Analytical study of initial flame kernel in laser ignition

Abstract

The formation process of an initial flame kernel in laser ignition was analytically examined for understanding its experimentally-observed hugeness. First, we evaluated the thermodynamic state of the laser-heated plasma by examining the laser-absorption waves in the detonation mode and in the radiation mode, taking account of lateral energy loss. Second, we evaluated the mechanical energy loss during the plasma expansion to the initial pressure. In addition, we evaluated the thermodynamic state of the plasma after its expansion to the initial pressure. In this evaluation, we calculated not only the isentropic-expansion process but also the effects of thermal diffusion from the hot plasma to the ambient gas in an approximate manner. During the course of this study, we developed some empirical formulas for the properties of air plasma to examine analytically the formation process of an initial flame kernel in laser ignition. It has been found that the laser-absorption wave must be in the detonation mode for typical laser-ignition conditions, and that the hugeness of the initial flame kernel is ascribed not only to the hydrodynamic expansion of the high-pressure laser-heated plasma but also to the thermal diffusion from the high-temperature plasma to the ambient gas. Finally, we derived the scaling laws for the size, internal energy, and temperature of the initial flame kernel with respect to the incident energy flux and absorbed energy of the igniting laser.