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Benchmark Modeling of Electron Beam Transport in Nail and Wire Experiments Using Three Independent

PIC Codes

Mingsheng Wei

Annual Fusion Science Center MeetingAugust 4-5, 2007

San Diego

Center For Energy ResearchUniversity of California, San Diego

This work was supported by the US Dept of Energy through various grants from the Office of Fusion Energy

Sciences.

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Voss Scientific

RAC

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Lawrence Livermore National Laboratory

R.R. Freeman, L. Van Woerkom, D. Offerman, K. Highbarger,R. Weber

D. Hey

M.H. Key, A.J. MacKinnon,

A. MacPhee, S. Le Pape,

P. Patel, S. Wilks

R.B. Stephens

J. Pasley, T. Ma, J. King, E. Shipton, F.N. Beg

A. SolodovY. Sentoku

R. MasonRAC

D.R. Welch

Collaborators

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Outline

• Motivation

• Benchmark experiments using novel nail and wire targets

• Codes used

• Simulation results

• Summary and future work

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• Details of transport of fast electrons with huge currents remains uncertain

• Numerical simulations help to understand instabilities, electron beam spreading, energy loss and heating mechanisms etc. in the transport process

10nc 1000nc

High intensity laser

Fast electrons

40µm

100’s µm

Density gradient in conventionalFI via hole boring

Density gradient in cone guided FI

MeV electrons have to propagate through 10’s to 100’s µm to heat the compressed fuel

500nc 5000nc

High intensity laser

~ 50 µm

Guiding cone

Electron transport is a key issue for fast ignition

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• millimeter scale target • ps short pulse with ns pedestal

• Full scale modeling is impossible• Simulations are descriptive

Modeling

Experiments

Benchmark simulations against a simple experiment to validate the algorithms and transport models used in the codes

— using simple target geometry— known laser parameters— well-characterized preformed plasmas

— hydro code to model the preformed plasma— hybrid PIC codes to study the electron transport

We need a simple experiment to validate transport codes

Experiments

Simulations

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Benchmark experiments using low mass wire targets

have been performed on the Titan laser at LLNL

• Wire targets are accessible to various diagnostics

• Targets are small enough to be included in the simulations

• K imagers diagnose the production and transport of the fast electrons

• XUV imagers provide information of target heating

Titan Laser parameters: Energy ~ 130 J Pulse length ~ 500 fs Spot size ~ 10 µm Peak intensity ~ 1020 W/cm2

Simple Ti wire: 50 µm in diameter

Cu nail targetHead:100 µm diameterWire: 20 µm diameterwith 2 µm Ti coating on the surfaceto examine surface vs. bulk transport

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Typical experimental observations

4.5 keV 8.0 keV

100 µm100 µm100 µm100 µm

Ti K emission from the surface

Cu K emission from

the bulkLong range surface heating

68 eV XUV

1 mm

~800um

• Energy concentrated in the nail head

• Limited propagation lengths along the wire

• Long range plasma thermal emissions from the wire surface

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We aim to accurately model the wire experiments

• That means modeling the experiment as fielded, in addition to properly simulating the physics:

- Target geometry- Preformed plasma produced by the nanosecond prepulse- Physically generate current- Direct comparison with the experimental data

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Preformed plasma is modeled by the 2D hydro code h2d

• Laser prepulse creates substantial preformed plasma, i.e., critical surface has moved away from original target surface by ~ 30 µm

• Such preformed plasmas are included in the hybrid simulations

the measured prepulse profile of the Titan short pulse laser

Initial target surface

Critical surface (on axis)

Ne~1020 cm-3 (on axis)

h2d simulation results

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PICLS e-PLAS LSP

2D (Cartesian) EXPLICIT PIC code

All kinetic equations

Full relativistic Coulomb collision between e-e, e-ion, ion-ion

Tc threshold 10 eV

2-D (Cartesian) IMPLICIT hybrid PIC code (use of momentum equ.)

Fluid background electrons, & ions, kinetic for selected species (hot electrons)

Relativistic corrected Spitzer collision model

Tc initial 100 eV

Fully 3D (cylindrical or Cartesian) IMPLICIT hybrid PIC code (direct approach)

Fluid background electrons, & ions, kinetic for selected species (hot electrons and ions)

Classic Spitzer collision model

TC initial 100 eV

Self consistent model of hot electron production

Conventional laser deposition package, critical surface can be tracked

Hot electrons produced by heuristic scaling and excited at the critical surface

Electrons can either be self-consistently produced from LPI or excited from the background electrons

Three PIC codes used to model the transport experiments

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Fast electrons are trapped near the interaction region

R = 1 µm

R = 7.6 µm

R = 25 µm

Initial interface of kinetic electrons and fluid electrons

Z (µm)0 100 200 300 400

0

10

20

30

R (µ

m)

laser

e-PLASLSP

13.3

-13.3

v/c

0 300X(m)

trapping near criticalby intense B-fields hot e-

phase space

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Fast electrons have a overall limited propagation length of

~ 100 µm - 200 µmLSP e-PLAS

PICLS

Nu

mb

er

de

nsi

ty

(cm

-3)

1023

1022

1021

1020

1019

1018

• In both LSP and e-PLAS, nehot drops to

1020cm-3 in a distance of ~ 100 µm

• In PICLS, electron energy density decreases by more than one order of magnitude in about 200 µm (this difference could be due to a lower e-

number density used in the simulations)

0 100 200 300 400Z (µm)

on-axis e- energy density

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Long range surface currents and the resultant surface heating have been observed in simulations

PICLS

100 500 1000Temperature (eV)

1000

100

0 100 200 300 400Z (µm)

Te

mp

era

ture

(e

V)

near axis

at surface

LSP

e-PLAShigher Tc on surface

•At a greater distance, the wire surface is heated more than the inside due to the ohmic heating by the surface current

• Pronounced surface heating in PICLS simulations

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Strong electric and magnetic fields are observed

Z (µm)0 200 400

-30 B (MG) 30

0

10

20

30

40

50

R (

µm

)-40 B (MG) 40

BZ contours BZ (MG)-400 0 400

laser

LSP

e-PLAS

- 1.5e7 Er (kV/cm) 1.5e7

Z (µm)0 200 400

• Surface radial E field : MV/µm

• Surface azimuthal B field: 10’s MG in LSP

100 - 200 MG in e-PLAS

• E&B fields are consistent with surface transport

• Intense azimuthal B field is also produced at the deformed interaction region

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SUMMARY

• Benchmark simulations using implicit/hybrid PIC codes, LSP and e-PLAS as well as the fully PIC code, PICLS, have been performed to study the fast electron beam transport in the nail/wire experiments

• Simulations have shown good qualitative agreement among the codes, which are also in consistent with the experiments: Localized energy deposition due to trapping of the fast electrons by B-fields. Overall propagation length of about 100 µm in the bulk of the target

predominantly due to resistive inhibition and B-field trapping at the interaction region

Long range surface current and surface heating Intense surface E & B fields which guide the surface current

• Quantitative differences are also observed: – Higher degree target heating in PICLS --- a lower density being used – Pronounced surface current (?) in PICLS --- a lower density being used

– e-PLAS predicts extremely high surface B-fields (200 MG) – Low temperature in LSP due to the low laser energy in the input.

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On-going and future work using the LSP code

Calculate K production and transport using the ITS code coupled to LSP

Analyze the simulation results in terms of diagnostics

Use more accurate EOS models to obtain background temperatures (currently, ideal gas model for all three codes,

temperatures over estimated)

Continue the integrated LSP simulations to study short-pulse hot electron driven heating experiments using low-mass targets

Model electron beam transport and target heating in Omega EP FI experiments

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Supplemental slides attached next

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Fast electrons produced in the latest integrated LSP simulations have a two-temperature energy

distribution

• >40% of the laser energy is transferred to the fast electrons

• Average energy in the hot tail is comparable to the ponderomotive energy

• The not-so-hot component fits to an average energy of 0.5 - 1 MeV

10-9

10-8

10-7

10-6

10-5

0 1 2 3 4 5

200 fs300fs400fs

Kinetic Energy (MeV)

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0ns 3.5ns

7ns

#3 18th Sept #5 18th Sept

#5 14th Sept

E-M wave from

boundary

PIC (kinetic) electrons and ions

Fluid electrons

and ions

• E-M wave is launched from the boundary

• Energetic electrons are self-consistently produced from laser plasma

interaction (LPI)

• Solid wire targets are treated as fluid background.

450 µm

50 µm

Ipeak ~ 71019 W/cm2

= 0.5 PS (FWHM)=15 µm

15 µm thick preformed plasma (1020 - 51022 cm-3)

Ti wire:z=15, ne=8.451023 cm-3, initial temperature 100 eV

Simulation box

Integrated LSP simulation setup

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PICLS 2D simulation setup

• Laser (Titan):a=8, I=6.4•1019 W/cm2, pulse length=500 fs (gaussian)spot=20um (gaussian), Energy input=130 J

• Target: nail target, Z=15, Cuion density=4•1022 1/cm3, e- density=6•1023 1/cm3

wire diameter=20umpreplasma (5µm scale length, 1020-22 1/cm3) at top of nail

• System size: 400um x 100um

Ion energy density (n/n0): 1eV-100keV t=1.5ps

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e-PLAS simulation setup

Laser: I=1.7 x 1020 W/cm2, 1 ps pulse (top hat), 10 µm spot Target: copper wire (z=15) preceded with a 20 µm density

ramp; initial temperature 100 eV Electron beam generation: hot electrons are promoted from the critical surface with an isotropic Maxwellian spectrum at ponderomotive energies ( = 10.5) System size: 100 µm by 300 µm

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2D LSP simulations using the excitation model for fast electron generation without the preformed

plasma

Fast Electron Density – Plasma Temperature at 1.5 ps

r=0 r=7 µm r=10 µm

Cu15+ nail target

Laser: 81 J, I = 51019 W/cm2, gaussian pulse 0.5 ps (fwhm), focal spot size 16.4 µm (fwhm)

• Energy concentrated in the nail head

• Surface current and resultant surface heating• Surface E and B fields