The flip-over effect in self-similar laser-induced plasma expansion

We present a rigorous study of a dynamical model for a nonsymmetric expansion of laser-induced plasma plumes into the vacuum. The model is used in the laser film deposition technique and for remote chemical analysis in the so-called laser-induced breakdown spectroscopy. It defines a particular class of solutions of the hydrodynamics equations when the (plasma) mass density, pressure, and temperature as functions of position have level surfaces that are ellipsoids. The time evolution of ellipsoid semiaxes is determined by the dynamical model. In this model we investigate the flip-over effect: A pancakelike shape of the plasma plume turns into a cigarlike shape and vice versa in due course of its expansion. The effect has been observed in experiments as well as in numerical simulations. In many practical cases, axially symmetric plasma plumes with the adiabatic constant of (5/3) (ideal gas) are used. For this case we prove that the flip-over effect occurs exactly once in the above dynamical model. This rigorous result agrees with the earlier experimental and numerical evidence and, hence, validates a wide applicability of the model