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

Abstract

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)

The Coulomb logarithm evaluation effects on the inverse Bremsstrahlung absorption (IBA) in laser fusion plasmas

“…[11] In fact, Figure 4 shows a comparison of the electron heating processes between the Spitzer model (solid curve) and the BPS model (dashed curve). It should be noted that the reliability of this algorithm has been proved in previous work.…”

“…It should be noted that the reliability of this algorithm has been proved in previous work. [11] In fact, Figure 4 shows a comparison of the electron heating processes between the Spitzer model (solid curve) and the BPS model (dashed curve). In this case, the laser parameters are chosen for a rectangular laser pulse with = 0.351 μm, pulse duration 0 = 4 ns, and intensity I = 6 × 10 20 erg/cm 2 .…”

“…[11] Using this numerical algorithm, comparisons between the IBA mechanisms in the Spitzer model and the BPS model will be presented. Thus, understanding the physics of laser fusion plasmas needs to use a consistent numerical model of the heat transfer process.…”

“…In this context, a reliable hybrid approach using the Crank-Nicolson and Newton-Raphson methods for solving the non-linear heat transfer equation has been already introduced. [11] Using this numerical algorithm, comparisons between the IBA mechanisms in the Spitzer model and the BPS model will be presented. Moreover, the thermal diffusion and absorption terms will also be investigated.…”

Heat Transfer in a Porous Radial Fin: Analysis of Numerically Obtained Solutions

“…In this research we will require such a technique, known as the Newton-Raphson method, given the presence of the nonlinear sink terms. The Crank-Nicolson method incorporating the NewtonRaphson method has been used to determine the solution of a nonlinear diffusion equation (see Kouhia [41] and Habibi et al [42]) to model the electron heat transfer process in laser inertial fusion for the energy transport mechanism from the region of energy decomposition into the ablation surface. The method proved to be efficient as per the numerical results obtained and hence is a natural extension of the method employed in the previous subsection.…”