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PIC Simulations of Short-Pulse, High-Intensity Light
Impinging on Structured Targets
Presented to:
9th International Fast Ignitor Workshop
Cambridge, Massachusetts
Barbara F. Lasinski, A. Bruce Langdon, C. H. Still,
Max Tabak, and Richard P. J. Town
Lawrence Livermore National Laboratory
November 5, 2006.
This work was performed under the auspices of the U.S. Department of Energy by the University of California
Lawrence Livermore National Laboratory under Contract No. W-7405-Eng-48.
Lawrence Livermore National Laboratory, P.O. Box 808, Livermore, CA 94551-0808
Identifying Marker. 1
PIC simulations of structured targets
have high laser absorption.
• Simple cone target modeling shows
•
•
•
•
light interference within the cone
a wide angular spread of the energetic electrons.
ion motion is important.
beam pointing shifts don’t significantly change these results
• More realistic cone targets have similar properties.
• We find enhanced laser absorption with structured surfaces
•
•
But the challenge is to find a shape which collimates the hot
electrons.
Two-dimensional grooves give higher absorption than threedimensional divots.
FIW/BFL et al. 2
First, we studied simple cone targets to
assess the key physical processes.
• These initial PIC simulations were done in 2D(x,z)
with our massively parallel code Z3.
40
z(mm)
• The cones each have a half-angle of ~13
• For these simulations, ne = 16nc, Te = 10 keV,
Zmi/me = 3600, and ZTe/Ti = 20.
laser
20
• The incident laser propagates along the z-direction.
0
10
20
30
This spatial profile is relatively
constant as the beam propagates.
5mm
20
laser
z(mm)
30
10
0
10
20
x(mm)
• Beam spatial amplitude at the entrance
plane is 1-sin8(x/(2xspot)) where xspot = 6mm.
The beam spot size is larger than the
diameter of the inner wall of the cone.
30
amp
0
x(mm)
• The temporal profile is flat, with a sharp rise to an
intensity of 1019 W/cm2 for 1mm light.
FIW/BFL et al. 3
The incident laser is either pointed down the
center of the cone or is shifted spatially by 3mm
2-D, 1019 W/cm2, 16nc, Te = 10 keV
• In Z3, we apply a low pass temporal filter to fields and fluxes to highlight
the low frequency component. These filtered quantities have the subscript s.
• Plots of the Poynting flux, (Pz)s vs (x,z), at t=0.03 ps showing two problem
initializations with the solid white lines indicating the initial plasma boundary.
Shifted beam
p-polarization
Centered beam
s-polarization
Laser vacuum intensity
on this color map.
z(mm)
z(mm)
• Have laser electric field
in (p), or out (s) of the
simulation plane for all 4
cases.
• At this early time,
there is little reflected
light.
x(mm)
x(mm)
FIW/BFL et al. 4
Find light interference effects as the beam
propagates.
2-D, 1019 W/cm2, 16nc, Te = 10 keV
Shifted beam
p-polarization
t = 0.15 ps
z(mm)
Poynting
flux, (Pz)s,
vs (x,z)
x(mm)
Beam has not yet
reached the cone tip
Laser vacuum
intensity on
this color
map.
z(mm)
Centered beam
s-polarization
t = 0.09 ps.
x(mm)
Significant reflection
FIW/BFL et al. 5
The relativistic critical surface becomes
deformed
2-D, 1019 W/cm2, 16nc, Te = 10 keV
Centered irradiation onto flat inner surface cone; p-polarization; t = 0.38 ps
(Pz)s vs
(x,z)
Laser
vacuum
intensity
on this
color map.
z(mm)
z(mm)
ne vs
(x,z)
ncr
x(mm)
log(ne)
vs (x,z)
z(mm)
ncr
On this log scale, ne ranges from
0.03 to 33. and the change from
red to green is at ne = 1.0
There is ~ 5 mm of plasma at ne ~ 0.3
in the beam path.
x(mm)
FIW/BFL et al. 6
For pointed cones, gouging out of the tip
becomes visible before 0.5 ps
2-D, 1019 W/cm2, 16nc, Te = 10 keV
Centered irradiation onto pointed inner surface cone; p-polarization; t = 0.46 ps
ne vs
(x,z)
(Pz)s vs
(x,z)
z(mm)
z(mm)
Laser vacuum
intensity on this
color map.
ncr
x(mm)
log(ne)
vs (x,z)
z(mm)
ncr
x(mm)
On this log scale, ne
ranges from 0.03 to
33. and the change
from red to green is
at ne = 1.0
There is a
sharp focus
in the
underdense
plasma
blowoff.
FIW/BFL et al. 7
Energetic particles have a wide angular
distribution.
2-D, 1019 W/cm2, 16nc, Te = 10 keV
Plot positions of electrons with energy > 0.8 MeV (g > 2.6) at t=0.15 ps
100
from simulations in p-polarization.
40
60
z(mm)
z(mm)
Centered
irradiation
80
20
40
20
0
0
20
0
100
100
40
30
Shifted beam
irradiation
80
80
20
40
10
20
0
0
10
20
x(mm)
30
0
20
40
z(mm)
z(mm)
60
60
20
0
0
x(mm)20
0
FIW/BFL et al. 8
Static fields illustrate strong surface currents.
2-D, 1019 W/cm2, 16nc, Te = 10 keV
Centered irradiation
p-polarization
(Jz)s vs
(x,z) at
t=0.25 ps
z(mm)
These static B
fields are
comparable to
the laser field.
Note sign
changes at the
cone wall closer
to the shifted
incident beam.
z(mm)
(By)s vs
(x,z) at
t=0.25 ps
Shifted beam irradiation
p-polarization
x(mm)
x(mm)
FIW/BFL et al. 9
Find little difference in absorption into hot electrons
between centered and shifted beam pointings.
2-D, 1019 W/cm2, 16nc, Te = 10 keV
Solid; Centered irradiation
Dotted; Shifted irradiation
Fraction
of
incident
energy
absorbed
by
electrons.
Pointed top, p-polarization
Flat top, p-polarization
Pointed top, s-polarization
Flat top, s-polarization
t(ps)
FIW/BFL et al. 10
With fixed ions, simulations of flat top cones
lead to lower absorption.
2-D, 1019 W/cm2, 16nc, Te = 10 keV
• We ascribe this difference to the role of the deformation of the relativistic
critical surface in the absorption process.
• Absorption (
) and reflection (
) vs time; dotted curves
are from the simulation with fixed ions.
fraction
p-polarization
Absorption into
heated electrons
with mobile ions.
Fixed ions.
Reflection with
mobile ions.
t(ps)
FIW/BFL et al. 11
The heated electrons are more collimated for
flat top cone simulations with fixed ions.
2-D, 1019 W/cm2, 16nc, Te = 10 keV
z(mm)
z(mm)
Plot positions of electrons with energy > 0.8 MeV (g > 2.6) at t=0.15 ps
from simulations of centered beam in p-polarization.
Fixed Ions
Mobile Ions
x(mm)
x(mm)
FIW/BFL et al. 12
For cones with pointed tops, little difference
between fixed and mobile ion simulations.
2-D, 1019 W/cm2, 16nc, Te = 10 keV
• We infer that relativistic critical surface deformation is less important for
cones with pointed tops at these early time as the laser is efficiently
absorbed along the upper side walls in both cases
Absorption (
) and
reflection (
) vs time;
dotted curves are from the
simulation with fixed ions.
Positions of electrons with
energy > 0.8 MeV (g > 2.6) at
t=0.15 ps from centered
irradiation in p-polarization.
Wide angular
distribution as
with mobile
ions
z(mm)
fraction
p-polarization
t(ps)
x(mm)
• Expect greater differences at later times.
FIW/BFL et al. 13
Results so far are insensitive to beam
and cone shapes.
• 2D simulations at an intensity of 1019 W/cm2, p-polarization, 15 cone half
angle, ne = 16nc, Te = 10 keV, Zmi/me = 3600 and ZTe/Ti = 20.
• (Pz)s vs (x,z) at t=0.08 ps
• Proportions are closer to those in
experiments
z(mm)
• Curved plasma surfaces; the initial
plasma boundary is shown by the
green and red curves.
z(mm)
• Positions of electrons with
energy > 0.8 MeV at t=0.5 ps
• Intense part of the beam is approximately
half the width of the cone inner wall.
• With wings, whose intensity is ¼ that
of the central region, this entire beam
profile is wider than the cone inner wall.
• A companion simulation with a
Gaussian beam gives similar results.
x(mm)
FIW/BFL et al. 14
Do textured surfaces help?
We have seen that the cone geometry with the pointed top
produces high absorption into heated electrons.
Will shaped surfaces increase the absorption into heated,
collimated electrons?
Divot shapes with depth of 6mm.
Depth
z(mm)
Series of simulations of
plane waves interacting with a
“divot.” Varied depth of divot
from 2 mm to 8 mm.
Conditions: ne=25nc, Te=10 keV,
Zmi/me = 3600, and ZTe/Ti = 20 at
an incident intensity of 1019 W/cm2
in both s- and p-polarization.
x(mm)
FIW/BFL et al. 15
Divots impact the laser-matter interaction.
2-D, 1019 W/cm2, 25nc, Te = 10 keV
z(mm)
Model one divot, but take advantage of
periodicity transverse to the laser beam when
making snapshot plots.
x(mm)
• (Pz)s vs (x,z) at
t=0.08 ps
z(mm)
z(mm)
z(mm)
• ne vs (x,z) at
t=0.21 ps
• (Pz)s vs (x,z) at
t=0.21 ps
ncr
x(mm)
x(mm)
x(mm)
• There is strong focusing in the plasma that blows off the sides of the divot
in this p-polarization simulation.
Laser vacuum intensity on this color map.
FIW/BFL et al. 16
Divots increase the absorption into heated
electrons compared to a flat slab.
Absorption fraction into heated electrons.
z(mm)
2-D, 1019 W/cm2, 25nc, Te = 10 keV
x(mm)
fraction
8 mm deep, p-polarization
6 mm deep, p-polarization
4 mm deep, p-polarization
2 mm deep, p-polarization
no divot, p-polarization
6 mm deep, s-polarization
no divot, s-polarization
t(ps)
FIW/BFL et al. 17
Unfortunately the heated electrons are not
very collimated.
2-D, 1019 W/cm2, 25nc, Te = 10 keV
Positions of electrons with energy > 0.8 MeV (g > 2.6) at t=0.15 ps from
simulation in p-polarization.
7
6
20
5
z(mm)
4
3
10
Heated electrons appear to be
produced in a ~ 30 cone near
the tip of the divot.
2
1
0
0
10
20
0
x(mm)
FIW/BFL et al. 18
In 3D simulations, grooves (2D structures) are
better than divots (full 3D structures).
3-D, 1019 W/cm2, 25ne, Te = 40 keV
fraction
Fraction of light reflected, or absorbed into heated electrons.
Solid: groove with
laser electric field in the plane
of the groove
Dotted: divot
t(ps)
Titan experiments on divots are planned to look for optimum structures
and to use Ka signature to investigate hot electrons.
We identify these results on 2D vs 3D structures with experiments reported
by Ditmire, Cowan et al on s- and p-polarization irradiations of wedge
targets and the accompanying PIC simulations by Sentoku et al.
FIW/BFL et al. 19
PIC simulations of structured targets
have high laser absorption.
• Simple cone target modeling shows
•
•
•
•
light interference within the cone
a wide angular spread of the energetic electrons.
ion motion is important.
beam pointing shifts don’t significantly change these results
• More realistic cone targets have similar properties.
• We find enhanced laser absorption with structured surfaces
•
•
But the challenge is to find a shape which collimates the hot
electrons.
Two-dimensional grooves give higher absorption than threedimensional divots.
FIW/BFL et al. 20
Backup viewgraphs.
FIW/BFL et al. 21
From the incident and net fluence at the entrance
plane, we compute the fraction of reflected light.
2-D, 1019 W/cm2, 16nc, Te = 10 keV
• In the code, accumulate in time the net fluence at the incident (z = 0) plane
and compare to the incident fluence to find the fraction of reflected light.
• Example: cone with flat inner surface, centered irradiation.
little reflection
more reflection
s-polarization
incident fluence
p-polarization
fraction
fraction
net fluence
t(ps)
t(ps)
• In these simulations with a relativistic overdense plasma,
what is not reflected appears as field and particle energy.
FIW/BFL et al. 22
The energetics of the simulation are monitored.
2-D, 1019 W/cm2, 16nc, Te = 10 keV
Energy; arbitrary units.
• Example: cone with flat inner surface, centered irradiation.
s-polarization
p-polarization
Particle kinetic energy
Electron kinetic energy
Field energy
Energy error
Net fluence at the
incident plane.
t(ps)
t(ps)
• The change in each quantity is plotted.
• Readily observe that p-polarization has higher absorption
and lower reflection than s-polarization
FIW/BFL et al. 23
Geometric ratios in this cone irradiation study
are guided by experiment.
•2D (x, z) Z3 simulations in p-polarization at 1019 W/cm2, 15 cone half angle,
ne = 16 nc, Te = 10 keV, Zmi/me = 3600, and ZTe/Ti = 20.
• Plot Poynting flux with laser frequency filtered out, (Pz)s vs (x,z), at
t=0.08 ps, to show the problem initialization for this beam with a central
intense region and lower intensity wings.
• Intense part of the beam is
approximately half the width
of the cone inner wall.
z(mm)
• With wings, whose intensity is
¼ that of the centered region,
this entire beam profile is wider
than the cone inner wall.
• At this early time, only the
wings of the beam are interacting
with the inner cone walls.
x(mm)
• Companion simulation with a Gaussian beam produces similar results.
FIW/BFL et al. 24
The laser-plasma interaction is predominantly
at the inner cone wall at 0.7 ps.
2-D, 1019 W/cm2, p-polarization, 16nc, Te = 10 keV
ne vs (x,z)
z(mm)
z(mm)
(Pz)s vs (x,z)
x(mm)
x(mm)
Laser vacuum intensity on this color map.
Green and white curves show the initial plasma boundary.
There is reflection along the sides of the beam
Relativistic critical surface now has complex structure.
FIW/BFL et al. 25
Energetic electrons appear to come from the
inner cone wall with a wide angular distribution.
2-D, 1019 W/cm2, p-polarization, 16nc, Te = 10 keV
• Plot positions of electrons with energy > 0.8 MeV (g > 2.6)
t = 0.5 ps
t = 0.55 ps
z(mm)
t = 0.4 ps
x(mm)
x(mm)
x(mm)
FIW/BFL et al. 26
There is ~ 25% reflection in this cone simulation.
fraction
2-D, 1019 W/cm2, p-polarization, 16nc, Te = 10 keV
• Accumulate the net fluence at the incident plane
(z = 0) and compare to the incident fluence to
determine the fraction of reflected light.
• Fluences are normalized to the
maximum incident fluence.
incident fluence
net fluence
fraction
absorption into heated electrons
reflection
t(ps)
FIW/BFL et al. 27
What is optimum shape? This study is ongoing
2-D, 1019 W/cm2, 25ne, Te = 10 keV
z(mm)
Have started looking at more complicated
shapes; this new one still has problems.
x(mm)
Positions of electrons
with energy > 0.8 MeV) at
t=0.1125 ps
(Pz)s vs (x,z) at
t=0.3 ps
(Pz)s vs (x,z) at
t=0.03 ps
15
14
12
z(mm)
20
10
z(mm)
z(mm)
8
6
10
4
2
0
x(mm)
0
x(mm)
10
20
0
x(mm)
Laser vacuum intensity on this color map.
FIW/BFL et al. 28