Analytic solutions for delocalized heat transport

Abstract

Comprehensive understanding of nonlocal transport is mandatory for many applications of laser–plasma interaction physics, such as inertial confinement fusion and modeling of astrophysical phenomena in the laboratory. Theoretical description is important for guiding numerical simulations and experiments. In this article, an analytic approach is developed: by using a simple integral differential model, we calculate the preheating of plasma upstream of the heat front associated with nonlocal transport. A detailed comparison of various transport configurations as a function of the boundary conditions and the nonlinearity parameter is presented in the context of laser–plasma interaction. Three important results are demonstrated in this paper. First, analytical expressions for all possible self-similar solutions of local nonlinear transport are obtained. Second, a systematic comparison of various nonlocal kernels and forms of the delocalization length is performed. Third, an analytic expression for the temperature profile upstream of the heat front is obtained.