wave A 2 is the ion acoustic waves. The former is called stimulated Raman
scattering (SRS), and the latter is called stimulated Brillouin scattering (SBS).
Raman and Brillouin have found the light scattering phenomena with frequency
shifts, when the irradiating light is scattered from molecules, liquids, and solids. In
the case of Raman scatter, the frequency shift is due to the coupling with the optical
mode by electrons, while Brillouin scattering is due to the phonon mode in solid.
However, both are just scattering and no instability, so they are called just scattering,
Raman scattering, and Brillouin scattering. They are due to the coupling of incident
light with the waves in materials with enough amplitude. They can be evaluated with
given amplitude on RHS in (4.6.5) and they are not instability.
The reason for “stimulated” in the names in case of plasmas is due to the
enhancement of scattering by the parametric instability. Since the detailed theoretical
analysis of SRS and SBS is given in the text by Kruer (Chap. 1, Ref. [2]), it is not
necessary to repeat the same in the present book. Let us obtain the growth rates for
uniform plasma, based on the model equation of the three coupled oscillators. The
growth rate of the SRS was almost calculated in the previous section, and it is easy to
obtain the following:
γ SRS ¼
ω p0 cosθ 1
j
j
2
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
ω ek ω 0 À ω ek
ð
Þ
p
kV os ,
ð4:7:1Þ
where ω ek is the frequency of the plasma wave.
From (4.7.1), it is clear that SRS grows predominantly to the forward (θ 1 ¼ 0) or
backward (θ 1 ¼ π) directions. As clear in (4.6.6), there is no ponderomotive force to
induce the electrostatic waves for the perpendicular scattering (side scattering). The
growth time τ (¼1/γ SRS ) in (4.7.1) is roughly equal to kV os, and k is roughly the
wavenumber of laser; therefore, the growth time is approximately:
τ $
1
k 0 V os
ð4:7:2Þ
In the assumption of uniform plasmas, it is required that the plasma length L should
be much longer than the following length:
L $ cτ %
λ L
2πa 0
¼
0:16
a 0
μm
½ ,
ð4:7:3Þ
where the last relation is for laser wavelength λ L ¼ 1 μm. This is a very small number
in the under-dense plasmas expanding to the vacuum, for example, L ¼ 16 μm for
the laser intensity of 10
14 W/cm
2 . It is natural to assume that the plasma scale length
increases as the laser intensity and pulse duration increases. In (2.5.23), the
absorption rate is increase in proportion to the pulse duration, but SRS prevents
the penetration of laser near the turning point where the dominant classical
absorption is taken place.
4.7 Stimulated Raman and Brillouin Scattering
153
scattering (SRS), and the latter is called stimulated Brillouin scattering (SBS).
Raman and Brillouin have found the light scattering phenomena with frequency
shifts, when the irradiating light is scattered from molecules, liquids, and solids. In
the case of Raman scatter, the frequency shift is due to the coupling with the optical
mode by electrons, while Brillouin scattering is due to the phonon mode in solid.
However, both are just scattering and no instability, so they are called just scattering,
Raman scattering, and Brillouin scattering. They are due to the coupling of incident
light with the waves in materials with enough amplitude. They can be evaluated with
given amplitude on RHS in (4.6.5) and they are not instability.
The reason for “stimulated” in the names in case of plasmas is due to the
enhancement of scattering by the parametric instability. Since the detailed theoretical
analysis of SRS and SBS is given in the text by Kruer (Chap. 1, Ref. [2]), it is not
necessary to repeat the same in the present book. Let us obtain the growth rates for
uniform plasma, based on the model equation of the three coupled oscillators. The
growth rate of the SRS was almost calculated in the previous section, and it is easy to
obtain the following:
γ SRS ¼
ω p0 cosθ 1
j
j
2
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
ω ek ω 0 À ω ek
ð
Þ
p
kV os ,
ð4:7:1Þ
where ω ek is the frequency of the plasma wave.
From (4.7.1), it is clear that SRS grows predominantly to the forward (θ 1 ¼ 0) or
backward (θ 1 ¼ π) directions. As clear in (4.6.6), there is no ponderomotive force to
induce the electrostatic waves for the perpendicular scattering (side scattering). The
growth time τ (¼1/γ SRS ) in (4.7.1) is roughly equal to kV os, and k is roughly the
wavenumber of laser; therefore, the growth time is approximately:
τ $
1
k 0 V os
ð4:7:2Þ
In the assumption of uniform plasmas, it is required that the plasma length L should
be much longer than the following length:
L $ cτ %
λ L
2πa 0
¼
0:16
a 0
μm
½ ,
ð4:7:3Þ
where the last relation is for laser wavelength λ L ¼ 1 μm. This is a very small number
in the under-dense plasmas expanding to the vacuum, for example, L ¼ 16 μm for
the laser intensity of 10
14 W/cm
2 . It is natural to assume that the plasma scale length
increases as the laser intensity and pulse duration increases. In (2.5.23), the
absorption rate is increase in proportion to the pulse duration, but SRS prevents
the penetration of laser near the turning point where the dominant classical
absorption is taken place.
4.7 Stimulated Raman and Brillouin Scattering
153