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Influence of spatial geometrical curvature on nonlocal electron heat transport in expanding plasmas

Zheng Wei-Zhen Zhao Bin Hu Guang-Yue Zheng Jian

Influence of spatial geometrical curvature on nonlocal electron heat transport in expanding plasmas

Zheng Wei-Zhen, Zhao Bin, Hu Guang-Yue, Zheng Jian
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  • The electron thermal transport in fluid theory would be inaccurate when the collisionality is not enough, and the Fokker-Planck (FP) simulations are usually employed to resolve the inadequacies. In this paper, the one-dimensional Fokker-Planck code is extended to handle the cylindrical and spherical geometries in which the electron distribution functions are solved in the reference frame of the ion fluid. The FP code is validated in the fluid limit by comparing with fluid (MULTI) simulations. Then, the expansions of plasmas in different spatial geometries are simulated with the FP and fluid codes. As the main characters of nonlocal transport, the electron thermal transport inhibition and preheating are investigated in expanding plasmas. The spherical nonlocal theory can give the thermal transport inhibition and preheating phenomenon, which is exploited to fit the heat flux with variation of fitting parameter . The spherical nonlocal theory will reproduce Spizer-Hrm expression as = 0. Then we analyze the heat flux after the plasma expanding 200 ps with a uniform initial temperature T = 100 eV and density ne= 1 1021 /cm3. By comparing the heat flux computed by spherical nonlocal thermal transport theory and FP simulation, it is found that (n-1)/r term in Eq. (3a) cannot be neglected when the radius is small and the geometrical curvature effect will decrease the nonlocality of transport in outer expanding plasmas. The geometrical curvature effect leads to a smaller thermal transport inhibition and preheating in the expanding plasmas as comparing the spherical case with the planar one. The expansions of plasmas in different spatial geometries are also simulated with the FP and fluid codes under the initial conditions which are similar to the inertial confinement fusion. The same influence of geometrical curvature on nonlocal electron thermal transport are also obtained.
      Corresponding author: Zhao Bin, zhaobin@mail.ustc.edu.cn
    • Funds: Project supported by the Natural Science Foundation of China (Grant No. 11275202).
    [1]

    Spitzer L J, Hrm R 1953 Phys. Rev. 89 977

    [2]

    Bell A R 1996 Transport in Laser-Produced Plasmas, in Laser Plasma Interactions 5 : Inertial Confinement Fusion (Scottish Universities Summer School in Physics Institute of Physics press) pp139-168

    [3]

    Bell A R 1983 Phys. Fluids 26 279

    [4]

    Luciani J F, Mora P, Virmont J 1983 Phys. Rev. Lett. 51 1664

    [5]

    Malone R C, McCrory R L, Morse R L 1975 Phys. Rev. Lett. 34 721

    [6]

    Gotchev O V, Goncharov V N, Knauer J P, Boehly T R, Collins T J B, Epstein R, Jaanimagi P A, Meyerhofer D D 2006 Phys. Rev. Lett. 96 115005

    [7]

    Hu S X, Smalyuk V A, Goncharov V N, Skupsky S, Sangster T C, Meyerhofer D D, Shvarts D 2008 Phys. Rev. Lett. 101 055002

    [8]

    Sunahara A, Delettrez J A, Stoeckl C, Short R W, Skupsky S 2003 Phys. Rev. Lett. 91 095003

    [9]

    Epperlein E M, Short R W 1991 Phys. Fluids B 3 3092

    [10]

    Bychenkov V Y, Rozmus W, Tikhonchuk V T 1995 Phys. Rev. Lett. 75 4405

    [11]

    Weng S M, Sheng Z M, Zhang J 2009 Acta Phys. Sin. 58 454 (in Chinese) [翁苏明, 盛政明, 张杰 2009 物理学报 58 454]

    [12]

    Thomas A G R, Tzoufras M, Robinson A P L, Kingham R J, Ridgers C P, Sherlock M, Bell A R 2012 Journal of Computational Physics 231 1051

    [13]

    Bychenkov V Y, Matte J P, Johnston T W 1996 Phys. Plasmas 3 3518

    [14]

    Bychenkov V Y, Matte J P, Johnston T W 1996 Phys. Plasmas 3 1280

    [15]

    Soboleva T K, Krasheninnikov S I, Catto P J 2004 Contrib. Plasma Phys. 44 95

    [16]

    Epperlein E M 1994 Laser and Particle Beams 12 257

    [17]

    Zhao B, Zheng J 2008 Plasma Sci. Technol. 10 22

    [18]

    Li J, Zhao B, Li H, Zheng J 2010 Plasma Phys. Control. Fusion 52 085008

    [19]

    Atzeni S, Meyer-ter-Vehn J 2004 The Physics of Inertial Fusion Oxford Science Pub. pp133-135

  • [1]

    Spitzer L J, Hrm R 1953 Phys. Rev. 89 977

    [2]

    Bell A R 1996 Transport in Laser-Produced Plasmas, in Laser Plasma Interactions 5 : Inertial Confinement Fusion (Scottish Universities Summer School in Physics Institute of Physics press) pp139-168

    [3]

    Bell A R 1983 Phys. Fluids 26 279

    [4]

    Luciani J F, Mora P, Virmont J 1983 Phys. Rev. Lett. 51 1664

    [5]

    Malone R C, McCrory R L, Morse R L 1975 Phys. Rev. Lett. 34 721

    [6]

    Gotchev O V, Goncharov V N, Knauer J P, Boehly T R, Collins T J B, Epstein R, Jaanimagi P A, Meyerhofer D D 2006 Phys. Rev. Lett. 96 115005

    [7]

    Hu S X, Smalyuk V A, Goncharov V N, Skupsky S, Sangster T C, Meyerhofer D D, Shvarts D 2008 Phys. Rev. Lett. 101 055002

    [8]

    Sunahara A, Delettrez J A, Stoeckl C, Short R W, Skupsky S 2003 Phys. Rev. Lett. 91 095003

    [9]

    Epperlein E M, Short R W 1991 Phys. Fluids B 3 3092

    [10]

    Bychenkov V Y, Rozmus W, Tikhonchuk V T 1995 Phys. Rev. Lett. 75 4405

    [11]

    Weng S M, Sheng Z M, Zhang J 2009 Acta Phys. Sin. 58 454 (in Chinese) [翁苏明, 盛政明, 张杰 2009 物理学报 58 454]

    [12]

    Thomas A G R, Tzoufras M, Robinson A P L, Kingham R J, Ridgers C P, Sherlock M, Bell A R 2012 Journal of Computational Physics 231 1051

    [13]

    Bychenkov V Y, Matte J P, Johnston T W 1996 Phys. Plasmas 3 3518

    [14]

    Bychenkov V Y, Matte J P, Johnston T W 1996 Phys. Plasmas 3 1280

    [15]

    Soboleva T K, Krasheninnikov S I, Catto P J 2004 Contrib. Plasma Phys. 44 95

    [16]

    Epperlein E M 1994 Laser and Particle Beams 12 257

    [17]

    Zhao B, Zheng J 2008 Plasma Sci. Technol. 10 22

    [18]

    Li J, Zhao B, Li H, Zheng J 2010 Plasma Phys. Control. Fusion 52 085008

    [19]

    Atzeni S, Meyer-ter-Vehn J 2004 The Physics of Inertial Fusion Oxford Science Pub. pp133-135

  • [1] Weng Su-Ming, Sheng Zheng-Ming, Zhang Jie. Generation of plasma current under arbitrary strong direct current electric field. Acta Physica Sinica, 2009, 58(12): 8454-8460. doi: 10.7498/aps.58.8454
    [2] QU ZHI-LIN, HU GANG. TIME-DEPENDENT SOLUTION OF THE FOKKER-PLANCK EQUATION OF NONLINEAR NONPOTENTIAL SYSTEMS. Acta Physica Sinica, 1992, 41(9): 1396-1405. doi: 10.7498/aps.41.1396
    [3] HU GANG. TIME DEPENDENT SOLUTION OF FOKKER-PLANCK EQUATION WITH NON-LINEAR DRIFT FORCE. Acta Physica Sinica, 1985, 34(5): 573-580. doi: 10.7498/aps.34.573
    [4] HU GANG, WANG SHENG-GUI. TIME-DEPENDENT PROBLEM OF FOKKER-PLANCK EQUATION OF MANY VARIABLES WITH A MULTI-STABLE POTENTIAL. Acta Physica Sinica, 1986, 35(6): 771-778. doi: 10.7498/aps.35.771
    [5] Yang Hui-Hui, Ning Li-Juan. Approximate time-dependent solution of Fokker-Planck equation with non-linear drift force. Acta Physica Sinica, 2013, 62(18): 180501. doi: 10.7498/aps.62.180501
    [6] Zhao Chao-Ying, Tan Wei-Han, Guo Qi-Zhi. The solution of the Fokker-Planck equation of non-degenerate parametric amplific ation system for generation of squeezed light. Acta Physica Sinica, 2003, 52(11): 2694-2699. doi: 10.7498/aps.52.2694
    [7] ZHENG WEI-MOU. EXACTLY SOLVABLE MODELS FOR THE FOKKER-PLANCK EQUATION. Acta Physica Sinica, 1986, 35(2): 247-253. doi: 10.7498/aps.35.247
    [8] LU ZHI-HENG, LIN JIAN-HENG, HU GANG. A NUMERICAL STUDY OF THE FOKKER-PLANCK EQUATION FOR STOCHASTIC RESONANCE PROBLEM. Acta Physica Sinica, 1993, 42(10): 1556-1566. doi: 10.7498/aps.42.1556
    [9] ZHU XUE-GUANG, KUANG GUANG-LI, ZHAO YAN-PING, LI YOU-YI, XIE JI-KANG. FOKKER-PLANCK EQUATION IN THE APPLICATION OF FAST WAVE HEATING. Acta Physica Sinica, 1998, 47(7): 1137-1142. doi: 10.7498/aps.47.1137
    [10] Zhu Chang-Chun, Bao Wen-Xing. Study of thermal conduction of carbon nanotube by molecular dynamics. Acta Physica Sinica, 2006, 55(7): 3552-3557. doi: 10.7498/aps.55.3552
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  • Received Date:  10 April 2015
  • Accepted Date:  14 May 2015
  • Published Online:  05 October 2015

Influence of spatial geometrical curvature on nonlocal electron heat transport in expanding plasmas

    Corresponding author: Zhao Bin, zhaobin@mail.ustc.edu.cn
  • 1. Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China;
  • 2. Department of Mathematics and Physics, Nanjing Institute of Technology, Nanjing 211167, China
Fund Project:  Project supported by the Natural Science Foundation of China (Grant No. 11275202).

Abstract: The electron thermal transport in fluid theory would be inaccurate when the collisionality is not enough, and the Fokker-Planck (FP) simulations are usually employed to resolve the inadequacies. In this paper, the one-dimensional Fokker-Planck code is extended to handle the cylindrical and spherical geometries in which the electron distribution functions are solved in the reference frame of the ion fluid. The FP code is validated in the fluid limit by comparing with fluid (MULTI) simulations. Then, the expansions of plasmas in different spatial geometries are simulated with the FP and fluid codes. As the main characters of nonlocal transport, the electron thermal transport inhibition and preheating are investigated in expanding plasmas. The spherical nonlocal theory can give the thermal transport inhibition and preheating phenomenon, which is exploited to fit the heat flux with variation of fitting parameter . The spherical nonlocal theory will reproduce Spizer-Hrm expression as = 0. Then we analyze the heat flux after the plasma expanding 200 ps with a uniform initial temperature T = 100 eV and density ne= 1 1021 /cm3. By comparing the heat flux computed by spherical nonlocal thermal transport theory and FP simulation, it is found that (n-1)/r term in Eq. (3a) cannot be neglected when the radius is small and the geometrical curvature effect will decrease the nonlocality of transport in outer expanding plasmas. The geometrical curvature effect leads to a smaller thermal transport inhibition and preheating in the expanding plasmas as comparing the spherical case with the planar one. The expansions of plasmas in different spatial geometries are also simulated with the FP and fluid codes under the initial conditions which are similar to the inertial confinement fusion. The same influence of geometrical curvature on nonlocal electron thermal transport are also obtained.

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