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Isolated Target

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laser

X2

X1

- 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 +
- 9104 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

- 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

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

Ponderomotive hot = mec2(sqrt(1+I2/1.37x1018)-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

k skin depth

kx2

kx1

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

Enhanced electric field fluctuations at skin depth

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.

~ 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

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

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

tail

notail

kx=.93 c/pvphase= .86c

= .8 p p=100

53 pe-1

k skin depth

Periodic Spectral Run

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

- 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)

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

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

Filamentation @ target

Mass build up/compression & strong electric field

t ~ 350 fs

Weibel

instability

Return currents

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

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

- 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

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

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

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

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

No collisions

Collisions