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Growth, Saturation, and Energetic Electron Generation in Two-Plasmon Decay Instabilities in Direct-Drive Inertial Confinement Fusion University of Rochester1

Inertial Confinement Fusion (ICF) aims to make fusion a clean and unlimited energy sourceLaser heating pellet surfacerocket liftoff of ablator -> inward shock waveA hot spot is created in the dense core and reaction starts~1 mm The National Ignition Facility (NIF) is aiming to achieve ignition within this year

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Current ICF schemes1-stepDirect-drive compressionIndirect-drive compressionMulti-stepFast ignitionChanneling (underdense) and/or hole boring (overdense)Cone Shock ignitionhttp://www.lle.rochester.edu

1. R. Betti et al.,Phys. Rev. Lett., 98, 155001 (2007)A shock ignition pulse13The two-plasmon-decay (TPD) instability is a laser-plasma-interaction (LPI) process in underdense plasmaThe matching conditionk0=k1+k20=p1+p2Since p1,p2 are close to pe, TPD can only take place at n~1/4 ncr.LaserPlasma wave 1Plasma wave 2

*Simon et al., Phys. Fluids 26, 3107 (1983)4Effective compression of ICF targets requires fuel shells in low adiabatic states during implosion.

Energetic (hot) electrons generated from laser-plasma interactions can preheat the shell and degrade the implosion

The two-plasmon decay instability is a significant concern as a hot electron source.

Two-plasmon decay (TPD) is a potential danger for direct drive ICF5Linear regimeQuasi-steady stateOutline6Long-time-scale PIC simulations with OSIRIS1 have been performed for a range of parameterslaserxy00

Plane wave and Gaussian beams are used with the peak intensity range: 6e14-2e15W/cm2The simulation box is transversely periodic and thermal bath is applied at longitudinal boundaries.Diagnostics on the thermal-bath boundaries record the energy loss through the boundaries and the distribution of electrons having reached the boundaries.1, R. A. Fonseca, L. O. Silva, F. S. Tsung et al., Lect Notes Comput Sc 2331, 342 (2002)Simulation configuration for OMEGA parameters7A linear fluid code has been developed to study the linear regime of TPD

The fluid code solves the linear equations:8Linear regimeThresholdGrowth rateConvective gain L=150m, T=2keV, I=1e15 W/cm2 Mi/me=3410 (OMEGA relevant parameters)9

A broad spectrum of plasma waves is observed in PIC simulations

The reduction of the PIC growth rate in the low k region is due to pump depletion.The spatial location where the high k modes grow is in agreement with the homogeneous theory.

1, A. Simon, R. W. Short, E. A. Williams, and T. Dewandre, Phys.Fluids, 26, 3107 (1983)2, B. B. Afeyan, E. A. Williams, Phys. Plasmas 4, 3827 (1997)10Fluid simulations are used to determine the nature of those high k modes

A similar spectrum to the PIC simulations was observed in the fluid simulations

FluidPIC11High k modes can be identified as convective modes by fluid simulationsAbsolute modes can grow exponentially without limit in a linear system.Convective modes can only grow exponentially at early time and then saturate (separate).

12The convective gains observed in the fluid simulations are in agreement with the three-wave theory resultsThe TPD equations can be cast into the standard 3-wave form.1

The order and trend of convective modes amplification can be estimated by e .

The convective gain isnt sensitive to k. This explains the broad spectrum in PIC simulations

1, M. N. Rosenbluth, R. B. White, and C. S. Liu, Phys. Rev. Lett., 31, 1190 (1973)

Amplification ~ exp[]13The high k modes are energetically important in both linear and non-linear stages in the large-L PIC simulation

The linear growth of TPD is interrupted by ion density fluctuationsThe convective modes are saturated before reaching the convective gain because the initial noise has only been amplified by ~30 in amplitude

Initial noise level X10014

The convective modes are relatively more important in higher cases

E1

E1

I=1e15 W/cm2 ,L=150m, T=2keV =3 I=8e14 W/cm2 ,L=150m, T=3keV =1.6Quasi-steady stateEnergetic electron generationCollision and speckle effects16Net particle energy flux reaches a quasi-steady state after ~5psIn the quasi-steady state, Absorbed laser energy is balanced by the energy flux exiting the boxThe particle and field energies in the simulation box are essentially constantt (ps)Net particle energy fluxEnergy flux/Laser flux17

Most hot electrons are produced in the nonlinear stage L=150mTe=3keVI=6X1014W/cm2

Electron >50keV distribution in px-py spacelinearsaturationquasi-steady statePy(mec)Px(mec)Px(mec)18The net energy flux exiting the right boundary includes significant contribution from the hot electrons Energy flux/Laser fluxNormalized instant net e- energy flux at t=9.9psElectron Energy19Electrons trapped in a plasma wave

e-e-Phase velocityElectrons could be trapped in a plasma wave if their velocities are close to the phase velocity

20It is difficult to accelerate thermal electrons in a high-phase-velocity plasma wave Only the electrons with velocities close to Vph can be coupled by the plasma wave

These electrons are located at the tail of distribution function and the amount is small

fv

Electron distribution21The hot electrons are generated through staged acceleration initiated by new TPD modes with low phase velocity in the nonlinear stage

Ex in kx-x space (A. U.)e-(>50keV) phase spaceforward

critical surface22

Ion density fluctuations are driven by plasma waves propagating to lower density regionsThe region of ion density fluctuations is spreading at the group velocity of plasma waves with the largest k.

Ion fluctuations at the low density region can induce new TPD modes locally.Vg=0.013c

n0 (nc)t (ps)Ex energy (A. U.)t (ps)Density fluctuationn (nc)23Fluid simulations are performed to study the new modes in the nonlinear stage

The fluid code solves the linear TPD equations

The density fluctuation is modeled by a static n = n0(x) + nFluid simulations produce modes similar to PIC simulationsThe background density profile is read from OSIRIS simulation results

The spectrum obtained in the fluid simulation is similar to that from the PIC simulation

The differences in the relative amplitudes may be due to e- acceleration.FluidPIC

25I14maxT(keV)/Ti(keV)L*Total Abs.Hot (>50kev) electrons33/1.51500.6~0~063/1.51501.242%17%83/1.51501.452%24%6 (collisional)3/1.51501.233%5.5%

*Simon et al., Phys. Fluids 26, 3107 (1983)Electron-ion collision significantly reduces hot electron production in PIC simulations

Using high-Z materials as the ablator can increasethe e-i collision and reduce the hot e- productionLaser speckle can also reduce the hot electron generationIn experiments, polarization smoothing changes laser polarization even within a single speckle, which can reduce the region for electron accelerationSimulation with a narrow beam has shown a reduced hot electron generation

I14maxT(keV)/Ti(keV)L*Total Abs.Hot (>50kev) electrons63/1.51501.242%17%8 (W=4m)3/1.51501.422%5%Broad spectra of plasma waves are observed in PIC and fluid simulationsThe high- k modes are identified as convective modes by fluid simulations. They can become energetically dominant and cause pump depletion in high casesA convective gain formula retaining the dependence on Te and k is obtainedIn PIC simulations, significant laser absorption and hot electron generation occur in the nonlinear stageGeneration of hot electrons is correlated with new TPD modes correlated with ion density fluctuations in the lower density region in the nonlinear stageHot electrons are accelerated from the low density region to the high density region through a staged processBoth collision and speckle can reduce the hot electron generation Summary29Chart100.304295970.269397080.24993880.23700830.227208770.218203710.210532230.209530690.211020.213110110.214882160.217864760.220038570.222117860.224518530.227504690.231616510.236444170.242464320.249254530.260192250.272923780.289934650.310644330.341337220.379581390.433840720.509846540.609993390.756273910.945668391.20588471.58062651.94043162.54332963.06950923.65724324.26157044.64611445.20574175.33372445.57667515.71016675.96953676.10477586.37960925.33352845.57680485.71020485.96987466.1043446.37745096.54735446.62478556.91352116.9309027.08239147.30970117.17216227.36280347.46250517.51976697.56177877.68469647.82311237.98631158.11900218.15533098.27415788.35967018.48895768.55236288.62576188.61839558.87103988.85735178.98586218.89833948.85562468.87883248.94818398.89215049.02776459.05942938.95413688.90024538.9341778.75564768.93419498.75528658.90752398.67971058.7076088.78102388.68095618.77464468.70250838.83888619.03048248.79218778.84292948.99297378.7478618.66387788.68110188.66144938.68471098.70576748.54357448.5323428.52621468.62537528.54956298.43518658.39648938.46466118.47468588.40031398.32686698.28524788.42432398.33403348.21578848.40846138.40369148.4495198.53704668.45867338.50137378.43158158.48811998.581938.52854968.49746528.50752338.44424918.38894718.45690918.49467768.41492678.34283148.37148868.29963968.35857478.17464948.17230438.22499588.19121658.4947368.41461158.34416228.36897028.29536728.35609598.16757998.16116238.22575968.19490448.35320778.34055918.34645278.42990028.51553818.41681258.46035328.45513578.55340078.44698548.30323148.33214988.37871888.40224758.44429828.2436758.29581998.33016258.33106488.3325128.17085458.3814948.22122478.2501798.34600678.17102238.38219428.22146448.25108858.346798.34416678.34121538.2774718.25433318.3961858.3590538.35849948.34936428.31817738.25825068.22081838.23941558.32761278.45718388.38041078.2365878.43920978.31831028.3720548.41264898.39255948.46691318.46983318.56576928.50670148.52034168.45500728.4859188.48296288.44397398.52828748.48688.47708718.4342926

E1time(ps)Ex energy(Arb. Unit)

fld_eneIterTimeB1B2B3E1E2E3Time in psE100000000002000282.89.59E-039.12E-030.803828470.304295971.15151916.14E-030.05004512560.304295974000565.69.26E-038.38E-032.90002150.269397083.88391854.64E-030.10009025110.269397086000848.48.91E-037.69E-034.93707860.24993886.61498063.25E-030.15013537670.249938880001131.28.70E-037.50E-036.01477990.23700838.21794132.61E-030.20018050220.23700831000014148.50E-037.41E-035.89567420.227208778.41701532.28E-030.25022562780.22720877120001696.88.37E-037.37E-035.70952960.218203718.69545662.07E-030.30027075330.21820371140001979.68.32E-037.38E-035.58580320.210532238.87156041.90E-030.35031587890.21053223160002262.48.30E-037.41E-035.52063930.209530698.95488581.77E-030.40036100440.20953069180002545.28.24E-037.38E-035.4537830.211029.03928671.67E-030.450406130.211022000028288.18E-037.38E-035.38092220.213110119.12885731.57E-030.50045125560.21311011220003110.88.23E-037.43E-035.30516060.214882169.21313651.49E-030.55049638110.21488216240003393.68.15E-037.39E-035.23985260.217864769.28928841.43E-030.60054150670.21786476260003676.48.18E-037.42E-035.19002160.220038579.35279561.37E-030.65058663220.22003857280003959.28.13E-037.48E-035.14948920.222117869.40327151.33E-030.70063175780.222117863000042428.17E-037.46E-035.12196330.224518539.43554711.29E-030.75067688330.22451853320004524.88.07E-037.39E-035.10881240.227504699.44845181.25E-030.80072200890.22750469340004807.68.09E-037.45E-035.1024470.231616519.44805221.22E-030.85076713440.23161651360005090.48.06E-037.43E-035.10696530.236444179.43757731.20E-030.900812260.23644417380005373.28.04E-037.42E-035.11505360.242464329.41831231.17E-030.95085738550.242464324000056568.04E-037.44E-035.13713070.249254539.38550161.15E-031.00090251110.24925453420005938.88.07E-037.47E-035.17441180.260192259.32977691.13E-031.05094763670.26019225440006221.68.01E-037.44E-035.22246670.272923789.25816331.11E-031.10099276220.27292378460006504.48.01E-037.47E-035.27701270.289934659.17595551.11E-031.15103788780.28993465480006787.28.03E-037.41E-035.33128820.310644339.09287871.10E-031.20108301330.310644335000070708.02E-037.41E-035.38949540.341337229.0015821.09E-031.25112813890.34133722520007352.88.06E-037.51E-035.4526410.379581398.90472551.08E-031.30117326440.37958139540007635.68.01E-037.44E-035.51368720.433840728.78692621.08E-031.351218390.43384072560007918.48.04E-037.46E-035.57109830.509846548.68447921.08E-031.40126351550.50984654580008201.27.96E-037.42E-035.62264680.609993398.55557781.08E-031.45130864110.609993396000084847.98E-037.51E-035.65857390.756273918.4390441.07E-031.50135376670.75627391620008766.88.04E-037.50E-035.6689180.945668398.31573621.07E-031.55139889220.94566839640009049.67.96E-037.49E-035.63840471.20588478.23181871.07E-031.60144401781.2058847660009332.47.98E-037.50E-035.58156031.58062658.2167341.06E-031.65148914331.5806265680009615.27.98E-037.49E-035.49777371.94043168.19203421.08E-031.70153426891.94043167000098987.99E-037.48E-035.39851772.54332968.31686931.07E-031.75157939442.54332967200010180.87.95E-037.50E-035.3063153.06950928.48665141.09E-031.801624523.06950927400010463.67.96E-037.50E-035.27500013.65724328.80645741.10E-031.85166964553.65724327600010746.47.95E-037.49E-035.32345344.26157049.26543361.11E-031.90171477114.26157047800011029.27.99E-037.48E-035.49825814.64611449.57812981.14E-031.95175989674.646114480000113127.93E-037.48E-035.74326735.205741710.0769391.16E-032.00180502225.20574178200011594.87.95E-037.51E-035.87538075.333724410.3442461.20E-032.05185014785.33372448400011877.67.94E-037.52E-035.94636565.576675110.6491851.22E-032.10189527335.57667518600012160.47.91E-037.48E-035.96274075.710166710.5625571.21E-032.15194039895.71016678800012443.27.92E-037.51E-035.95932235.969536710.3840911.24E-032.20198552445.969536790000127268.00E-037.60E-035.900026.104775810.4143081.25E-032.252030656.10477589200013008.87.97E-037.55E-035.944186.379609210.4553021.25E-032.30207577556.37960928200011594.87.94E-037.51E-035.87503145.333528410.3440941.20E-032.05185014785.33352848400011877.67.96E-037.55E-035.94718655.576804810.6493491.21E-032.10189527335.57680488600012160.47.98E-037.49E-035.96349075.710204810.5617791.21E-032.15194039895.71020488800012443.27.97E-037.53E-035.95982185.969874610.3833671.24E-032.20198552445.969874690000127268.01E-037.54E-035.90222856.10434410.4141061.25E-032.252030656.1043449200013008.87.95E-037.54E-035.93963636.377450910.4546921.25E-032.30207577556.37745099400013291.67.92E-037.56E-035.87056446.547354410.7200581.28E-032.35212090116.54735449600013574.47.95E-037.53E-035.80541766.624785510.7985581.28E-032.40216602676.62478559800013857.27.95E-037.55E-035.77490386.913521110.8644231.31E-032.45221115226.9135211100000141407.98E-037.54E-035.73455186.93090210.981031.32E-032.50225627786.93090210200014422.87.96E-037.53E-035.75962157.082391411.1498621.35E-032.55230140337.082391410400014705.67.94E-037.50E-035.64328767.309701111.2745291.37E-032.60234652897.309701110600014988.47.96E-037.58E-035.50424347.172162211.3854881.37E-032.65239165447.172162210800015271.27.95E-037.50E-035.49163957.362803411.4596911.42E-032.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fld_ene

E1

E1time(ps)Ex energy(Arb. Unit)