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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




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








Flux diagnostic planes

Magnetic filamentation and hot region
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

Plasma modifies energy spectrum of electrons carrying energy forward
Plasma Modifies Energy Spectrum of Electrons Carrying Energy Forward










Sampled Region


32 95 127

X1 m

Core Edge

Peak energy


Shock Front

Energy Flux Density (net)

2226 ps, 2x1020 W/cm2

Does ponderomotive scaling work at higher intensity
Does Ponderomotive Scaling Work at Higher Intensity? Forward

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


Thot =1.11MeV


Thot =2.62MeV


Thot =5.68MeV


Thot =11.84MeV

Temperature of electron spectrum softens down stream
“Temperature” of Electron spectrum softens down stream Forward

k skin depth



E1 k-spectrum 5x1019 W/cm2 at 557 fs

Enhanced electric field fluctuations at skin depth

Well defined simulations of hot tail
Well Defined Simulations Forwardof Hot Tail





Initial P1 vs P2 (log)

F(Electron Energy)

Periodic Spectral Simulation (Parsec).

Energy and Momentum conserved.

Initialized with no net current.

High intensity laser delivers power to core more efficiently
High Intensity Laser Delivers ForwardPower to Core more Efficiently

~ 50x


To Laser


~ 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

Laser self focusing speeds hole boring
Laser Self Focusing Speeds Hole Boring Forward

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

Isolated target

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

Coherent waves are weakly damped with k near c
Coherent waves are weakly damped with Targets/k near c



kx=.93 c/p vphase= .86c

= .8 p p=100

53 pe-1

k skin depth

Periodic Spectral Run

Shocks accelerate return current in fast ignition isolated target simulations
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

Summary Target) Simulations

  • 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)

How does laser accelerate electrons poster tonight josh may
How Does Laser Accelerate Electrons? Target) SimulationsPoster 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

Electrons accelerate in vacuum
Electrons Accelerate in Vacuum Target) Simulations

Relativistic shock simulation setup
Relativistic Shock Simulation Setup Target) Simulations

Physical Parameters


50 nc

Ignition laser

  • λ0 = 1μm

  • I0 = 1.25x1019 - 5x1021 W/cm2

  • p-polarization & s-polarization


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

Dynamics in front surface of target
Dynamics in Front Surface of Target Target) Simulations

Filamentation @ target

Mass build up/compression & strong electric field

t ~ 350 fs



Return currents

Relativistic shock is launched
Relativistic Shock is Launched Target) Simulations

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

Outline Target) Simulations

  • Describe Isolated Target

  • Power Delivered Target Core

  • Energy Transport in Isolated Target

  • Energy Transport Across Density Gradient

  • Enhanced Fluctuations (Turbulence)

  • Electromagnetic Shock

  • Ponderomotive Scaling

Can we use higher intensity ignition lasers how will fast ignition without cone targets work
Can we use higher intensity ignition lasers? Target) SimulationsHow 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

Net electron energy flux spectrum peaks at low energy
Net Electron Energy Flux Spectrum Peaks at Low Energy* Target) Simulations

Through plane 0.8 mm in front of core


8x1020 W/cm2

2x1020 W/cm2

5x1019 W/cm2

.25 MeV

.9 MeV

2.6 MeV

*compared to ponderomotive



Scaled to laser power @ 2.5 ps

Energy is transported in hot bulk
Energy is Transported in Hot Bulk Target) Simulations

80% - 90%

of NET energy flux


Peaks at -0.1 mec

Sample Region










P1 (mec)




Hot Bulk


P1 (mec)

Distribution at 1.5 ps

Does peak in net electron energy flux spectrum move lower at higher density
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

Density gradient simulation shows lower peak in electron energy flux spectrum at higher density
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

Addition of monte carlo collisions doesn t change results in density gradient simulation
Addition of Monte Carlo Collisions Doesn’t Change Results in Density Gradient Simulation

No collisions