Theory and simulation of non-local thermal smoothing for arbitrary scale length modulation

We present a theory that describes the non-local heat transport and associated thermal smoothing modeling the non-uniform laser illumination by solving the steady state Fokker-Planck (FP) equation. A method that connects higher order Chapman-Enskog expansion for low energy electrons and convolution formula for high energy ones through the self-consistent determination of the electric field is developed. The theory explicitly expresses the heat flux for arbitrary periodic temperature modulation given by ( ) sin a T T T kx δ ε = with moderate wave number 0.1 e kλ ≤ , where e λ is the electron mean free path. The theory is compared with onedimensional FP simulations by which we investigate the relaxation of sinusoidal temperature perturbations. Reduction of the heat flux from the Spitzer-Härm (SH) theory and the hysteresis nature are found to be reproduced. As the wavelength of the modulation becomes shorter, the contribution from high energy electrons to the heat flux is found to increase whereas the total amount of the heat flux is reduced in proportion to ( ) e kλ .