RLE Progress Report No - Research Laboratory of Electronics - MIT

1
0.1
ne
Te
Ti
0.01
100 200 300 400
Location from target (z) in µ m
Figure 1: Laser produced plasma in TRIDENT; n e in units of n e /n cr ,
T e and T i in keV (from Ref.1).
The basic experimental setup is illustrated in Figure 13 of our last report 2 , where a laser beam is
focused into a plasma that is created from a plastic foil. 1 The plasma is approximately
homogeneous along the beam path, but changes its density and temperature as it flows away
from the target. By focusing the laser at different positions from the target, experimentalists have
studied the SRS backscattering for the different parameters shown in Figure 1.
Considering a weak nonlinear interaction of the five waves, we express this as nonlinearly
coupled field amplitudes that change slowly in time and space. The equations that describe the
interaction between the slowly varying amplitudes ( a 1
, a ,
2
a ,
3
a and
4
a , for the Laser, BEMW,
5
EPW, BEPW and IAW, respectively) are:
( ∂ + v ∂ + γ ) a = −K
a SRS
a , (1)
t g1
x 1 1
t
+ vg2∂
x
+ 2
)
2 =
2
1
3
3
( ∂ γ a K a SRS
a , (2)
( ∂ + v ∂ + γ ) a = K a a − K a a , (3)
t
g3
x 3 3 SRS 1 2
t
+ vg4∂
x
+ 4)
a4
=
LDI
t
+ vg5∂
x
+ 5)
a5
=
LDI
3
LDI
( ∂ γ K a a , (4)
3
5
( ∂ γ K a a . (5)
4
4
5
2
In Eqs. (1)–(5), a
= W
/ ω ,
W ,
v and
g
γ are the wave action density, wave energy density,
group velocity and damping rate of mode . The nonlinear coupling coefficients are:
K
SRS
≈
2
ε
o
1/ 2
2
e k ⎛ ω ⎞
3 pe ,
m
e
⎜ ⎟
4
⎝ω1ω
2ω
3 ⎠
K
LDI
≈
2
ε
o
m e
1/ 2
e ω pe ⎛ ω ⎞
5
4v
⎜
⎟
.
Te ⎝ω3ω
4 ⎠
Such model equations have also been considered in the past 3 but their solution was not explored
in much detail nor related to experiments in relatively homogeneous plasmas.
2 R. J. Focia, A. Bers, and A. K. Ram., “Plasma Electrodynamics and Applications: Section 5 – Electromagnetic Decay
Instability in Single Hot Spot Geometry”, Progress Report No. 142, MIT Research Laboratory of Electronics, Cambridge,
2000 (http://rleweb.mit.edu/Publications/pr142/bers142.pdf).
3 J. A. Heikkinen and S. J. Karttunen, “Intensity Saturation of Stimulated Raman Scattering by Ion-Wave Coupling,” Phys.
Fluids, 29(4), 1291 (1986).