On the self-similar solution of laser ablated plasma expansion R. Fermous a , D. Doumaz b and M. Djebli a a Theoretical Physics Laboratory, Faculty of Physics U.S.T.H.B. 16079 Algiers, Algeria. b Centre de D´ eveloppement des Technologies Avanc´ ees. Baba Hassen 16303 Algiers, Algeria ABSTRACT The expansion of plasma plume produced by a laser ablation is investigated using the self-similar approach. Based on the fluid model and the quasi-neutral assumption, the one dimensional expansion of an either vapor or partially ionized gas is studied for a collisionless plasma in the presence of electrons in thermal equilibrium. The uniqueness of the self-similar solution is questioned. Two different self-similar transformations for the ion density are proposed, one commonly used for free plasma expansion and the other corresponds to the expansion with diffusion. The density profiles and the self-similar parameter limit, corresponding to the end of the expansion, are found to be strongly affected by the transformation. A comparison is made with experimental results of a plasma produced by nanosecond laser pulse interacting with a metallic titanium target in a vacuum. Keywords: laser ablated plasma, expansion 1. INTRODUCTION The removal of material from an irradiated target surfaces by a high-intensity laser pulse i.e, laser ablation is becoming a dominant technology for direct solid sampling, among other applications. The techniques based on the mechanism of laser-solid interaction, in different regimes of laser irradiance, include different domains such as pulsed laser deposition, nanoparticles manufacturing, micromachining as well as chemical analysis. 1 The entire process of laser ablation involves mainly two stages: 1. absorption of laser light that leads to heating and ionizing the formed vapor 2. plume expansion As the characteristic time of the expansion of the laser induced plasma after the end of the laser pulse is much longer than the time of plasma formation and initial plasma expansion duration, the two stages can be considered separately. 2 Plume expansion into a vacuum environment can be fully predicted by means of essentially three different theoretical approaches: (i) analytical (ii) fluid dynamic and (iii) Monte Carlo. 3 During the expansion, the plasma behavior becomes more complicated due to the rise of new physical process such as deceleration, shock wave formation and clustering. Using hydrodynamical approach is advantageous for providing density, velocity and temperature profile across the plasma plume as a function of time. 4 However, there are two limitations: all the simulated species including neutral atoms and ions have the same velocity as the fluid and numerical implementation is performed for short time. The latter is attributed to the free boundary problem associated to the moving expanding front. An alternative approach is to use the self-similar formalism. The self-similar analysis of nonlinear partial differential equations leads to rigorous solutions for problems in fluid mechanics such as diffusion and wave propagation where there is no scaling length or time. The importance of self-similar solutions is that the transformation of variables which achieves a reduction in the number of independent variables in a system of equations. 5 Thus, partial differential equations are transformed to ordinary ones depending only on one self similar variable which combine the time and the coordinates ξ = ξ (x, t). This is approach is largely used to study solitary waves and expansion of both gas vapor and plasma. For quasi-neutral plasma expansion, Gurevich et al. 6 were the first to present a self-similar solution which indicates that there is an ion acceleration driven by the ambipolar electric field created by charge separation. The self-similar approach Author to whom correspondence should be addressed E-mail: mdjebli@usthb.dz Fundamentals of Laser-Assisted Micro- and Nanotechnologies 2010, edited by Vadim P. Veiko, Tigran A. Vartanyan, Proc. of SPIE Vol. 7996, 79960V · © 2011 SPIE · CCC code: 0277-786X/11/$18 · doi: 10.1117/12.888920 Proc. of SPIE Vol. 7996 79960V-1 Downloaded from SPIE Digital Library on 18 Mar 2012 to 193.194.64.99. Terms of Use: http://spiedl.org/terms