mingsheng wei
DESCRIPTION
Benchmark Modeling of Electron Beam Transport in Nail and Wire Experiments Using Three Independent PIC Codes. Center For Energy Research University of California, San Diego. Voss Scientific. RAC. Mingsheng Wei. FSC. Annual Fusion Science Center Meeting August 4-5, 2007 San Diego. - PowerPoint PPT PresentationTRANSCRIPT
1FSC
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.
FSC
Voss Scientific
RAC
2FSC
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
3FSC
Outline
• Motivation
• Benchmark experiments using novel nail and wire targets
• Codes used
• Simulation results
• Summary and future work
4FSC
• 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
5FSC
• 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
6FSC
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
7FSC
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
8FSC
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
9FSC
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
10FSC
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
11FSC
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
12FSC
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
13FSC
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
14FSC
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
15FSC
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.
16FSC
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
17FSC
Supplemental slides attached next
18FSC
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)
19FSC
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
20FSC
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
21FSC
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
22FSC
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