• Matter and Radiation at Extremes
  • Vol. 8, Issue 2, 026901 (2023)
Cheng-Jian Xiao*, Guang-Wei Meng, and Ying-Kui Zhao
Author Affiliations
  • Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
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    DOI: 10.1063/5.0119240 Cite this Article
    Cheng-Jian Xiao, Guang-Wei Meng, Ying-Kui Zhao. Theoretical model of radiation heat wave in two-dimensional cylinder with sleeve[J]. Matter and Radiation at Extremes, 2023, 8(2): 026901 Copy Citation Text show less

    Abstract

    A semi-analytical model is constructed to investigate two-dimensional radiation heat waves (Marshak waves) in a low-Z foam cylinder with a sleeve made of high-Z material. In this model, the energy loss to the high-Z wall is regarded as the primary two-dimensional effect and is taken into account via an indirect approach in which the energy loss is subtracted from the drive source and the wall loss is ignored. The interdependent Marshak waves in the low-Z foam and high-Z wall are used to estimate the energy loss. The energies and the heat front position calculated using the model under typical inertial confinement fusion conditions are verified by simulations. The validated model provides a theoretical tool for studying two-dimensional Marshak waves and should be helpful in providing further understanding of radiation transport.
    ρet=43x1KρσT4x,

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    e=fTβρμ,1K=gTαρλ,

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    ζ(x,t)=[1y(x,t)]1/(1ε),

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    xF2(t)=2+ε1εCHε(t)0tH(t1)dt1,

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    ζ(x,t)=T(x,t)Ts(t)4+α,

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    y(x,t)=x/xF(t),

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    H(t)=Ts(t)4+α,

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    C=164+αgσ3fρ2μ+λ.

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    Etotal(t)=0tF(0,t)Sdt,

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    F(0,t)=2σTDrive4(t)2σTs4(t),

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    Etotal(t)=xF(t)Hε(t)Sfρ(1μ)(1ε),

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    dEWall(z,t)dz=2πf̃T(z)β̃ρ1μ̃xFR(z,t)[xFR(z,t)+R(2+ξ)](2+ξ)(1+ξ),

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    EWall(t)=0xFZ(t)dEWall(z,t)dzdziEWalli(t),

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    EFoam(t)=xFZ(t)Hε(t)Sfρ(1μ)(1ε),

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    Etotal(t)=EFoam(t)+EWall(t)

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    g=1/9175g/cm2,α=3.53,λ=0.75,f=8.78MJ,β=1.1,μ=0.09,

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    g̃=1/7200g/cm2,α̃=1.5,λ̃=0.2,f̃=3.4MJ,β̃=1.6,μ̃=0.14.

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    g=1/2818.1g/cm2,α=2.79,λ=0.81,f=21.17MJ,μ=0.06,β=1.06.

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    Cheng-Jian Xiao, Guang-Wei Meng, Ying-Kui Zhao. Theoretical model of radiation heat wave in two-dimensional cylinder with sleeve[J]. Matter and Radiation at Extremes, 2023, 8(2): 026901
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