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Efficient Semi-Lagrangian Vlasov-Maxwell Simulations of High Order Harmonic Generation from Relativistic Laser-Plasma Interactions

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems Kinematics

Published online by Cambridge University Press:  31 August 2016

Götz Lehmann
Götz Lehmann*
Affiliation:
Institut für Theoretische Physik I, Heinrich-Heine Universität, 40225 Düsseldorf, Germany
*
*Corresponding author. Email address: goetz@tp1.uni-duesseldorf.de (G. Lehmann)
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Abstract

We describe a relativistic semi-Lagrangian scheme for the numerical solution of the relativistic Vlasov-Maxwell system. The implementation strategy on a modern non-unified memory access (NUMA) architecture using the OpenMP framework is discussed. We demonstrated that close to perfect scaling can be obtained on modern many-core, multi-socket systems. Application of this code to the problem of relativistic generation of high-harmonic laser radiation is demonstrated. The results are compared to particle-in-cell (PIC) simulations, indicating in particular that for warm plasma the Vlasov simulation is superior. We discuss the impact of plasma temperature on the radiation spectrum and show that the efficiency of harmonic generation depends on the plasma temperature.

Keywords

Relativistic Vlasov-Maxwell systemsemi-Lagrangemulti-threadingrelativistic laser-plasma interactionhigh-harmonic radiation generation

MSC classification

Secondary: 65Z05: Applications to physics 65M25: Method of characteristics 70B05: Kinematics of a particle
Type
Research Article
Information
Communications in Computational Physics , Volume 20 , Issue 3 , September 2016 , pp. 583 - 602
Copyright
Copyright © Global-Science Press 2016 

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References

[1] Pukhov, A.. Strong field interaction of laser radiation. Rep. Prog. Phys., 66:47–101, 2003.CrossRefGoogle Scholar
[2] Birdsall, C. K. and Langdon, A. B.. Plasma Physics Via Computer Simulation. McGraw-Hill, New York, 1985.Google Scholar
[3] Hockney, R. W. and Eastwood, J. W.. Computer Simulation Using Particles. Adam Hilger Publishers, Bristol, 1988.CrossRefGoogle Scholar
[4] Sonnendrücker, E., Roche, J., Bertrand, P., and Ghizzo, A.. The semi-Lagrangian method for the numerical resolution of the Vlasov equation. J. Comput. Phys., 149(2):201–220, 1999.CrossRefGoogle Scholar
[5] Bégué, M. L., Ghizzo, A., Bertrand, P., Sonnendrücker, E., and Couldaud, O.. Two-dimensional semi-Lagrangian Vlasov simulations of laser-plasma interaction in the relativistic regime. J. Plasma Phys., 62:367–388, 1999.CrossRefGoogle Scholar
[6] Huot, F., Ghizzo, A., Bertrand, P., Sonnendrücker, E., and Coulaud, O.. Instability of the time splitting scheme for the one-dimensional and relativistic Vlasov-Maxwell system. J. Comput. Phys., 185(2):512–531, 2003.CrossRefGoogle Scholar
[7] Ghizzo, A., Huot, F., and Bertrand, P.. A non-periodic 2D semi-Lagrangian Vlasov code for laser-plasma interaction on parallel computer. J. Comput. Phys., 186(1):47–69, 2003.CrossRefGoogle Scholar
[8] Shoucri, M.. Numerical simulation of wake-field acceleration using an Eulerian Vlasov code. Commun. Comput. Phys., 4:703–718, 2008.Google Scholar
[9] Sircombe, N. J. and Arber, T. D.. Valis: A split-conservative scheme for the relativistic 2D Vlasov-Maxwell system. J. Comput. Phys., 228:4773–4788, 2009.CrossRefGoogle Scholar
[10] Wu, S., Zhang, H., Zhou, C., Zhu, S., and He, X.. Relativistic Vlasov code development for high energy density plasmas. Euro Phys. J. D, 68(7), 2014.CrossRefGoogle Scholar
[11] Grassi, A., Fedeli, L., Macchi, A., Bulanov, S., and Pegoraro, F.. Phase space dynamics after the breaking of a relativistic Langmuir wave in a thermal plasma. Eur. Phys. J. D, 68(6), 2014.CrossRefGoogle Scholar
[12] Cheng, C. Z. and Knorr, G.. The integration of the Vlasov equation in configuration space. J. Comput. Phys., 22(3):330–351, 1976.CrossRefGoogle Scholar
[13] Büchner, J.. Advanced Methods for Space Simulations. Terrapub Tokyo, 2007.Google Scholar
[14] Staniforth, A. and Côté, J.. Semi-Lagrangian integration schemes for atmospheric models – a review. Mon. Wea. Rev., 119:2206–2223, 1991.2.0.CO;2>CrossRefGoogle Scholar
[15] Shoucri, M., Lavocat-Dubuis, X., Matte, J.P., and Vidal, F.. Numerical study of ion acceleration and plasma jet formation in the interaction of an intense laser beam normally incident on an overdense plasma. Laser Part. Beams, 29:315–332, 2011.CrossRefGoogle Scholar
[16] Del Sarto, D., Ghizzo, A., Réveillé, T., Besse, N., and Bertrand, P.. Application of a semi-Lagrangian scheme in the relativistic regime of laser interaction with an overdense plasma slab. Commun. Nonlinear Sci. Numer. Simul., 13(1):59–64, 2008. Vlasovia 2006: The Second International Workshop on the Theory and Applications of the Vlasov Equation.CrossRefGoogle Scholar
[17] Besse, N., Latu, G., Ghizzo, A., Sonnendrücker, E., and Bertrand, P.. A wavelet-MRA-based adaptive semi-Lagrangian method for the relativistic Vlasov-Maxwell system. J. Comput. Phys., 227(16):7889–7916, 2008.CrossRefGoogle Scholar
[18] Shoucri, M.. Eulerian codes for the numerical solution of the Vlasov equation. Commun. Nonlinear Sci. Numer. Simul., 13(1):174–182, 2008. Vlasovia 2006: The Second International Workshop on the Theory and Applications of the Vlasov Equation.CrossRefGoogle Scholar
[19] Shoucri, M.. Numerical Solution of Hyperbolic Differential Equations. Nova Science Publishers, New York, 2008.Google Scholar
[20] Crouseilles, N., Latu, G., and Sonnendrücker, E.. A parallel Vlasov solver base on local cubic spline interpolation on patches. J. Comput. Phys., 228:1429, 2009.CrossRefGoogle Scholar
[21] de Boor, C.. A practical guide to splines. Springer, 2001.Google Scholar
[22] Treibig, J., Hager, G., and Wellein, G.. Likwid: A lightweight performance-oriented tool suite for x86 multicore environments. In Parallel Processing Workshops (ICPPW), 2010 39th International Conference on, pages 207–216, Sept. 2010.CrossRefGoogle Scholar
[23] Lehmann, G. and Spatschek, K. H.. Nonlinear Brillouin amplification of finite-duration seeds in the strong coupling regime. Phys. Plasmas, 20(7):073112, 2013.CrossRefGoogle Scholar
[24] Lehmann, G., Spatschek, K. H., and Sewell, G.. Pulse shaping during raman-seed amplification for short laser pulses. Phys. Rev. E, 87:063107, Jun 2013.CrossRefGoogle ScholarPubMed
[25] Lehmann, G. and Spatschek, K. H.. Non-filamentated ultra-intense and ultra-short pulse fronts in three-dimensional raman seed amplification. Phys. Plasmas, 21(5):053101, 2014.CrossRefGoogle Scholar
[26] Shoucri, M.. Ion acceleration and plasma jet formation in the interaction of an intense laser beam normally incident on an overdense plasma: a Vlasov code simulation. Comput. Sci. Disc., 5:014005, 2012.CrossRefGoogle Scholar
[27] Lehmann, G. and Spatschek, K. H.. Temperature dependence of seed pulse amplitude and density grating in Brillouin amplification. Phys. Plasmas, 23(2), 2016.CrossRefGoogle Scholar
[28] Sanchez-Arriaga, G., Sanz, J., Debayle, A., and Lehmann, G.. The behavior of the electron plasma boundary in ultraintense laser-highly overdense plasma interaction. Physics of Plasmas, 21(12), 2014.CrossRefGoogle Scholar
[29] Tsakiris, G. D., Eidmann, K., Meyer-ter Vehn, J., and Krausz, F.. Route to intense single attosecond pulses. New J. Phys., 8(1):19, 2006.CrossRefGoogle Scholar
[30] Gordienko, S., Pukhov, A., Shorokhov, O., and Baeva, T.. Relativistic doppler effect: Universal spectra and zeptosecond pulses. Phys. Rev. Lett., 93:115002, Sep. 2004.CrossRefGoogle ScholarPubMed
[31] Teubner, U. and Gibbon, P.. High-order harmonics from laser-irradiated plasma surfaces. Rev. Mod. Phys., 81:445–479, 2009.CrossRefGoogle Scholar
[32] Rödel, C., an der Brügge, D., Bierbach, J., Yeung, M., Hahn, T., Dromey, B., Herzer, S., Fuchs, S., Galestian Pour, A., Eckner, E., Behmke, M., Cerchez, M., Jäckel, O., Hemmers, D., Toncian, T., Kaluza, M. C., Belyanin, A., Pretzler, G., Willi, O., Pukhov, A., Zepf, M., and Paulus, G. G.. Harmonic generation from relativistic plasma surfaces in ultrasteep plasma density gradients. Phys. Rev. Lett., 109:125002, Sep. 2012.CrossRefGoogle ScholarPubMed
[33] Lichters, R., Meyer-ter Vehn, J., and Pukhov, A.. Shortpulse laser harmonics from oscillating plasma surfaces driven at relativistic intensity. Phys. Plasmas, 3(9):3425–3437, 1996.CrossRefGoogle Scholar
[34] Gibbon, P.. Harmonic generation by femtosecond laser-solid interaction: A coherent “water-window” light source? Phys. Rev. Lett., 76:50–53, Jan. 1996.CrossRefGoogle ScholarPubMed
[35] Geissler, M., Rykovanov, S., Schreiber, J., Meyer-ter Vehn, J., and Tsakiris, G. D.. 3d simulations of surface harmonic generation with few-cycle laser pulses. New J. Phys., 9(7):218, 2007.CrossRefGoogle Scholar
[36] Bulanov, S. V., Naumova, N. M., and Pegoraro, F.. Interaction of an ultrashort, relativistically strong laser pulse with an overdense plasma. Phys. Plasmas, 1(3):745–757, 1994.CrossRefGoogle Scholar
[37] von der Linde, D. and Rzízewski, K.. High-order optical harmonic generation from solid surfaces. Appl. Phys. B, 63(5):499–506, 1996.CrossRefGoogle Scholar
[38] Sanz, J., Debayle, A., and Mima, K.. Model for ultraintense laser-plasma interaction at normal incidence. Phys. Rev. E, 85:046411, Apr 2012.CrossRefGoogle ScholarPubMed
[39] Debayle, A., Sanz, J., Gremillet, L., and Mima, K.. Toward a self-consistent model of the interaction between an ultra-intense, normally incident laser pulse with an overdense plasma. Phys. Plasmas, 20(5):053107, 2013.CrossRefGoogle Scholar
[40] Baeva, T., Gordienko, S., and Pukhov, A.. Relativistic plasma control for single attosecond x-ray burst generation. Phys. Rev. E, 74:065401, Dec. 2006.CrossRefGoogle ScholarPubMed
[41] Tarasevitch, A., Lobov, K., Wünsche, C., and von der Linde, D.. Transition to the relativistic regime in high order harmonic generation. Phys. Rev. Lett., 98:103902, Mar. 2007.CrossRefGoogle Scholar
[42] Arber, T. D., Bennett, K., Brady, C. S., Lawrence-Douglas, A., Ramsay, M. G., Sircombe, N. J., Gillies, P., Evans, R. G., Schmitz, H., Bell, A. R., and Ridgers, C. P.. Contemporary particle-in-cell approach to laser-plasma modelling. Plasma Phys. Contr. F., 57(11):1–26, November 2015.CrossRefGoogle Scholar