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Kinetics of the Raman scattering in a laser corona using a transform method

Published online by Cambridge University Press:  06 November 2017

M. Mašek*
Affiliation:
Institute of Physics, Academy of Sciences of the Czech Rep., Na Slovance 2, 182 21 Prague 8, Czech Republic
K. Rohlena
Affiliation:
Institute of Physics, Academy of Sciences of the Czech Rep., Na Slovance 2, 182 21 Prague 8, Czech Republic
*
Address correspondence and reprint requests to: M. Mašek, Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, 182 21 Prague 8, Czech Republic. E-mail: masekm@fzu.cz

Abstract

This paper is an extension of our previous paper (Mašek and Rohlena, 2015), where we applied a transform method for the solution of Vlasov–Maxwell set of equations in a one-dimensional geometry to describe the Raman backscattering of the heating ns laser wave in the external corona of the generated laser plasma in a strongly non-linear regime. The method is stabilized by a simplified Fokker–Planck collision term, which, in turn, is used for a study of the influence of collisional and collisionless damping mechanisms of the daughter electron plasma wave (EPW) on the instability development and their competition resulting in a different instability behavior in various plasma configurations. The physics of trapped electrons is studied in detail and compared to the resulting Raman reflectivity. The Raman reflectivity was found to depend strongly on the intensity of laser irradiation in the different regions of the plasma corona. This is discussed in detail from the point of view of trapped electrons behavior in the EPW. Moreover, a study of the Raman reflectivity dependence on the electron–ion collision frequency (average plasma ionization) is presented, too. The results supplement the physical picture of the collision and collisionless processes influencing the Raman instability non-linear development.

Type
Research Article
Copyright
Copyright © Cambridge University Press 2017 

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References

REFERENCES

Albrecht-Marc, M., Ghizzo, A., Johnston, T.W., Rveill, T., Sarto, D.D. & Bertrand, P. (2007). Saturation process induced by vortex-merging in numerical Vlasov-Maxwell experiments of stimulated Raman backscattering. Phys. Plasmas 14, 072704.CrossRefGoogle Scholar
Armstrong, T.P. (1967). Numerical studies of the nonlinear Vlasov equation. Phys. Fluids 10, 12691280.Google Scholar
Betti, R., Zhou, C.D., Anderson, K.S., Perkins, L.J., Theobald, W. & Solodov, A.A. (2007). Shock ignition of thermonuclear fuel with high areal density. Phys. Rev. Lett. 98, 155001.Google Scholar
Bourdiec, S.L., de Vuyst, F. & Jacquet, L. (2006). Numerical solution of the Vlasov-Poisson system using generalized Hermite functions. Comput. Phys. Commun. 175, 528544.Google Scholar
Brunner, S. & Valeo, E.J. (2004). Trapped-particle instability leading to bursting in stimulated Raman scattering simulations. Phys. Rev. Lett. 93, 145003.Google Scholar
Camporeale, E., Delzanno, G., Bergen, B. & Moulton, J. (2016). On the velocity space discretization for the Vlasov-Poisson system: comparison between implicit Hermite spectral and Particle-in-Cell methods. Comput. Phys. Commun. 198, 4758.Google Scholar
Cheng, C. & Knorr, G. (1976). The integration of the Vlasov equation in configuration space. J. Comput. Phys. 22, 330351.Google Scholar
Delzanno, G. (2015). Multi-dimensional, fully-implicit, spectral method for the Vlasov-Maxwell equations with exact conservation laws in discrete form. J. Comput. Phys. 301, 338356.Google Scholar
Drake, J.F., Kaw, P.K., Lee, Y.C., Schmid, G., Liu, C.S. & Rosenbluth, M.N. (1974). Parametric instabilities of electromagnetic waves in plasmas. Phys. Fluids 17, 778785.Google Scholar
Eliezer, S. (2002). The Interaction of High-Power Lasers with Plasmas, Series in Plasma Physics, Bristol and Philadelphia: IoP Publishing.Google Scholar
Grant, F.C. & Feix, M.R. (1967). Fourier-Hermite solutions of the Vlasov equations in the linearized limit. Phys. Fluids 10, 696702.Google Scholar
Hou, T.Y. & Li, R. (2007). Computing nearly singular solutions using pseudospectral methods. J. Comput. Phys. 226, 379397.Google Scholar
Joyce, G., Knorr, G. & Meier, H.K. (1971). Numerical integration methods of the Vlasov equation. J. Comput. Phys. 8, 5363.Google Scholar
Kruer, W.L. & Dawson, J.M. (1969). Trapped-particle instability. Phys. Rev. Lett. 23, 838841.Google Scholar
Lindl, J. (1995). Development of the indirect-drive approach to inertial confinement fusion and the target physics basis for ignition and gain. Phys. Plasmas 2, 39334024.Google Scholar
Liu, Z.J., Ping Zhu, S., Cao, L.H., Zheng, C.Y., He, X.T. & Wang, Y. (2009). Enhancement of backward Raman scattering by electron-ion collisions. Phys. Plasmas 16, 112703.Google Scholar
Mašek, M. & Rohlena, K. (2005). Kinetics of the Raman instability in laser plasma. Czech. J. Phys. 55, 973988.Google Scholar
Mašek, M. & Rohlena, K. (2008). Stimulated Raman scattering in the presence of trapped particle instability. Commun. Nonlinear Sci. Numer. Simul. 13, 125129.CrossRefGoogle Scholar
Mašek, M. & Rohlena, K. (2010). Novel features of non-linear Raman instability in a laser plasma. Eur. Phys. J. D 56, 7990.Google Scholar
Mašek, M. & Rohlena, K. (2015). Intensity dependence of non-linear kinetic behaviour of stimulated Raman scattering in fusion relevant plasmas. Eur. Phys. J. D 69, 109.Google Scholar
Parker, J.T. & Dellar, P.J. (2015). Fourier-Hermite spectral representation for the Vlasov-Poisson system in the weakly collisional limit. J. Plasma Phys. 81(2), 305810203.Google Scholar
Schumer, J.W. & Holloway, J.P. (1998). Vlasov simulations using velocity-scaled Hermite representations. J. Comput. Phys. 144, 626661.Google Scholar
Shoucri, M. & Gagne, R. (1976). Numerical solution of the Vlasov equation by transform methods. J. Comput. Phys. 21, 238242.Google Scholar
Theobald, W., Nora, R., Lafon, M., Casner, A., Ribeyre, X., Anderson, K.S., Betti, R., Delettrez, J.A., Frenje, J.A., Glebov, V.Y., Gotchev, O.V., Hohenberger, M., Hu, S.X., Marshall, F.J., Meyerhofer, D.D., Sangster, T.C., Schurtz, G., Seka, W., Smalyuk, V.A., Stoeckl, C. & Yaakobi, B. (2012). Spherical shock-ignition experiments with the 40 + 20-beam configuration on OMEGA. Phys. Plasmas 19, 102706.CrossRefGoogle Scholar
Vencels, J., Delzanno, G.L., Manzini, G., Markidis, S., Peng, I.B. & Roytershteyn, V. (2016). Spectralplasmasolver: a spectral code for multiscale simulations of collisionless, magnetized plasmas. J. Phys.: Conf. Ser. 719, 012022.Google Scholar