Predictive three dimensional modeling of Stimulated Brillouin Scattering in ignition-scale experiments Page: 4 of 7
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FIG. 1: Plasma parameters at t=700 ps along the hohlraum
axis calculated by HYDRA. Electron density, temperature,
ion temperature and flow are used as initial conditions for
We chose to model the experiment at a time when the
plasma electron temperature is close to 3 keV and the
density profile is relatively uniform.
Second, a realistic description of the laser beam is
needed. We use the measured continuous phase plate
(CPP) phase mask used on the interaction beam and
a model for Omega beam aberrations. Figure 2 shows
transverse and longitudinal slices through the middle of
the resulting beam intensity while Fig. 2c shows a 3D
rendering of the laser beam propagating through the
plasma. The simulation resolves both the envelop of the
beam, which is close to a Gaussian with 150 pm FWHM
at best focus and the f/6.7 speckles at the micron scale.
The typical resolution required by the paraxial approx-
imation used for laser propagation is dx dy 1.3A0
and dz 4A0. The plasma volume modeled encompasses
more than a billion cells. It is difficult to define an av-
erage laser intensity for such a beam, but a benefit of
3D whole beam simulations is that only the beam power
(here in the 100-400 GW range) is needed as an input
parameter. As a reference, the intensity averaged over
a 50 pm3 volume at best focus is 1.15 1015W.cm-2 for
an input power of 100 GW. Additional beam smoothing
techniques are equally accurately modeled. When polar-
ization smoothing (PS)  is used, pF3d solves paraxial
equations for each polarization component, with the two
speckle patterns being offset in the far field by the ex-
perimentally measured shift induced by the PS wedge.
Smoothing by spectral dispersion (SSD)  is modeled
using the correct modulator, grating geometry and depth
+( - 2ikocaz - caV2)Sn =aaoa*
where ao (resp. ai) are the normalized field amplitude
of the incoming (resp. backscattered) light. The Vlasov-
Landau kinetic dispersion relation for SBS-driven ion-
acoustic waves at k ka is solved at each position in
the plasma to account for detuning due to all plasma pa-
rameters and the most unstable local solution provides
the local acoustic frequency oa and Landau damping
va. The sound speed is defined as ca Oa/ka. At the
center of the target, the values are Wa 13ps-1 and
va 0.15wa.The coupling coefficient ra is obtained by
matching the resulting convective amplification to the
1D fully kinetic result. This linear kinetic treatment
of SBS-driven acoustic waves provides a correct descrip-
tion of the time evolution of SBS, which is important
to correctly model the coupling to other time-dependent
LPI processes such as filamentation and SRS and the
effect of temporal beam smoothing. Ion-acoustic waves
in a multi-ion-species plasma are described by an aver-
FIG. 2: Beam intensity profiles in a plane perpendicular to
the direction of propagation (a, at best focus) and parallel (b).
three dimensional rendering of the whole beam as simulated
by pF3d (c)
Third, a detailed fluid-based model has been developed
to describe the response of the plasma to the pondero-
motive drive and is described in [berger98]. Here we will
focus on the details of the SBS model which was dom-
inant in the experiment. Stimulated Raman backscat-
ter was below measurement threshold for all powers and
negligible in simulations too, as expected in low den-
sity, high temperature plasmas where Landau damping
is large. The electron density perturbation 6n associ-
ated with the SBS-driven acoustic wave is enveloped in
space at ka 2ko, but not in time to describe correctly
the modified decay regime when the SBS growth rate
becomes larger than the acoustic frequency co in high
intensity speckles. The resulting differential equation is
(at + u.V + 2ikouz + va)2Sn
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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/m1/4/: accessed January 21, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.