2. Centre de PhysiqueThéorique 1. DAM; Bruyères-le-Châtel DCSA 1. : M. Casanova 1., 2. : Thomas...
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Transcript of 2. Centre de PhysiqueThéorique 1. DAM; Bruyères-le-Châtel DCSA 1. : M. Casanova 1., 2. : Thomas...
2. Centre de PhysiqueThéorique
1. DAM; Bruyères-le-ChâtelDCSA
1. : M. Casanova
1., 2. : Thomas Fouquet
2. : S. Hüller, D. Pesme
HEDP Summer School
UC Berkeley, 2005
Nonlinear Evolution of Stimulated Raman Scattering
driven by a RPP Laser Beam in a 2D Inhomogeneous Plasma
CPHT
Aim : Study the Stimulated Raman Scattering (SRS) and its saturation via the coupling of the plasma waves generated by this instability, with the sound waves; in the case of an inhomogeneous plasma in density.
2D modelization
case of a linear density profile
laser beam : monospeckle or RPP
Raman instability results of the coupling of an incident laser wave with a plasma electronic wave to give birth to a transverse wave named scattered : it is a three waves coupling process.The conditions of the resoning coupling imply that this instability can be developed in a field called 'under quarter critical'. This field corresponds to ne< nc/4 densities.
0a )exp( 0zikRa )exp( zikR
Rkk ,0 Lk )exp( zikL
RL kkk 0
Model and equations
)()( znnzN hydroerefhydro . )(zNhydro
.erefn
)(znhydro
La Rkk ,0
LSISLRIPLL aazikaaaD )exp(*0
RsISLLIPRR aazikaaaD )exp().( *0
000 )exp().( aazikaaaD sISLLRIP
22
0
22RLISSS aaanD
RamanAutofocalisation
Raman
Raman LDI
Autofocalisation
ponderomotive forces
pump
backscattered
plasma
sound
DLinear propagator
Envelope and paraxial approximation for the pump and backscattered waves
Inhomogeneity
Inhomogeneity
Inhomogeneity
shydros nzna )(
SRS in a 2D homogeneous plasma
Test of the numerical scheme
Monospeckle pump wave
5# f
pst 10 pst 15
221420 /.10.8 cmmWI L =L = m65
Backscattered wave
pst 10 pst 15
Plasma wave
pst 10 pst 15
Gaussian beam
15.0n
n
c
ref
Transmission
2
0
2
0
),0(
),(onTransmissi
ya
yLa 2
0
2
),0(
),0(tyReflectivi
ya
yaR
Reflectivity
Energy conservation OK !
time time
T R
Raman in an inhomogeneous 1D plasma
0 )(0 z « finite length » effect
Resonance conditions cannot be satisfied in the whole plasma slab
),( )()( kD ),,( )()( zkD
),(),(),( 000000 zkzkzk RLRR
: Solutions of parametric resonance conditions in
0zz
)0(k
)()()( 0)0(
)( zkzzkzk
)(zk
.
.
2 effects of distinct nature :
Dispersion relation is local
)()()()( 0 zkzkzkzk LR
« Linear « Linear profile » profile » ::
)())(()( 00
zzzkzkzzz
Monotonous profile of density
Rosenbluth’s result :Finite spatial amplification
LIGRos )( 2
0)( 0 zk
)(
1
zkL
z
PRL 1972
Non robust
Absolute instability
z
Mismatch : /
)(zNhydro.
!!
Difficulty !!!
Numerical difficulties :
Non robustness of the Rosenbluth’s result
Realistic plasma = finite length + inhomogeneous in density
Numerical techniques in order to control the behaviour at the boundaries :
Difficulties = Numerical artefacts
. numerical dampings
. « window » function in the simulation box
absolute instability
If the variation is too fast
SRS without its coupling to the IAWs :inhomogeneous plasma with a linear density profile;RPP laser beam
pump backscattered
plasma
3# f 221520 /.10.5 cmmWI
52 Ros G
2.0DeLk 11.0n
n03.0
c
6.0eT keV
5P
P
c
t = 1ps
t = 2ps
L= L m150=
m65L //plasma
pump backscattered
plasma
Raman
reflectivity
w.o LDI
t = 3ps
t = 5ps
SRS reflectivity saturates at ~ 10% :
-filamentation
-finite amplification gain=
RosGtime
R
pump backscattered
plasma sound
01,0s
s
SRS with its coupling to the IAWs (LDI)* :inhomogeneous plasma with a linear density profile;RPP laser beam
t = 2ps
t = 1psand same parameters as used before
*generalizing in a 2D inhomogeneous plasma, the results investigated by Bezzerides, DuBois, Rose, Rozmus, Russel, Tikhonchuk, Vu
pump plasma soundbackscattered
1,0005,0
Sn
n
t = 3ps
t = 5ps
Ramanreflectivityw. LDI w. LDI
red : Ramanreflectivity
black : Raman
reflectivityw.o LDI
}
Evidence of saturation effects due to LDI
SRS reflectivity saturates at ~ 1.5% when plasma and sound waves are coupled; compared to 10% without coupling to the IAW’s
R
time
Summary/conclusions
*Design of a 2D numerical code :-inhomogeneous plasma-SRS coupled to LDI
*First simulations of SRS with LDI in an inhomogeneous 2D plasma
*Evidence of saturation due to LDI; generalizing in an inhomogeneous plasma the results already seen in a homogeneous one