Matter and Radiation at Extremes, Volume. 7, Issue 4, 045901(2022)

Nonlocal thermal transport in magnetized plasma along different directions

Hanzhi Zhao1...2, Zhengming Sheng1,2,3, and Suming Weng12,a) |Show fewer author(s)
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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    Figures & Tables(9)
    Dependence of transport coefficients (a) κ⊥, (b) κ∧, (c) β⊥, and (d) β∧ on the Hall coefficient ωτei.
    Heat transport in a plasma for a temperature gradient λe/LT ∼ 5 × 10−5 in a magnetic field B = Bxex + Bzez, with eBxτn/me = ωxτn = 0.1 and eBzτn/me = ωzτn = 0.1, where the heat fluxes along the x, y, and z directions obtained from the simulation (dots) are compared with those from Braginskii’s local theory (solid lines), and the temperature profile is shown by the blue line.
    Heat flux distributions in the absence and presence of a magnetic field B = Bzez. (a) and (b) Heat flux components Qx and Qy along the x and y directions, respectively, for a moderately large temperature gradient λe/LT ≈ 0.01 at t = 200τn (the time at which the heat wave front roughly reaches the boundary). (c) and (d) Heat flux components Qx and Qy, respectively, for an extremely large temperature gradient λe/LT ≈ 0.05 at t = 20τn. The blue solid line shows the initial temperature profile. The VFP simulation results are shown by the solid lines with ωzτn = 0.05 (red) or ωzτn = 0 (black), and the dotted lines are calculated from Eq. (9) with ωzτn = 0.05 (red) or ωzτn = 0 (black), where the instantaneous density and temperature profiles obtained from the VFP simulations are employed. Note that Qy = 0 in the case Bz = 0.
    Heat flux distributions with a purely transverse magnetic field Bz or a magnetic field B = Bxex + Bzez at t = 20τn. (a)–(c) Heat flux components Qx, Qy, and Qz, respectively, for a temperature gradient λe/LT ≈ 0.05. The green lines are for ωxτn = 0.1 and ωzτn = 0.1, and the red lines are for ωxτn = 0 and ωzτn = 0.1, with the solid lines being from the simulation and the dotted lines from the Braginskii theory.
    Dependence of the time-averaged ratio QVFP/QBrag of the heat flux obtained from the VFP simulation to that estimated by the Braginskii theory within the first 100 collision cycles at xmax/2, where λe/LT ≈ 0.05 and the distribution function is calculated up to harmonic order ℓ = 8. Different lines correspond to different strengths of the transverse magnetic field component Bz, and the dotted line in (a) corresponds to the heat flux in the absence of a magnetic field.
    Time evolution of the heat flux components Qx, Qy, and Qz and the instantaneous scale length of the temperature gradient LT at the point xmax/2. The initial scale length of the temperature gradient and the applied magnetic field B = Bxex + Bzez are the same as the parameters in Fig. 4. The solid lines show the heat flux in the x (black), y (red), and z (green) directions, while the dotted line represents the instantaneous scale length of the temperature gradient. The simulation is carried out with a spherical harmonic expansion up to order ℓ = 8.
    Ratios of the higher-order spherical harmonic terms f10, f20, f30, and f40 to the zeroth-order (isotropic) term f00 of the EDF at longitudinal positions (a) x = xmax/3, (b) x = xmax/2, and (c) x = 2xmax/3.
    (a)–(c) Time evolution of the heat flux components Qx, Qy, and Qz, respectively, at the point x = xmax/2, where the comparison is made for different orders of the spherical harmonic expansion under a temperature gradient λe/LT ≈ 0.05 and a magnetic field B = Bxex + Bzez, with eBxτn/me = ωxτn = 0.1 and eBzτn/me = ωzτn = 0.1.
    (a)–(c) Heat flux distributions Qx, Qy, and Qz, respectively, at t = 20τn. The plasma and the magnetic field parameters are as in Fig. 8. The black lines and red lines are obtained with the first and ℓ = 8 spherical harmonic expansion orders, respectively, and the dotted line is the result from the Braginskii theory.
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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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    Paper Information

    Category: Inertial Confinement Fusion Physics

    Received: Jan. 28, 2022

    Accepted: May. 15, 2022

    Published Online: Aug. 8, 2022

    The Author Email: Weng Suming (wengsuming@sjtu.edu.cn)

    DOI:10.1063/5.0086783

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