Since the absorption is linear process, the absorption rate is not altered even for the
broadband case, if the density scale is given. However, due to the delocalization of
resonance, point Δx cr ~Δω/ω 0 L changes the density scale length longer than that for
the coherent case, reducing the absorption efficiency.
It is noted that such broadband lasers are now standard for the purpose to drive
high pressure and idealistic hydrodynamic phenomena with intense lasers.
4.6 Principle of Parametric Instabilities
When an intense laser is irradiated into plasmas, the laser propagates as
electromagnetic waves in the plasmas by following the basic equation in (2.5.2).
Most of the parametric instabilities are induced by the nonlinear external current j ext .
When the laser propagates in plasmas, it may couple with another two waves
fluctuating in the plasmas as thermal noise. In the case the laser field has its
frequency and wavenumber, (ω 0 , k 0 ), consider coupling with the two waves
characterized with (ω 1 , k 1 ) and (ω 2 , k 2 ). Although the amplitude of the latter two
waves in plasmas is very small, their amplitudes also increase due to the parametric
instabilities, and the energy conversion from the laser to these waves happens in
plasmas. Very compact and precise explanation on such parametric instabilities in
laser plasmas is given in a textbook by Kruer (Chap. 1, Ref. [2]), and the readers are
recommended this book to know more details. In the present book, intuitive
explanation is described below for readers to be familiar with the parametric
instabilities.
The nonlinear external current in (2.5.2) is expressed as:
j NL ¼ Àeδn e δv e
ð4:6:1Þ
Assume, for example, that the velocity perturbation is due to electromagnetic
fluctuation and the density perturbation is due to electrostatic fluctuation. If the
three waves satisfy the following condition, the nonlinear current becomes a
resonant force to the third wave:
ω 0 ¼ ω 1 þ ω 2
k 0 ¼ k 1 þ k 2
ð4:6:2Þ
This is called matching condition of three waves, and the condition of the
wavenumber is plotted in Fig. 4.6. Different from the forced oscillation discussed
in Sect. 3.7, the laser plays as energy source to the force term and contributes to the
amplification of the nonlinear force. This is parametric instability, and the wave
equations for the two fluctuating waves have the external source term as nonlinear
force to amplify them.
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4 Nonlinear Physics of Laser-Plasma Interaction
broadband case, if the density scale is given. However, due to the delocalization of
resonance, point Δx cr ~Δω/ω 0 L changes the density scale length longer than that for
the coherent case, reducing the absorption efficiency.
It is noted that such broadband lasers are now standard for the purpose to drive
high pressure and idealistic hydrodynamic phenomena with intense lasers.
4.6 Principle of Parametric Instabilities
When an intense laser is irradiated into plasmas, the laser propagates as
electromagnetic waves in the plasmas by following the basic equation in (2.5.2).
Most of the parametric instabilities are induced by the nonlinear external current j ext .
When the laser propagates in plasmas, it may couple with another two waves
fluctuating in the plasmas as thermal noise. In the case the laser field has its
frequency and wavenumber, (ω 0 , k 0 ), consider coupling with the two waves
characterized with (ω 1 , k 1 ) and (ω 2 , k 2 ). Although the amplitude of the latter two
waves in plasmas is very small, their amplitudes also increase due to the parametric
instabilities, and the energy conversion from the laser to these waves happens in
plasmas. Very compact and precise explanation on such parametric instabilities in
laser plasmas is given in a textbook by Kruer (Chap. 1, Ref. [2]), and the readers are
recommended this book to know more details. In the present book, intuitive
explanation is described below for readers to be familiar with the parametric
instabilities.
The nonlinear external current in (2.5.2) is expressed as:
j NL ¼ Àeδn e δv e
ð4:6:1Þ
Assume, for example, that the velocity perturbation is due to electromagnetic
fluctuation and the density perturbation is due to electrostatic fluctuation. If the
three waves satisfy the following condition, the nonlinear current becomes a
resonant force to the third wave:
ω 0 ¼ ω 1 þ ω 2
k 0 ¼ k 1 þ k 2
ð4:6:2Þ
This is called matching condition of three waves, and the condition of the
wavenumber is plotted in Fig. 4.6. Different from the forced oscillation discussed
in Sect. 3.7, the laser plays as energy source to the force term and contributes to the
amplification of the nonlinear force. This is parametric instability, and the wave
equations for the two fluctuating waves have the external source term as nonlinear
force to amplify them.
146
4 Nonlinear Physics of Laser-Plasma Interaction