Nonlinear Electron Heat Conduction Equation and Self-Similar Method for 1-D Thermal Waves in the Laser Heating of Solid Density DT Fuel

A highly nonlinear parabolic partial differential equation that models the electron heat transfer process in laser inertial fusion has been solved numerically. The strong temperature dependence of the electron thermal conductivity and heat loss term (Bremsstrahlung emission) makes this a highly nonlinear process. In this case, an efficient numerical method is developed for the energy transport mechanism from the region of energy deposition into the ablation surface by a combination of the Crank‐Nicolson scheme and the Newton‐Raphson method. The quantitative behavior of the electron temperature and the comparison between analytic and numerical solutions are also investigated. For more clarification, the accuracy and conservation of energy in the computations are tested. The numerical results can be used to evaluate the nonlinear electron heat conduction, considering the released energy of the laser pulse at the Deuterium‐Tritium (DT) targets and preheating by heat conduction ahead of a compression shock in the inertial confinement fusion (ICF) approach. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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Numerical Investigation Into the Highly Nonlinear Heat Transfer Equation with Bremsstrahlung Emission in the Inertial Confinement Fusion Plasmas

Habibi

Oloumi

Hosseinkhani

et al. 2015

Contrib. Plasma Phys.

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Effect of quantum correction on nonlinear thermal wave of electrons driven by laser heating

Nafari

Ghoranneviss

2016

Physics of Plasmas

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In thermal interaction of laser pulse with a deuterium-tritium (DT) plane, the thermal waves of electrons are generated instantly. Since the thermal conductivity of electron is a nonlinear function of temperature, a nonlinear heat conduction equation is used to investigate the propagation of waves in solid DT. This paper presents a self-similar analytic solution for the nonlinear heat conduction equation in a planar geometry. The thickness of the target material is finite in numerical computation, and it is assumed that the laser energy is deposited at a finite initial thickness at the initial time which results in a finite temperature for electrons at initial time. Since the required temperature range for solid DT ignition is higher than the critical temperature which equals 35.9 eV, the effects of quantum correction in thermal conductivity should be considered. This letter investigates the effects of quantum correction on characteristic features of nonlinear thermal wave, including temperature, penetration depth, velocity, heat flux, and heating and cooling domains. Although this effect increases electron temperature and thermal flux, penetration depth and propagation velocity are smaller. This effect is also applied to re-evaluate the side-on laser ignition of uncompressed DT.

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Nonlinear Electron Heat Conduction Equation and Self-Similar Method for 1-D Thermal Waves in the Laser Heating of Solid Density DT Fuel

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References 41 publications

Numerical Investigation Into the Highly Nonlinear Heat Transfer Equation with Bremsstrahlung Emission in the Inertial Confinement Fusion Plasmas

Numerical Investigation Into the Highly Nonlinear Heat Transfer Equation with Bremsstrahlung Emission in the Inertial Confinement Fusion Plasmas

Effect of quantum correction on nonlinear thermal wave of electrons driven by laser heating

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