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Isolated Target

laser. X2. X1. Isolated Target. Isolated boundaries- we believe this is essential 100 n c Plasma 20 m radius resistive core particle drag Force = -k p  -2 passes low and high energy particles (<50KeV, >10MeV) Box size 150  x130  5x10 8 cell Grid size: 0.05 c/ 0 , 0.5 c/  p

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Isolated Target

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  1. laser X2 X1 Isolated Target • Isolated boundaries- we believe this is essential • 100 nc Plasma • 20 m radius resistive core • particle drag Force = -k p -2 • passes low and high energy particles (<50KeV, >10MeV) • Box size 150  x130  • 5x108 cell • Grid size: 0.05 c/0 , 0.5 c/ p • 4 electrons per cell, 109 particles • Te = 1.0 keV, mI= 3672me • Duration 2.5ps + • 9104 time steps • 1 - 2 months real time • 1-laser, W0 = 20  • Spot size matches core 41µ 20µ 51µ 130µ 44m 0.8m 150µ Flux diagnostic planes

  2. Magnetic Filamentation and Hot Region • Hot spot and magnetic filamentation are spatially correlated. • Weibel instability relaxes anisotropic particle distributions as well as filamenting currents. • Magnetic fields reach over 100MG for high laser intensity runs - channeling usable 2 MeV energy electrons in x1 direction. 8x1020 W/cm2 @ 1 ps

  3. Plasma Modifies Energy Spectrum of Electrons Carrying Energy Forward 4 10 5 0 laser 2 AU MeV 0 Sampled Region -2 32 95 127 X1 m Core Edge Peak energy reduction Shock Front Energy Flux Density (net) 2226 ps, 2x1020 W/cm2

  4. Does Ponderomotive Scaling Work at Higher Intensity? Ponderomotive hot = mec2(sqrt(1+I2/1.37x1018)-1) Hot electron scaling drops to hot/2 at higher intensities Up to 2x predicted Thot - 85% of energy flux is below 2x predicted Thot I=1.25x1019 Thot =1.11MeV I=5x1019 Thot =2.62MeV I=2x1020 Thot =5.68MeV I=8x1020 Thot =11.84MeV

  5. “Temperature” of Electron spectrum softens down stream k skin depth kx2 kx1 E1 k-spectrum 5x1019 W/cm2 at 557 fs Enhanced electric field fluctuations at skin depth

  6. Well Defined Simulations of Hot Tail 10 -10 20 MeV Initial P1 vs P2 (log) F(Electron Energy) Periodic Spectral Simulation (Parsec). Energy and Momentum conserved. Initialized with no net current.

  7. High Intensity Laser DeliversPower to Core more Efficiently ~ 50x Scaled To Laser Intensity ~ 10x Laser Intensity 8x1020 W/cm2 2x1020 W/cm2 5x1019 W/cm2 8x1020 W/cm2 laser delivers: 5x the Power of 2x1020 W/cm2 laser 50x the Power of 5x1019 W/cm2 laser

  8. Laser Self Focusing Speeds Hole Boring Whole boring Distance* for Initial Density Profile I=2x1020 W/cm2 Electron Density • Isolated transverse boundaries • Thermal boundary at back of target • Exponential density profile: max 20 nc • Target size 85  x 85  • Grid size: 0.05 c/0 • 4 electrons per cell • Te = 0.1keV, mI= 3672me • 1-laser, W0 = 5  I=6x1020 W/cm2 Pointing flux *Calculated Wilks, prl, 92

  9. PIC Simulation of Electron Transport In Fast Ignition Targetswith Ultra-High Intensity Ignition Laser J. Tonge, J. May, F.S. Tsung, W. B. Mori C. Ren* F. Fíuza, M. Marti**, L. Silva** UCLA, *Rochester,**Insituto Superior Técnico Anomalous Absorption 0608 Williamsburg, VA

  10. Coherent waves are weakly damped with /k near c tail notail kx=.93 c/p vphase= .86c = .8 p p=100 53 pe-1 k skin depth Periodic Spectral Run

  11. Shocks Accelerate return current in Fast Ignition (Isolated Target) Simulations Return current does not have enough energy to traverse magnetic field. Electric Field Builds Return current electrons accelerate and filament moving magnetic field (and shock) forward. Electric Field Magnetic Field

  12. Summary • Power Delivered Target Core • Higher intensity laser are more efficient for energy transport. • Higher intensity delivers much more energy density • Electron Energy Transport • Most (80-90%) of the energy is transported in the hot bulk • Enhanced Fluctuations • Turbulent electric field causes relaxation of energetic tail electrons • Electromagnetic Shock • Energy of energy flux spectrum is reduced at shock • Ponderomotive Scaling • At higher intensity (>=5x1019W/cm2) Thot is 50% predicted below 2x predicted Thot • 85% of energy flux is below 2x predicted Thot (p-polarized 2D)

  13. How Does Laser Accelerate Electrons?Poster Tonight: Josh May Electrons are pulled out into vacuum and accelerated by lasers electric field and rotated back into plasma by lasers magnetic field 30nc, I=5x1019 W/cm2, Plane Wave, ~2 0 target width

  14. Electrons Accelerate in Vacuum

  15. Relativistic Shock Simulation Setup Physical Parameters Laser 50 nc Ignition laser • λ0 = 1μm • I0 = 1.25x1019 - 5x1021 W/cm2 • p-polarization & s-polarization Plasma Numerical Parameters • 60 μm x 17 μm • ne0 = 5x1022 - 1023 cm-3 • mi/me = 3672 (D+) • Ti0 = Te0 = 1 keV • Dx⊥ kp = 0.4 • Dz kp = 0.4 • Particles per cell = 4

  16. Dynamics in Front Surface of Target Filamentation @ target Mass build up/compression & strong electric field t ~ 350 fs Weibel instability Return currents

  17. Relativistic Shock is Launched Ion phase space & electron density Pressure behind front drives shock Ions reflected @ shock front with 2 vsh vsh ~ 0.1 c Plateau in electron density due to reflected ions vhb ~ 0.075 c Relativistic shock is mediated by Weibel driven magnetic fields ≠ high Mach number ion acoustic shocks ≈ relativistic shocks in astrophysics

  18. Outline • Describe Isolated Target • Power Delivered Target Core • Energy Transport in Isolated Target • Energy Transport Across Density Gradient • Enhanced Fluctuations (Turbulence) • Electromagnetic Shock • Ponderomotive Scaling

  19. Can we use higher intensity ignition lasers?How will fast ignition without cone targets work? • Concerns: • If ponderomotive scaling* holds then e- spectrum is too hot. • Electrons are generated too far from core. • Advantages: • Smaller spot sizes & more hole boring • Simplicity of target design • 3 Simulations to examine laser intensity *Wilks et al. prl, aug 92

  20. Net Electron Energy Flux Spectrum Peaks at Low Energy* Through plane 0.8 mm in front of core Intensity 8x1020 W/cm2 2x1020 W/cm2 5x1019 W/cm2 .25 MeV .9 MeV 2.6 MeV *compared to ponderomotive scaling MeV Scaled to laser power @ 2.5 ps

  21. Energy is Transported in Hot Bulk 80% - 90% of NET energy flux laser Peaks at -0.1 mec Sample Region 6 F (log(n)) P2 (mec) -10 0 20 -6 P1 (mec) -6 0 10 Hot Bulk Tail P1 (mec) Distribution at 1.5 ps

  22. Does Peak in net Electron Energy Flux Spectrum move lower at higher density? As energy flux carrying electrons move up the density ramp in a real target return current will be carried by more lower energy electrons. This will “uncover” more of the energy distribution of the forward energy flux causing the peak of the net flux to move lower in energy. Electron Energy Flux SpectrumI = 8x1020 W/cm2 @ 1 ps .8 in front of core

  23. Density Gradient Simulation Shows Lower Peak in Electron Energy Flux Spectrum at Higher Density Flux planes 100 nc 300 nc 800 nc Target Density Profile Energy Flux • Isolated transverse boundaries • Thermal boundary at back of target • Exponential density profile: max 1000 nc • Target size 15  x13  • Grid size: 0.5 c/ p at 1000nc • 4 electrons per cell • Te = 0.1keV, mI= 3672me • 1-laser, W0 = 3  • 27 times the computational cost of isolated target simulation Energy Spectrum of Net Energy Flux at 1ps

  24. Addition of Monte Carlo Collisions Doesn’t Change Results in Density Gradient Simulation No collisions Collisions

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