Transcript ELECTRON TRANSPORT IN NAIL/WIRE TARGETS

Benchmark Modeling of Electron Beam Transport in Nail and
Wire Experiments Using Three Independent PIC Codes
Mingsheng Wei
Center For Energy Research
University of California, San Diego
RAC
Voss Scientific
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Annual Fusion Science Center Meeting
August 4-5, 2007
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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Collaborators
J. Pasley, T. Ma, J. King, E. Shipton, F.N. Beg
R.B. Stephens
RAC R. Mason
Y. Sentoku
A. Solodov
D.R. Welch
R.R. Freeman, L. Van Woerkom, D. Offerman, K. Highbarger,
R. Weber
D. Hey
Lawrence
Livermore
National
Laboratory
M.H. Key, A.J. MacKinnon,
A. MacPhee, S. Le Pape,
P. Patel, S. Wilks
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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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Electron transport is a key issue for fast ignition
MeV electrons have to propagate through 10’s to 100’s µm to heat the compressed fuel
10nc
1000nc
Fast electrons
40µm
High intensity laser
Guiding cone
500nc
5000nc
100’s µm
High intensity laser
Density gradient in conventional
FI via hole boring
~ 50 µm
Density gradient in cone guided FI
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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
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We need a simple experiment to validate transport codes
Modeling
• Full scale modeling is impossible
• Simulations are descriptive
— hydro code to model the preformed plasma
— hybrid PIC codes to study the electron transport
Simulations
Benchmark simulations against a simple experiment to validate the
algorithms and transport models used in the codes
Experiments
— using simple target geometry
— known laser parameters
— well-characterized preformed plasmas
Experiments
• millimeter scale target
• ps short pulse with ns pedestal
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Benchmark experiments using low mass wire targets
have been performed on the Titan laser at LLNL
Simple Ti wire:
50 µm in diameter
Cu nail target
Head:100 µm diameter
Wire: 20 µm diameter
with 2 µm Ti coating on the surface
to examine surface vs. bulk transport
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Titan Laser parameters:
Energy ~ 130 J
Pulse length ~ 500 fs
Spot size ~ 10 µm
Peak intensity ~ 1020 W/cm2
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
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Typical experimental observations
100 µm
4.5 keV
Ti K emission from the
surface
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Energy concentrated in the
nail head
Limited propagation lengths
along the wire
Long range plasma thermal
emissions from the wire surface
100 µm
8.0 keV
~800um
Cu K emission
from the bulk
Long range surface
heating
1 mm
68 eV XUV
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We aim to accurately model the wire experiments
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That means modeling the experiment as fielded, in addition to
properly simulating the physics:
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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
h2d simulation results
Initial target surface
Critical surface (on
axis)
Ne~1020 cm-3 (on
axis)
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the measured prepulse profile
of the Titan short pulse laser
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
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Three PIC codes used to model the transport experiments
PICLS
2D (Cartesian) EXPLICIT PIC
code
e-PLAS
LSP
2-D (Cartesian) IMPLICIT hybrid
PIC code (use of momentum equ.)
Fully 3D (cylindrical or
Cartesian) IMPLICIT hybrid PIC
code (direct approach)
All kinetic equations
Fluid background electrons, &
ions, kinetic for selected species
(hot electrons)
Full relativistic Coulomb
collision between e-e, e-ion, ionion
Relativistic corrected Spitzer
collision model
Tc threshold 10 eV
Tc initial 100 eV
Conventional laser deposition
package, critical surface can be
tracked
Self consistent model of hot
electron production
Hot electrons produced by
heuristic scaling and excited at
the critical surface
Fluid background electrons, &
ions, kinetic for selected
species (hot electrons and
ions)
Classic Spitzer collision model
TC initial 100 eV
Electrons can either be selfconsistently produced from LPI
or excited from the background
electrons
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Fast electrons are trapped near the interaction region
LSP
0
100
e-PLAS
Z (µm)
200
300
400
laser
0
10
R (µm)
20
30
Initial interface of kinetic
electrons and fluid electrons
trapping
near critical
by intense
B-fields
13.3
hot ephase space
vg/c
R = 1 µm
R = 7.6 µm
R = 25 µm
-13.3
0
X(mm)
300
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Fast electrons have a overall limited propagation length of
~ 100 µm - 200 µm
LSP
e-PLAS
Number density (cm-3)
1023
1022
1021
1020
1019
1018
0
100
200
Z (µm)
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300
400
PICLS
on-axis e- energy density
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 enumber density used in the simulations)
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Long range surface currents and the resultant surface
heating have been observed in simulations
PICLS
LSP
e-PLAS
higher Tc
on surface
100
500
Temperature (eV)
1000
1000
than the inside due to the ohmic heating by the surface
current
Temperature
(eV)
•At a greater distance, the wire surface is heated more
near axis
at surface
100
0
100
200
300
400
Z (µm)
• Pronounced surface heating in PICLS simulations
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Strong electric and magnetic fields are observed
LSP
0 0
Z (µm)
200
400
0
Z (µm)
200
400
10
R (µm)
laser
20
30
40
50
-40
B (MG)
40
-30
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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
B (MG)
30
- 1.5e7 Er (kV/cm) 1.5e7
e-PLAS
BZ contours
-400
BZ (MG)
0
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SUMMARY
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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
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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
 Analyze the simulation results in terms of diagnostics
 Use more accurate EOS models to obtain background temperatures
LSP
(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
200 fs
300fs
400fs
10-5
Numbers (a.u.)
10-6
10-7
10-8
10-9
0
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2
3
Kinetic Energy (MeV)
4
5
>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
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Integrated LSP simulation setup
th
#5 18th Sept
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#3 18 Sept
E-M wave is launched from
0ns the boundary
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Energetic electrons are self-consistently
produced from laser plasma interaction (LPI) E-M wave from
boundary
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Solid wire targets are treated as fluid
background.
3.5ns
and ions
7ns
15 µm thick preformed plasma
(1020 - 51022 cm-3)
PIC (kinetic) electrons and
ions
#5 14th Sept
Ti wire:
z=15, ne=8.451023 cm-3,
initial temperature 100 eV
Simulation box
50 µm
Ipeak ~ 71019 W/cm2
= 0.5 PS (FWHM)
=15 µm
Fluid
electrons
450 µm
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PICLS 2D simulation setup
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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, Cu
ion density=4•1022 1/cm3, e- density=6•1023 1/cm3
wire diameter=20um
preplasma (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
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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 (g = 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
Laser: 81 J, I = 5 1019 W/cm2, gaussian pulse 0.5 ps (fwhm), focal spot size 16.4 µm (fwhm)
Fast Electron Density – Plasma Temperature at 1.5 ps
Cu15+
nail target
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r=0
r=7 µm
Energy concentrated in the
nail head
Surface current and resultant
surface heating
Surface E and B fields
r=10 µm
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