Predictive three dimensional modeling of Stimulated Brillouin Scattering in ignition-scale experiments Page: 3 of 7
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Predictive three dimensional modeling of Stimulated Brillouin Scattering in
L. Divol, R. L. Berger, N. B. Meezan, D. H. Froula, S. Dixit, L. Suter and S. H. Glenzer
L-399, Lawrence Livermore National Laboratory,
University of California P. O. Box 808, CA 94551, U.S.A.
(Dated: November 7, 2007)
The first three-dimensional (3D) simulations of a high power 0.351pm laser beam propagating
through a high temperature hohlraum plasma are reported. We show that 3D linear kinetic modeling
of Stimulated Brillouin scattering reproduces quantitatively the experimental measurements, pro-
vided it is coupled to detailed hydrodynamics simulation and a realistic description of the laser beam
from its millimeter-size envelop down to the micron scale speckles. These simulations accurately
predict the strong reduction of SBS measured when polarization smoothing is used.
PACS numbers: PACS numbers: 52.40.Nk, 52.35.Mw, 05.10.Gg, 02.50.Ey
One of the grand challenge of laser-plasma interac-
tion (LPI) studies is to provide guidance for the design of
hohlraum targets on the next generation of laser facilities
for ignition attempts [1, 2, 4]. Modeling LPI processes
in real-size experiments has been recognized as a difficult
task. One of the main difficulties is the vast parameter
space in electron density, temperature and spatial scales
that are typically spanned by an ignition relevant laser-
plasma experiment on current laser facilities. This leads
to a plethora of (usually coupled) LPI processes such
as absorption, refraction, diffraction, filamentation and
parametric backscattering instabilities. Another chal-
lenge is the proper description of the spatially smoothed
laser beams used on all modern facilities, which exhibit
intensity structures from the hundreds of microns down
to the micron scale.
There are two main numerical modeling approaches
for LPI. Particle-in-cell or Focker-Plank type codes solve
consistently a set of Maxwell-Vlasov-like equations and
are limited to short timescales (picoseconds), small
plasma volumes (typically one laser speckle) or low di-
mensionality (1 or 2 dimensions). While 3-dimensional
PIC simulations of diffraction limited short pulse ex-
periments are becoming common tasks due to increas-
ingly powerful computers, long pulse (nanosecond) igni-
tion scale (cubic millimeter) LPI experiments are still out
of reach for such numerical tools. Another approach is
to use a fluid-based description of LPI processes[6 8, 11].
This allows relaxing both spatial and temporal resolu-
tions and no discretization in particle velocity space is
In this letter, we report on the first three dimen-
sional simulations of a whole laser beam propagating
through an ignition-scale experiment, using the fluid
paraxial code pF3d. These simulations include models
for both stimulated Raman (SRS) and Brillouin (SBS)
backscattering. We show that a fluid-based modeling of
SBS including linear kinetic correction, coupled to accu-
rate hydrodynamics profiles and a realistic description of
the laser intensity pattern generated by various smooth-
ing options leads to quantitative agreement between the
measured and calculated reflectivities over many order of
magnitude and for different smoothing techniques (polar-
ization smoothing and smoothing by spectral dispersion).
We are interested here in validating LPI modeling
tools in conditions close to future ignition experiments.
In this letter we model a series of recent experiments
performed at the Omega laser facility (LLE/Rochester).
An interaction beam propagating along the axis of a
hydrocarbon-filled hohlraum heated by up to 17 kJ of
heater beam energy interacts with a millimeter-scale un-
derdense (Ne 6.5% critical) uniform plasma at electron
temperatures Te around 3 keV. The interaction beam
power was varied between 50 and 500 GW, at a wave-
length of A= 0.351 m. Using a 150 pm CPP, the aver-
age intensity on axis was varied between 5 1014W.cm-2
and 4 10"W.cm--2. Absolutely calibrated diagnostics
measure the backscattered light. These laser-plasma con-
ditions are close to those encountered in current ignition
A number of steps are necessary in order to confidently
compare pF3d simulation results with the measured re-
First we need accurate plasma parameters as input
for pF3d. Extensive Thomson scattering measurements
 in the multispecies plasma (C and H atoms) allowed
to measure both the electron and ion temperatures at
the center of the target, as well as the density evolu-
tion. These time-resolved measurements were success-
fully compared to HYDRA simulations and show rel-
ative insensitivity to the exact heat conduction model
employed. We can then directly use HYDRA three-
dimensional hydrodynamics maps (electron density Ne
and temperature Te, ion temperature Ti and plasma
flow) as initial conditions for pF3d. We perform post-
shot HYDRA simulations to account for variation in
heater beam energy (typically < 4%) and gas fill pres-
sure (< 10%) between shots. Figure 1 shows the plasma
parameters along the hohlraum axis as used in the sim-
ulation. The transverse variations were also included.
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Divol, L; Berger, R; Meezan, N; Froula, D H; Dixit, S; Suter, L et al. Predictive three dimensional modeling of Stimulated Brillouin Scattering in ignition-scale experiments, article, November 7, 2007; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc895748/m1/3/: accessed January 21, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.