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A Global Simulation for Laser Driven MeV Electrons in Fast Ignition

Chuang RenUniversity of Rochester

in collaboration withM. Tzoufras, J. Tonge, F. Tsung, and W. Mori (UCLA)

FSC Annual MeetingRochester, NY, Jan 26, 2006

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Target Size & Global e- Trajectories Can Affect Hot e- Distribution

• Significant e- refilling is needed to absorb laser energy It = (nE) L– L~190 m for I=1020 w/cm2,

t=1ps, =0.3, E=1 MeV, and n=10nc

• Hot e- distribution will be affected by simulation size and boundary conditions– Limited heat capacity

L

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• Vacuum region between target and boundary

• Initial Te=7.4 keV and Ti=1 keV– 1203212032 grids x=3D =0.33 c/p

– Spline current deposition & smoothing allow simulation of 100 nc-1 keV plasmas

• I=1020-21 w/cm2 (for =1m), spot size (FWHM) 7.5 m, 1 ps long, s- & p-polarized.

• 2.4 108 particles and 6104 steps

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100μm

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40nc

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16μmlaser

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25.5μmcoronal plasma

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Laser-plasma Interface shows complex & dynamic features

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Laser absorption efficiency changes dynamically

• Absorption increases as critical surface ripples.

– Additional heating for p-pol as E·n0

• I=1021W/cm2 produces >10 MeV e-.

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PxPy- phase space of e- in front of laser (t=454fs)

<-1>=1.4, Px/mc=2.9, Py/mc=2.0

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filamentation

• Huge forward current induces plasma return current to avoid Alfven current limit

– Zero net current

• Both forward & return currents filament due to current repulsion/attraction -filaments accompany j-filaments– Unequal Te ->Unequal pinch -> charge

imbalance

• Space charge resists further filamenting

– Single beam cannot filament

• New theory with SC-effects needed for FI

Forward (hot, low n)

Return (cold, high n)

---------++++++---------

---------

---------++++++

++++++

++++++

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The physics can be understood from non-relativistic model

• 3 particle species--- Maxwellian forward & return electrons

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f l 0(v,x) =nl

2π v tylv txlexp(−

vy2

2v tyl2

)exp(−(vx −Vdl )

2

2v txl2

)

--- Cold ion

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f30 = n3δ(vx )δ(vy )--- no net current & charge

• Linear analysis with Vlasov-Maxswell eqs reveals 2 instability regimes– Fast growth (immobile ions, space charges present)

– Slow growth (ions move to neutralize space charges)

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pl2 (Vdl

2 + v txl2 )

v tyl2

> k 2c 2 +ωpe2 + (

ωpl2Vdlv tyl

2)2[k 2 +

ωpl2

v tyl2

l=1

2

∑l=1

2

∑ ]−1

l=1

2

∑

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pl2 (Vdl

2 + v txl2 )

v tyl2

> k 2c 2 +ωpe2 +

l=1

2

∑ ωpi2

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Importance of Space Charges Is Verified by PIC Simulations

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-3 -2 -1 0 1 2 3

-3 -2 -1 0 1 2 3

Electron denstiy

p

681fsec

Ion mode

Stable

• Measured distribution function is divided into many beams

• Marginal instability found in the shock region

– Return current contribution important

• Outside the shock the mode is found stable

– Dilution of current density

Applying the theory to simulations

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Pukhov ‘97

Lack of efficient merging is consistent with large p2-spread

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• We are adding an absorbing region to eliminate recycled hot e- influence

– Adding particle tracking

• We want to know why hot e- spread and find remedy

– Detailing heating mechanisms

• Study channeling in corona

• Study e- transport in higher density region

– Including collisions