Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-26T20:42:53.746Z Has data issue: false hasContentIssue false
  • English
  • Français

Vlasov-Fokker-Planck Simulations for High-Power Laser-Plasma Interactions

Published online by Cambridge University Press:  20 August 2015

Su-Ming Weng ,
Zheng-Ming Sheng ,
Hui Xu  and
Jie Zhang
Su-Ming Weng*
Affiliation:
Beijing National Laboratory of Condensed Matter Physics, Institute of Physics, CAS, Beijing 100190, China Theoretical Quantum Electronics (TQE), Technische Universität Darmstadt, D-64289 Darmstadt, Germany
Zheng-Ming Sheng*
Affiliation:
Beijing National Laboratory of Condensed Matter Physics, Institute of Physics, CAS, Beijing 100190, China Key Laboratory for Laser Plasmas (MoE) and Department of Physics, Shanghai Jiaotong University, Shanghai 200240, China
Hui Xu
Affiliation:
Shandong Provincial Key Laboratory of Laser Polarization and Information Technology, Department of Physics, Qufu Normal University, Qufu 273165, China
Jie Zhang
Affiliation:
Beijing National Laboratory of Condensed Matter Physics, Institute of Physics, CAS, Beijing 100190, China Key Laboratory for Laser Plasmas (MoE) and Department of Physics, Shanghai Jiaotong University, Shanghai 200240, China
*
Email:[email protected]
Corresponding author.Email:[email protected]
Get access

Abstract

A review is presented on our recent Vlasov-Fokker-Planck (VFP) simulation code development and applications for high-power laser-plasma interactions. Numerical schemes are described for solving the kinetic VFP equation with both electron-electron and electron-ion collisions in one-spatial and two-velocity (1D2V) coordinates. They are based on the positive and flux conservation method and the finite volume method, and these two methods can insure the particle number conservation. Our simulation code can deal with problems in high-power laser/beam-plasma interactions, where highly non-Maxwellian electron distribution functions usually develop and the widely-used perturbation theories with the weak anisotropy assumption of the electron distribution function are no longer in point. We present some new results on three typical problems: firstly the plasma current generation in strong direct current electric fields beyond Spitzer-Härm’s transport theory, secondly the inverse bremsstrahlung absorption at high laser intensity beyond Langdon’s theory, and thirdly the heat transport with steep temperature and/or density gradients in laser-produced plasma. Finally, numerical parameters, performance, the particle number conservation, and the energy conservation in these simulations are provided.

Keywords

82D1082C3178M1280A20Vlasov-Fokker-Planck equationelectric conductivityinverse bremsstrahlungnonlocal heat transportpositive and flux conservation methodfinite volume method
Type
Research Article
Information
Communications in Computational Physics , Volume 11 , Issue 4 , April 2012 , pp. 1236 - 1260
Copyright
Copyright © Global Science Press Limited 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Spitzer, L. and Härm, R., Transport phenomena in a completely ionized gas, Phys. Rev., 89(1953), 977–981.Google Scholar
[2]Langdon, A. B., Nonlinear inverse bremsstrahlung and heated-electron distributions, Phys. Rev. Lett., 44(1980), 575–579.Google Scholar
[3]Filbet, F., Sonnendrücker, E. and Bertrand, P., Conservative numerical schemes for the Vlasov equation, J. Comput. Phys., 172(2001), 166–187.Google Scholar
[4]Fijalkow, E., A numerical solution to the Vlasov equation, Comput. Phys. Commun., 116(1999), 319–328.CrossRefGoogle Scholar
[5]Weng, S. M., Sheng, Z. M., He, M. Q., Wu, H. C., Dong, Q. L., and Zhang, J., Inverse bremsstrahlung absorption and the evolution of electron distributions accounting for electron-electron collisions, Phys. Plasmas, 13(2006), 113302.CrossRefGoogle Scholar
[6]Karney, C. F. F., Fokker-Planck and quasilinear codes, Comput. Phys. Rep., 4(1986), 183–244.Google Scholar
[7]Trubnikov, B. A., Particle imteractions in a fully ionized plasma, Reviews of Plasma Physics, 1(1965), 105–204.Google Scholar
[8]Chacón, L., Barnes, D. C., Knoll, D. A. and Miley, G. H., An implicit energy-conservative 2D Fokker-Planck algorithm: I. Difference scheme, J. Comput. Phys., 157(2000), 618–653.Google Scholar
[9]Chang, J. S. and Cooper, G., A practical difference scheme for Fokker-Planck equations, J. Comput. Phys., 6(1970), 1–16.Google Scholar
[10]Marchuk, G. I., Methods of numerical mathematics, Springer-Verlag, New York, 1975.Google Scholar
[11]Benage, J. F., Shanahan, W. R., and Murillo, M. S., Electrical resistivity measurements of hot dense aluminum, Phys. Rev. Lett., 83(1999), 2953–2956; Lencioni, D. E., Measurement of plasma conductivity for electric fields larger than the runaway field, Phys. Fluids, 14(1971), 566–569; Hui, B. H., Winsor, N. K., and Coppi, B., Collisional theory of electrical resistivity in trapped electron regimes, Phys. Fluids, 20(1977), 1275–1278.Google Scholar
[12]Shkarofsky, I. P., Shoucri, M. M., and Fuchs, V., Numerical solution of the Fokker-Planck equation with a dc electric field, Comput. Phys. Commun., 71(1992), 269–284.Google Scholar
[13]Shkarofsky, I. P., Johnston, T. W., and Bachynski, M. P., The particle kinetics of plasma, Addison-Wesley, Reading, Mass., 1966Google Scholar
[14]Weng, S. M., Sheng, Z. M., He, M. Q., Zhang, J., Norreys, P. A., Sherlock, M., and Robinson, A. P. L., Plasma currents and electron distribution functions under a dc electric field of arbitrary strength, Phys. Rev. Lett., 100(2008), 185001.CrossRefGoogle Scholar
[15]Dreicer, H., Electron and ion runaway in a fully ionized gas. I, Phys. Rev., 115(1959), 238–249;Google Scholar
Dreicer, H., Electron and ion runaway in a fully ionized gas. II, Phys. Rev., 115(1960), 329–342.Google Scholar
[16]Goldston, R. J. and Rutherford, P. H., Introduction to plasma physics, Institute of Physics Publishing, Bristol, 1995.Google Scholar
[17]Meyer-ter-Vehn, J.et al., On electron transport in fast ignition research and the use of few-cycle PW-range laser pulses, Plasma Phys. Controlled Fusion, 47(2005), B807–B813.CrossRefGoogle Scholar
[18]Honrubia, J. J. and Meyer-ter-Vehn, J., Three-dimensional fast electron transport for ignition-scale inertial fusion capsules, Nucl. Fusion, 46(2006), L25–L28.Google Scholar
[19]Pert, G. J., Inverse bremsstrahlung in strong radiation fields at low temperatures, Phys. Rev. E, 51(1995), 4778–4789.Google Scholar
[20]Betti, R., Zhou, C.D., Anderson, K. S.et al., Shock ignition of thermonuclear fuel with high areal density, Phys. Rev. Lett., 98(2007), 155001;Google Scholar
Perkins, L. J., Betti, R., LaFortune, K. N., and Williams, W. H., Shock ignition: a new approach to high gain inertial confinement fusion on the national ignition facility, Phys. Rev. Lett., 103(2009), 045004;Google Scholar
Ribeyre, X, Schurtz, G, Lafon, M, Galera, S and Weber, S, Shock ignition: an alternative scheme for HiPER, Plasma Phys. Control. Fusion, 51(2009), 015013.Google Scholar
[21]Murakami, M. and Nagatomo, H., A new twist for inertial fusion energy: Impact ignition, Nucl. Inst. and Meth. in Phys. Res. A, 544(2005), 67;Google Scholar
Murakami, M., Nagatomo, H., Azechi, H., Ogando, F., and Eliezer, S., Innovative ignition scheme for ICF-impact fast ignition, Nucl. Fu sion, 46(2006), 99; Karasik, M., Weaver, J. L., Aglitskiy, Y.et al., Acceleration to high velocities and heating by impact using Nike KrF laser, Phys. Plasmas, 17(2010), 056317.Google Scholar
[22]Ping, Y., Shepherd, R., Lasinski, B. F.et al., Absorption of short laser pulses on solid targets in the ultrarelativistic regime, Phys. Rev. Lett., 100(2008), 085004.CrossRefGoogle ScholarPubMed
[23]Gibbon, P., Short pulse laser interactions with matter, Imperial College Press, London, 2005.Google Scholar
[24]Wilks, S. C. and Kruer, W. L., Absorption of ultrashort, ultra-intense laser light by solids and overdense plasmas, IEEE J. Quantum Electron., 33(1997), 1954.Google Scholar
[25]Price, D. F., More, R.M., Walling, R. S.et al., Absorption of ultrashort laser pulses by solid targets heated rapidly to temperatures 1ł1000 eV, Phys. Rev. Lett., 75(1995), 252.Google Scholar
[26]Ridgers, C. P., Kingham, R. J., and Thomas, A. G. R., Magnetic cavitation and the reemergence of nonlocal transport in laser plasmas, Phys. Rev. Lett., 100(2008), 075003.Google Scholar
[27]Weng, S. M., Sheng, Z. M., and Zhang, J., Inverse bremsstrahlung absorption with nonlinear effects of high laser intensity and non-Maxwellian distribution, Phys. Rev. E, 80(2009), 056406.Google Scholar
[28]Mulser, P., Cornolti, F., Bésuelle, E., and Schneider, R., Time-dependent electron-ion collision frequency at arbitrary laser intensity-temperature ratio, Phys. Rev. E, 63(2000), 016406.Google Scholar
[29]Bésuelle, E., Salomaa, R. R. E., and Teychenné, D., Coulomb logarithm in femtosecond-laser-matter interaction, Phys. Rev. E, 60(1999), 2260–2263.Google Scholar
[30]David, N., Spence, D. J., and Hooker, S. M., Molecular-dynamic calculation of the inverse-bremsstrahlung heating of non-weakly-coupled plasmas, Phys. Rev. E, 70(2004), 056411.Google Scholar
[31]Bell, A. R. and Kingham, R. J., Resistive collimation of electron beams in laser-produced plasmas, Phys. Rev. Lett., 91(2003), 035003; and reference therein.Google Scholar
[32]Bell, A. R., Electron energy transport in ion waves and its relevance to laser-produced plasmas, Phys. Fluids, 26(1983), 279–284.Google Scholar
[33]Yu, Q. Z., Li, Y. T., Weng, S. M., Dong, Q. L., Liu, F., Zhang, Z., Zhao, J., Lu, X., Danson, C., Pepler, D., Jiang, X. H., Liu, Y. G., Huang, L. Z., Liu, S. Y., Ding, Y. K., Wang, Z. B., Gu, Y., He, X. T., Sheng, Z. M., and Zhang, J., Nonlocal heat transport in laser-produced aluminum plasmas, Phys. Plasmas, 17(2010), 043106.Google Scholar
[34]Fabbro, R., Max, C. and Fabre, E., Planar laser-driven ablation: Effect of inhibited electron thermal conduction, Phys. Fluids, 28(1985), 1463–1481.CrossRefGoogle Scholar
[35]Hawreliak, J., Chambers, D. M., Glenzer, S. H., Gouveia, A., Kingham, R. J., R. S. Marjorib-anks, Pinto, P. A., Renner, O., Soundhauss, P., Topping, S., Wolfrum, E., Young, P. E., and Wark, J. S., Thomson scattering measurements of heat flow in a laser-produced plasma, J. Phys. B, 37(2004), 1541–1551.Google Scholar
[36]Malone, R. C., McCrory, R. L. and Morse, R. L., Indications of strongly flux-limited electron thermal conduction in laser-target experiments, Phys. Rev. Lett., 34(1975), 721–724.Google Scholar
[37]Bell, A. R., Evans, R. and Nicholas, D. J., Elecron energy transport in steep temperature gradients in laser-produced plasmas, Phys. Rev. Lett., 46(1981), 243–246.Google Scholar
[38]Luciani, J. F. and Mora, P., Nonlocal heat transport due to steep temperature gradients, Phys. Rev. Lett., 51(1983), 1664–1667;Google Scholar
Schurtz, G. P., Nicoläı, Ph. D., and Busquet, M., A nonlocal electron conduction model for multidimensional radiation hydrodynamics codes, Phys. Plasmas, 7(2000), 4238.Google Scholar
[39]Albritton, J. R., Williams, E. A., and Bernstein, I. B., Nonlocal electron heat transport by not quite Maxwell-Boltzmann distributions, Phys. Rev. Lett., 57(1986), 1887–1890.Google Scholar
[40]Kishimoto, Y., Mima, K., and Haines, M. G., An extension of Spitzer-Härm theory on thermal transport to steep temperature gradient case. II. Integral representation, J. Phys. Soc. Jpn., 57(1988), 1972–1986.Google Scholar
[41]Goncharov, V. N., Gotchev, O. V., and Vianello, E., Early stage of implosion in inertial confinement fusion: Shock timing and perturbation evolution, Phys. Plasmas, 13(2006), 012702.Google Scholar
[42]Christiansen, J. P., Ashby, D. E. T. F. and Roberts, K. V., MEDUSA a one-dimensional laser fusion code, Comput. Phys. Commun., 7(1974), 271–287.Google Scholar