 W/cm2

  12. The ponderomotiveforce • Discovered in 1957 by Boot & Harvie in radio-frequency context (Nature180, 1187 (1957)) • Existence of a non-zero time-averagedforce in non-uniform fields (Landau, Mechanics 1940) FPond = − (e2/4meωo2)∇E2 • Ponderomotiveforceis an envelopeeffect*, relatedtothe light pressure, whichexists in: • 1) tranversedirection: kicks awayelectronsfrom high intensityzonesresulting in channeling, • densityperturbations, focusing, sidewayshocks (long-pulse) • 2) propagationdirection: particleacceleration (short-pulse), e.g. wakefield *quadratic in E, needsomewhathighintensity

  13. A real-lifelaser pulse  A laser pulse is not a Heaviside function in time (not even a Gaussian)  Thereisalmostalwaysalready a plasmawhen „your“ pulse arrives  Consequences also for simulation: can not alwaysconsiderthecomplete pulse

  14. High-intensitylaserinteractingwithplasma/matter ‘Underdense’ Plasma : ω0 > ωpe Laser propagatesinside the plasma, volume interaction. ‘Overdense’ Plasma : ω0 < ωpe Relativistic laser Mainly surface interaction Laser pulse • Next we‘llconsidercollectiveeffectsofweaklyor non-relativistic Laser-Plasma-Interaction, • i.e. manyparticlesinteractingin a coherentway in an underdenseplasma‚ ‘long‘ pulse

  15. Simulation of laser-plasma interaction (LPI)

  16. A hierarchy of modelsavailable •  Whysimulationat all ? Things arestronglynonlinearand multi-dimensional; • quantitative aspectsrequiresimulation. • Approach depends on thekind of physicsandcharacteristicscalestobesimulated • E.g.: particlemotion, multi-fluidmodels, 1 fluid model (MHD), kineticmodels • Laser-plasma interactionasweconsiderrequiresrelativistickineticapproach: • VLASOV equation for eachspecies ∂fs/∂t + (p/ms)∂fs/∂x + qs (E + (p/msγ) × B)∂fs/∂p = 0 •  Equationdescribestheevolutionoftheparticlesdistributionfunction • Equationcanbeintegrateddirectlyorsolvedusing a statisticalapproach (numerically) • Verywellsuitedfor high field, relativisticdomain

  17. Particle-in-cellapproach  Idea: initialconditionis a large number of particles with a giventemperaturedistribution - theythenevolveaccordingtothefollowingequations (Maxwell + Newton) Electromagnetic field ∇× E + ∂B/∂t = 0 ∇× B − (1/c2) ∂E/∂t = μ0J ∇E = ρ/ε0 ∇B = 0 Characteristics of Vlasov-eqn. dxp/dt=up/γp dup/dt= qp (Ep + up × Bp/γp) γp = (1 + p2/(mc)2)1/2 Reality versus simulation L >> λD, ND = O(102...106)  millionsofbillionsofparticleimpossible ! BUT: simulation same for 10 and 10.000 sincecollectivemotion, particles ‘enslaved‘ Constituentrelations for eachcell ρ = Σ qp J = Σ qpup/γp

  18. Computationalaspects: a casestudy from ICF • Need to resolve: 1/ωpe ,1/ωo& 1/ko • Particularcase: • 10 pslaserpropagating in theplasma • forsome 100 microns • (Δx = Δy = 0.18 ko-1 , Δt = 0.18 ωo-1 ; CFL: c Δx ≤ Δt) • 2.4 x 108 computationalcells • 1.4 x 105 time steps • 108...9macro-particles • (a smallfractionofthe real number!) • Order of 500‘000 CPU-hours !! (~1 monthrunning on 600 cores-57 yrs on 1 core) • Producinghundreds of GB data • Multidimensional kineticequationsrequire VERY BIG computers !!!

  19. Collective effectsparametric instabilities

  20. From wavepropagationtodispersion relation • A plasmasupports BOTH transverse electromagneticwaves (e.g. Laser propagatinginsidetheplasma) and longitudinal compressionwaves (electronsorions). Howtocharacterizethesewaves ? • Procedure: Choose governingequations, e.g. fluid eqnsorkineticeqn. Choosebackground (0th-order) (coldorhot, atrestor in mouvement, magnetizedor not) Study responseoftheplasmatosmallelectricorelectromagneticperturbations of the form exp{i(kr– ωt)} Determinedispersion relation, D(ω,k)= 0, andsolve for ω = ω(k) togetpossible combinations of frequency ωandwavevectork Find whichwavesaresupportedbytheplasma, i.e. naturaloscillationmodesoftheplasma* Plasma waves ‘Zoo‘ *analogoustopropagationofelectromagneticwaves in dielectricsω= kc√εorstudyofacousticwaves in gazω = kcs: naturalmodeoftheconsidered medium.

  21. Natural oscillationmodes in a non-magnetizedplasma Onlythree Electromagneticwave (EMW) ω2 = ωp2 + k2 c2  limiting frequency ω >= ωp Electronplasmawave (Langmuir wave, EPW) ω2epw ≈ ω2p + 3 k2epw v2Te ≈ ω2p (1 + 3 k2epw λ2D) Ion-acousticwave (IAW) ωiaw≈ cskiawcs<<vTe ωp = (4πne e2/me)1/2 ; vTe = (kBTe/me)1/2 ; λD = ve/ωp ; cs = (kBTe/mi)1/2  „Un“-naturalmodesare of greatinterestin LPI (seelater) !

  22. Backward, E&M Laser, E&M Wave coupling in a plasma Plasma EP wave ~~~~~~ • Waves in a plasmacancouple: • intensity of oneortwowavescangrow • attheexpenseoftheintensity of another • pre-existingwaveif a resonancecondition • isfulfilled: • ω0 = ω1 + ω2 (energy) • k0 = k1 + k2 (momentum) IA wave ~~~~~~ Decayor Backscattering EPW2 EPW1 ~~~~~~ Laser, E&M Twoplasmondecay ~~~~~~ • 3-wave coupling due to • conservation of energy and • momentum Plasma A classic exemple of Laser-Plasma Interaction (LPI): ParametricInstabilities (PI) Laser loosingitsenergy in favor of otherwaves

  23. ParametricInstabilitygrowth: from noisetocoherentmotion Laser intoplasma Plasma oscillations radiatescattered light Beating of 2 em. Waves ponderomotiveforce particlesintotroughs     Backscattering: fromnoisetocoherentmotion • Bunchingmatches • electrostaticmode • 3 waves resonant • growthofinstability: • generatesstrongerscatteredradiation

  24. TwoexampleswherePI play a role:“fromdetrimental to beneficial"

  25. 1. Example LPI for InertialConfinement Fusion (ICF)

  26. Need of a denseand HOT plasmatohavefusion  Nuclearreaction energy: ΔE = (mi – mf) c2

  27.  morethanonewaytoconfineparticles (plasma): n τ T > 3 x1018eV cm−3 s Andhowtogetthere ?

  28. LMJ Startingnow, onlypartof total energy NIF operating Large-scaleprojectsrelatedtoachievingfusion  Also activeprojects in China, Japan andRussia

  29. Laser Laser Laser Inertialconfinementfusion To heat and compress efficiently the target (plasma) many intense pulses need to be absorbed in the corona for a ‘long’ time ns. Laser Laser Laser How intense canthe laser pulses be?

  30. GOAL : absorbethelaser in the ‚absorptionzone‘. Limitationsaregivenbylaserpropagation in thelong-scaleunderdenseplasma Problem: parametricinstabilityactivityin theplasmacorona Froula et al. PPCF 54124016 (2012) Toavoid all thiskeepintensity `low` Ioλo2≈ 1013-14 Wμm2/cm2

  31.  Ofinterestfor a newfusionschemecalled ‚shockignition‘ ParametricInstabilitiesfor high laserintensity • High laserintensities but onlyforsome 10s ps: • Ioλo2≈ 1015...16 Wμm2/cm2 • longunderdenseplasmas: mm-scale • high temperatures: fewkeV •  stronglynonlinearprocesses (kinetics !) • an intricateinterplayofparametricinstabilities • SRS, SBS, LDI, TPD, filamentation& cavitation • a bigissue: hotelectronscreation

  32. Propagation ofthelaserstronglyaffectedbecauseofparametricinstabilities • Depending on Tedifferent instabilitiesruntheshow, strong backscattering • Goodchoiceofparameters: creationofhot, not toohoteIectron, efficentlaserabsorption A bigkineticsimulationfor Laser Plasma Interaction Laser intensity Laser intensity Density laser Laser depletion Initially, backscattered Randon Phase Plate effect, bettertransmission Cavitation • Significantabsorptionandhotelectronscreation BEFORE theabsorptionzone • CONCLUSION: PI areveryimportantfor ICF/SI, • need a verygoodunderstanding

  33. 2. Example Plasma Optics –Plasma Amplification

  34.  sinceinventionoflaser: constantpush towards increasingfocusedintensity ofthe light pulses High-intensity laser in time and space UHI light infrastructures in theworld from ICUIL 2011

  35. Chirped pulse amplification D. Strickland, G. Mourou, OpticsComm. 55, 219 (1985) G.A. Mourou et al., Phys. Today 51, 22 (1998) ⇒ ionisation intensity-limit: I ≤ 1012 W/cm2 ⇒ damage threshold of gratings: ≤ 1 J/cm2 ⇒ 1 EW & 10 fs → 10 kJ →surfaceareas of order 104 cm2 = 1m x 1m ⇒ difficult to produce and veryexpensive Laser-induceddamageofopticalcoatings The problem of damagethreshold for opticalmaterials  PLASMA OPTICS -> focus on plasmabasedlaseramplification

  36. ”NO” damagethresholdin plasmas high-energy long pump  low-intensityshortseed Standard parametricinstabilities : 3 wavecouplingwherethe plasmaresponseistakenupby • electronplasmawave −→ Raman • ion-acousticwave −→ Brillouin conservationequations • ωpump = ωseed+ ωplasma • kpump= kseed + kplasma time scales • Brillouinτs ≥ ωcs-1 ∼ 1 − 10 ps • Ramanτs ≥ ωpe−1 ∼ 5 − 10 fs pump   seed The basicprinciple of plasmaamplification interaction  amplifiedseed depleted pump  Raman allowshigherintensitysince contraction to shorterscales

  37. in contrasttobefore: sc-SBS isa non-resonant mode(not an eigen-mode) • Whenthelaserintensityisabove a tresholdthatdepends on theplasmatemperature, transitionfrom eigen-mode regime  quasi-mode regimecharacterizedby: • ωsc = (1 + i √3) 3.6 x 10-2 (I14 λ2o )1/3 (Zme/mi)1/3 (ne/nc)1/3 • i.e. pump wave (laser) determinesthepropertiesoftheelectrostaticwave ! • instabilitygrowth rate: γsc = Im(ωsc) • New characteristic time scalefor IAW: ~ 1/γsc  canbe a few 10s offs !! • More compression = higherintensity, andsomeadvantageswithrespectto Raman Brillouin in the strong-couplingregime (sc-SBS)

  38. amplificationprocesshastobeoptimised in concurrencewithotherplasmainstabilities! 1) avoidfilamentationfor pump andseed: τp,s/(1/γfil) < 1with γfil/ωo≈ 10-5 I14 λ2[μm](ne/nc) → upperlimitforτp & plasmaamplifierlength; Competing instabilities τpump = 300 fs ok forinstability But not muchenergytransfert τpump = O(10ps) toolongforthegivendensity

  39. 2) avoidSRS ifpossible:τp/(1/γsrs) < 1 with γsrs/ωo ≈ 4.3 x 10−3 √(I14 λ2[μm]) (ne/nc)1/4 • → 1/γsrs ≈ 25 fs !! • BUT canbecontrolledbyplasmaprofileandtemperature, associatedenergylossessmall • Other limitrelatedtoefficencyofenergytransfer: (1/γsc) ∼ τwb→ amax = vosc/c ≈ √(mi/Zme) (ne/nc) • → for ne = 0.05 nc get Imax ≈ 1018W/cm2 Competing instabilities cont’d • Fromtheseconsiderationoneobtains a parameterspaceofoperation • Optimizationisrequiredwrttoplasmaprofile, seedduration, pump intensities • Requires extensive 2D kineticsimulationwork

  40. Video on 1D* plasmaamplificationusing a PIC code * 1D simulation fullyreliable, once transverse filamentationinstabilityiscontrolled

  41. Ep = 2 J, Ip = 6.5 x 1016W/cm2 • τp = 3.5 ps • Es = 15mJ, Is = 5 x 1015W/cm2 • τs = 400 fs • pump & seed cross under angle • interactionlength: ≈ 100 μm • energyuptake of seed 45 mJ • amplification factor of 35 • (Is/Is0) achieved • pump depletionachieved ! • (100% on trajectory) • crossedpolarization ⇒ NO • amplification Experimental proof  L. Lancia et al. PRL (2010, 2016)

  42. Recordenergytransferbyscan in seedintensity Experimentconfirmed by theory and 3D simulations : optimum intensity Is ~ few % Ip • System enters more quicklyinto efficient self-similarregime • Favorspumpdepletionform the beginning : 2 Jenergy exchange and highestintensity gain.  J.R. Marquèset al. PRX (2019)

  43. 2D PIC simulationofamplificationover a large focalspot Possibility of quasi-relativisticintensity over large focal spot ( ~100 microns)!

  44. Tofocustheamplified pulse plasmaoptics • focusingplasmamirror Plasma focusingmirror– plasmalens Nakatsutsumi 2010 • plasmalensbased on relativisticself-focusing: • anothercontrolledinstabilityusage • 10PW focusing: • combiningconventionalmirror • plasmamirrorin 2-stage process Bin 2014

  45. Plasma amplification: a longterm perspective       The futureof UHI light pulse generation ?!

  46. Conclusion/outlook

  47. Conclusions Plasma physicsand LPI : many open questions/problems, theyareanything but simple research ! There is a multitude of researchtopics in thefield; onlytwowerepresented. Important also macroscopiceffectse.g. nonlocaltransport, whichisbigchapteroflaser-plasma interaction. LPI for high intensities also farfromunderstood Experiment andtheory/simulation will havetogohand in hand !!

  48. Thanks/Díky

  49. analysisofsingle hot-spot forstandard ICF conditions • in sc-regime reflectivitycanexhibit large oscillations (pulsationregime), whichcan • berelatedtocavitationandsolitonformation •  backscatteredBrillouinpulsesarestronglyamplified in an uncontrolledway Relation to ICF  Idea: makethetransition from randomprocessestocontrolledenvironment

  50. Manypossiblecouplingprocesses  3-wave resonant decayprocesses in laser-plasma interaction emw emw + epw (stimulated Raman scattering, SRS) emw emw + iaw(stimulatedBrillouinscattering, SBS) emw epw + epw (two-plasmon decayinstability, TPD) epw  epw + iaw(Langmuir decayinstability, LDI) emw epw + iaw (parametricdecayinstability) epw  emw + iaw (electromagneticdecayinstability) iaw  iaw + iaw (twoionwavedecay) TPD • othernonlinearprocesses: filamentation, self-focusing, modulationalinstability etc. etc.

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