• Matter and Radiation at Extremes
  • Vol. 7, Issue 4, 045901 (2022)
Hanzhi Zhao1、2, Zhengming Sheng1、2、3, and Suming Weng1、2、a)
Author Affiliations
  • 1Key Laboratory for Laser Plasmas (MoE), School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
  • 2Collaborative Innovation Center of IFSA, Shanghai Jiao Tong University, Shanghai 200240, China
  • 3Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai 200240, China
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    DOI: 10.1063/5.0086783 Cite this Article
    Hanzhi Zhao, Zhengming Sheng, Suming Weng. Nonlocal thermal transport in magnetized plasma along different directions[J]. Matter and Radiation at Extremes, 2022, 7(4): 045901 Copy Citation Text show less

    Abstract

    Nonlocal thermal transport in magnetized plasmas is studied theoretically and numerically with the Vlasov–Fokker–Planck (VFP) model, in which the magnetic field has nonzero components both perpendicular to and along the temperature gradient. Nonlocal heat transport is found in both the longitudinal and transverse directions, provided the temperature gradients are sufficiently large. The magnetic field tends to reduce the nonlocality of the thermal transport in the direction perpendicular to the magnetic field, i.e., the difference between the heat fluxes predicted by the Braginskii theory and the VFP simulation decreases with increasing magnetic field strength. When the initial temperature gradient is steep, the nonlocal heat flux depends not only on the present temperature profile, but also on its time history. Moreover, the contribution of high-order terms in the spherical harmonic expansion of the electron distribution function becomes important for a magnetized plasma, in particular for thermal transport in the direction perpendicular to the temperature gradient.
    ft+vfeEme+v×eBmecvf=Cee+Cei,

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    f(v,x,t)f0(v,x,t)+vvf1(v,x,t),

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    vf0eEmevf0eBmec×f1=νeif1,

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    f1=1νei2+ω2(νeigω×g),

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    g=vf0eEmevf0,

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    J=4πe3f1v3dv=c4π×B.

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    Q=2πme3f1v5dv=2πme3v5νei2+ω2(νeigω×g)dv.

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    eneE=Pe+J×B/c+αJ/neαb×J/neβTeβb×Te,

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    Q=β+52TeeJβTeeb×JκTeκb×Te,

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    κ=2TenemevTΩϕ11ϕ72ϕ7ϕ92+Ω2(ϕ11ϕ102+ϕ7ϕ1222ϕ9ϕ10ϕ12)ϕ72+Ω2ϕ102,κ=2TenemevTϕ14ϕ72+ϕ10ϕ92+2ϕ7ϕ9ϕ12+Ω2(ϕ14ϕ102ϕ10ϕ122)ϕ72+Ω2ϕ102,β=Ωϕ9ϕ7+Ω2ϕ12ϕ10ϕ72+Ω2ϕ10252,β=ϕ12ϕ7ϕ9ϕ10ϕ72+Ω2ϕ102,α=12menevTϕ7ϕ72+Ω2ϕ102,α=12menevTΩ1ϕ10ϕ72+Ω2ϕ102,

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    ϕn(Ω)=43πuneu2du1+Ω2u6.

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    ft+vxfxeEme+v×eBmecvf=Cee+Cei.

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    f(v,x,t)==0m=fm(v,x,t)Ym.

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    fmt+Am+Em+Bm=Cm.

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    vvvn,ttτn,xxλn,fvn3fnn,Eeτn2Emeλn,BeBτnme,

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    Te(x)=T0,x>2xmax/3,T0+2ΔT,x<xmax/3,T0+ΔTΔTcos3xxmaxπ,elsewhere.

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    Hanzhi Zhao, Zhengming Sheng, Suming Weng. Nonlocal thermal transport in magnetized plasma along different directions[J]. Matter and Radiation at Extremes, 2022, 7(4): 045901
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