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

TL;DR

This paper solves a nonlinear 1-D electron heat conduction equation using a self-similar method to analyze thermal wave propagation during laser heating of solid DT fuel in inertial confinement fusion.

Contribution

It introduces a self-similar analytical solution for the nonlinear electron heat conduction equation in laser-heated solid DT fuel.

Findings

Derived an exact self-similar solution for the nonlinear conduction equation

Analyzed thermal wave propagation in laser-heated DT fuel

Provided insights into rapid boundary layer heating in ICF

Abstract

Electron heat conduction is one of the ways that energy transports in laser heating of fusible target material. The aim of Inertial Confinement Fusion (ICF) is to show that the thermal conductivity is strongly dependent on temperature and the equation of electron heat conduction is a nonlinear equation. In this article, we solve the one-dimensional (1-D) nonlinear electron heat conduction equation with a self-similar method (SSM). This solution has been used to investigate the propagation of 1-D thermal wave from a deuterium-tritium (DT) plane source which occurs when a giant laser pulse impinges onto a DT solid target. It corresponds to the physical problem of rapid heating of a boundary layer of material in which the energy of laser pulse is released in a finite initial thickness.