Simulations of Electron Transport Experiments for Fast Ignition using LSP

1
Simulations of Electron Transport Experiments for
Fast Ignition using LSP

• Presented to
• 15th International Symposium on
• Heavy Ion Inertial Fusion
• Princeton University, NJ
• Richard P. J. Town
• AX-Division
• Lawrence Livermore National Laboratory
• June 7, 2004

2
The LSP code has been used to study fast ignition
relevant transport experiments

• A critical issue for Fast Ignition is
  understanding the transport of the ignitor
  electrons to the fuel.
• Experiments have shown a rapid increase in beam
  width followed by reasonable collimation with a
  20 half angle.
• We have used the LSP code to
• generate simulated K? images
• model XUV images and
• model cone focus experiments.
• The LSP code has been used to study the effect on
  beam transport of
• non-Spitzer conductivity and
• the initial beam divergence.

3
A critical issue for fast ignition is
understanding the transport of the ignitor
electrons to the fuel
Laser couples efficiently to the core
Laser couples inefficiently to the core
1026cm-3
1.1x1021cm-3
This is a major driver on the short-pulse laser
specification.
4
The XUV image can be used to estimate the
temperature of the rear surface

• A series of LASNEX calculations of isochorically
  heated Al targets establishes the relationship
  between temperature and intensity.

XUV image
5
Stephens et al.1 used a Bragg crystal mirror to
image a Cu fluor layer embedded in Al with a CCD
camera

• Fast electron transport is diagnosed by burying a
  layer of of high-Z (e.g., Cu or Ti) material
  within a low-Z plasma matrix (e.g., Al or CH).
• Electrons reaching the layer cause K-shell
  ionization and the emitted photons are imaged
  with a camera, thus characterizing energy
  transport within a dense plasma.

1R.B. Stephens, et al, to appear in Phys. Rev. E.
6
Experiments on MeV electron transport have been
performed by researchers around the world
250
200
X-ray (CH)
150
Spot Radius (?m)
100
X-ray (Al)
50
XUV
K? fluorescence
Laser spot
0
200
400
Thickness (?m)

• Experimental data1 show
• a rapid increase in beam size in the first few
  microns and
• a fairly collimated (20º half angle) beam in the
  bulk of the material.

1M. H. Key, et al, 5th Workshop on Fast Ignition
of Fusion Targets (2001).
7
LSP1 is a hybrid particle code used extensively
in the ion beam community

• Performed simulations using 2-D in cylindrical
  (r-z) geometry.
• Employs a direct implicit energy conserving
  electromagnetic algorithm.
• Hybrid fluid-kinetic descriptions for electrons
  with dynamic reallocation.
• Scattering between the beam and background plasma
  included.
• Ionization and excitation ignored.
• LSP has been coupled to ITS to enable the
  generation of Ka images to enable direct
  comparison with experimental data.
• Beam created by injection at the target boundary
  or by promotion within the plasma.

1D. R. Welch, et al, Nucl. Inst. Meth. Phys. Res.
A464, 134 (2001).
8
We have performed simulations of generic electron
transport experiments

• The targets are based on the experiments
  performed by Martinolli et al1 on the LULI and
  Vulcan laser.
• The big uncertainty is the initial hot electron
  beam parameters.

1E. Martinolli, et al., Laser Part. Beams 20,
171 (2002).
9
A significant halo surrounds the short-pulse
high intensity spot

• Typical data from Nova Petawatt laser shows about
  30 to 40 of the laser energy in the central
  spot.

• We have approximated the laser intensity pattern
  as two Gaussians.

10
Determining the input electron distribution is
based on experimental measurements

• The conversion efficiency into hot electrons has
  been measured by many experimentalists over a
  wide range of intensities

? 0.000175 I(W/cm2)0.2661
11
There are two well-known scaling laws for hot
electron temperature which we have used

• Pondermotive scaling
• Thot(MeV) (Il2/(1019W/cm2mm2))1/2
• Beg scaling
• Thot(MeV) 0.1(Il2/(1017W/cm2mm2))1/3

Pondermotive
Beg
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The current density and energy distribution can
now be defined in terms of laser intensity

• Using the new Python front end to LSP the
  injected beam energy and current density can be
  calculated from
• conversion efficiency and
• hot temperature scaling law.
• A thermal spread is also added.

Beg
rold 0.0 for i in range(400) r
(i0.5)0.00002 intensity Gaussian(r,
1.0e-3, 1.0e20, 0.0, 1.0e12)
Gaussian(r, 1.0e-2, 1.0e17, 0.0, 1.0e12) if
intensity gt 0.0 thot BegScaling(
intensity ) ehot 1.6022e-16thot
area pi(r2-rold2) lpower
intensityarea epower
lpowerconversionEfficiency(intensity)
Density 1.6022e-19epower/(areaehot) rold
r
Pondermotive
13
The LSP code uses Spitzer conductivity, which we
know is not valid at low temperatures.

• The calculated resistivity of aluminum at solid
  density increases with temperature.

10-5
Spitzer
Non-Spitzer
10-6
Resistivity (?m)
10-7
10-8
10-1
100
101
102
103
Temperature (eV)
14
Reduced filamentation is observed when the
conductivity is constant to 100eV

• Beam density at 1.6 ps

15
The Ka diagnostic gives time-integrated images of
the emission generated by the hot electron beam

• The diagnostic will record both Ka photons
  generated by the forward going and backward going
  refluxed electrons.

16
K? images were generated at various times
throughout the simulations

• A time history displaying the birth positions of
  the K? photons can be generated for each source.

Photons created ? 0.5ps
? 1.5ps
? 3.0ps
Y (mm)
Y (mm)
Y (mm)
R (microns)
X (mm)
X (mm)
X (mm)
Base source case Beg Temperature Scaling,
200keV transverse thermal energy
The time integrated diagnostic is a good measure
of hot electron beam transport.
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LSP calculations show reasonable agreement with
experimental data for moderate Al thicknesses

• There appears to be moderate agreement in the
  trend of increasing spot diameter with Al
  thickness, based on the average between vertical
  and horizontal line-outs.
• The large asymmetry in the horizontal direction
  is under investigation.

Experimental Data

• LSP calculations

Spot Diameter (?m)
Al Thickness (?m)
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We can also compare these source scenarios using
the K? spot diameter at half-max intensity

• A significant asymmetry was detected when taking
  similar line-outs in the horizontal direction,
  resulting in the relatively large error in spot
  diameter for many of the data points.

140 120 100 80 60 40 20 0
140 120 100 80 60 40 20 0
Spot Diameter (mm)
Spot Diameter (microns)
(I?2)1/3
(I?2)3/2
(I?2)1/2
2D Source Injection
0 100 200 300 400 500 600
Thermal transverse temperature (keV)
19
The LSP calculation matches the measured
temperature pattern at the rear surface of the
target

• 27J of hot electrons, in a 1-ps pulse, with Beg
  scaling and a thermal spread of 300keV injected
  into a 100mm Al3 plasma.
• The temperature was obtained by post-processing
  the LSP energy data at the rear surface with a
  realistic equation of state.

20
Z3 is being used to generate hot electrons from
LASNEX-predicted pre-pulse plasmas

• 1-D line out of plasma formed by 10mJ prepulse on
  a CH target
• (z,x) plots of electrons with energies gt 12 MeV

0.5 ps
1.0 ps
UCRL-PRES-204413-20
21
Extracting the correct electron distribution
function is more complicated for oblique incidence

• A 1019 W/cm2 laser incident on a 16 nc plasma
  (shown by white lines) at a 30o angle of
  incidence.
• (z,x) phase space plot of electrons with
  energies gt 5 MeV.

Electrons injected at a significant angle
0.3 ps
0.6 ps
We are using Python to closely couple Z3 output
to LSP input
0.5 ps
0.3 ps
22
We have recently started large scale cone
calculations using LSP

• Background electron density profile of a gold
  cone touching a perfect conductor.

2MeV electrons promoted along surface
23
Hot electrons start on inner edge and then
diffuse into the cone
0.16 ps
1.4 ps
Transport efficiency lt20 of hot electron out of
cone
24
The LSP code has been used to study fast ignition
relevant transport experiments

• A critical issue for Fast Ignition is
  understanding the transport of the ignitor
  electrons to the fuel.
• Experiments have shown a rapid increase in beam
  width followed by reasonable collimation with a
  20 half angle.
• We have used the LSP code to
• generate simulated K? images
• model XUV images and
• model cone focus experiments.
• The LSP code has been used to study the effect on
  beam transport of
• non-Spitzer conductivity and
• the initial beam divergence.

25
Collaborators

• C. Chen, L. A. Cottrill, M. H. Key, W. L. Kruer,
  A. B. Langdon,
• B. F. Lasinski, B. C. McCandless, R. A. Snavely,
  C. H. Still,
• M. Tabak, S. C. Wilks,
• LLNL, Livermore, CA, USA.
• D. R. Welch,
• MRC, Albuquerque, NM, USA.