Self similar nonlocal electron heat flow

The well known self similar heat diffusion solutions of Zel'dovich and Raizer [1], for a heat wave advancing from a boundary at a fixed temperature or a fixed heat flux do not keep the ratio R of the scale length to the mean free path constant. Instead, R increases and the solution becomes increasingly valid because Spitzer-Harm [2] heat flow is increasingly applicable. A self similar solution exists which keeps R constant, if one assumes that the boundary heat flux increases in time. Similarly, for the problem of a uniform density plasma heated by a finite width laser beam, a self similar solution keeping R constant can be obtained by assuming that the beam intensity and width increase in time. Such solutions will be studied with the electron kinetic code FPI [3], and compared to simulations with more usual laser characteristics. \newline [1] Ya. B. Zel'dovich and Yu. P. Raizer, ``Physics of Shock Waves {\ldots}'', Academic Press, New York, 1967. \newline [2] L. Spitzer and R. Harm, Phys. Rev. \textbf{89}, 977 (1953). \newline [3] J.-P. Matte \textit{et al.}, Phys. Rev. Lett. \textbf{53}, 1461 (1984)~; \textit{ibid }\textbf{49}, 1936 (1982).