Stimulated Raman scattering in a non-eigenmode regime Download: 601次
1 Introduction
Laser plasma interactions (LPIs) are widely associated with many applications such as inertial confinement fusion (ICF)[1–3], radiation sources[4], plasma optics[5, 6] and laboratory astrophysics[7, 8]. The concomitant parametric instabilities found in LPI are nonlinear processes, which can greatly affect the outcome[9]. Generally, laser plasma instabilities[10, 11], especially stimulated Raman scattering (SRS), stimulated Brillouin scattering (SBS) and two-plasmon decay (TPD) instability, have been mainly considered in ICF with the incident laser intensity less than
As well known, SRS usually develops in plasma density not larger than the quarter critical density
2 Theoretical analysis of SRS in the non-eigenmode regime
Generally, SRS is a three-wave instability where a laser decays into an electrostatic wave, with frequency equal to the eigen electron plasma wave, and a light wave. However, the stimulated electrostatic wave is no longer the eigenmode of the electron plasma wave in the SRS non-eigenmode regime, where both the frequencies of scattered light and electrostatic field are nearly half of the incident laser frequency. The mechanism of this instability can be described by the SRS dispersion relation at plasma density
Fig. 1. Amplitude thresholds for the development of eigenmode and non-eigenmode SRS in plasma above the quarter critical density. The threshold for the case of eigenmode SRS is due to the relativistic effect.
To investigate the non-eigenmode SRS mechanism in LPI, we first introduce the non-relativistic dispersion relation of SRS in cold plasma[10] where
Now we analytically solve Equation (
Substituting
For the density region just near the quarter critical density
In the following, we consider the relativistic modification of the SRS non-eigenmode in hot plasma. The dispersion of SRS under the relativistic intensity laser is[9, 25] where
Following the similar steps of the non-relativistic case, the imaginary part of Equation (
The comparisons between the numerical solutions of Equations (
Fig. 2. Numerical solutions of SRS dispersion equation at plasma density with laser amplitude . (a) The relativistic modification on the non-eigenmode SRS at . (b) The effect of electron temperature on non-eigenmode SRS. The dotted line and dashed line are the imaginary part and the real part of the solutions, respectively.
Phase-matching conditions are satisfied in the SRS non-eigenmode regime, and therefore the frequency of concomitant light is also
According to the linear parametric model of inhomogeneous plasma, the Rosenbluth gain saturation coefficient for convective instability is
In conclusion, different from normal SRS, a new type of non-eigenmode SRS can develop in plasma with density
3 Simulations for non-eigenmode SRS excitation
3.1 One-dimensional simulations for non-eigenmode SRS in homogeneous plasma
To validate the analytical predictions for non-eigenmode SRS, we have performed several one-dimensional simulations by using the
Fig. 3. Distributions of the electrostatic wave in space obtained for the time window at plasma density under (a) pump laser amplitude and (b) pump laser amplitude . (c) Distribution of the electromagnetic wave in space obtained under the same conditions as in (b). (d) Longitudinal phase space distribution of electrons under different laser amplitudes at .
Based on Equation (
3.2 Two-dimensional simulations for non-eigenmode SRS in homogeneous plasma
To further validate the linear development and nonlinear evolution of non-eigenmode SRS in high-dimensionality with mobile ions, we have performed several two-dimensional simulations. The plasma occupies a longitudinal region from
Fig. 4. The plasma density is for (a)–(d). (a) Distribution of the electrostatic wave in space obtained for the time window and transverse region . (b) Spatial distribution of electrostatic wave at . (c) Spatial distribution of electromagnetic wave at . (d) Spatial distribution of ion density at . The plasma density is for (e) and (f). (e) Distribution of the electrostatic wave in space obtained for the time window and transverse region . (f) Spatial distribution of the ion density at . and are normalized by , where and respectively are the electron mass and electron charge. is normalized by .
According to Equation (
Fig. 5. (a) The spatial–temporal distributions of electrostatic wave. (b) Distributions of the electrostatic wave in space obtained for the time window . (c) The spatial–temporal distributions of ion density. (d) Energy distributions of electrons at different times. and respectively are normalized by and .
The laser with peak amplitude
3.3 One-dimensional simulations for non-eigenmode SRS in inhomogeneous plasma
To study the non-eigenmode SRS in hot inhomogeneous plasma, we have performed a simulation for the inhomogeneous plasma
The spatial–temporal evolution of the electrostatic wave is exhibited in Figure
4 Summary
In summary, we have shown theoretically and numerically that the non-eigenmode SRS develops at plasma density
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Article Outline
Yao Zhao, Suming Weng, Zhengming Sheng, Jianqiang Zhu. Stimulated Raman scattering in a non-eigenmode regime[J]. High Power Laser Science and Engineering, 2020, 8(2): 02000e21.