A compact non-differential approach for modeling laser ablation plasma dynamics

Abstract

Various differentiable physical models are frequently used to describe the dynamics of laser-produced plasma plumes (e.g., kinetic models, two-fluid models, etc.). Given the complexity of all the phenomena involved in the laser-matter interactions, it is required to introduce the laser ablation plasma dynamic variable dependencies both on the space-time coordinates and on the resolution scales. Therefore, an adequate theoretical approach may be the use of non-differentiable physical models (fractal models). Continuing our previous work on the fractal hydrodynamic model for laser ablation plasma dynamics, we propose here a compact version for the analysis of the spatial and temporal evolution of some plasma dynamic variables, such as velocities, currents, number densities, or temperatures. Moreover, the influence of external factors on the ablation plasma dynamics is considered. The predictions of this model are compared with the experimental data obtained by using a Langmuir probe on an Aluminum laser-produced plasma.

Experimental and Theoretical Studies on the Dynamics of Transient Plasmas Generated by Laser Ablation in Various Temporal Regimes

“…Continuing our previous work [55,58,59,63] on the fractal hydrodynamic model for laser ablation plasma dynamics, we recently proposed a compact version for the analysis of the spatial and temporal evolution of some plasma dynamic variables [76]. This version of our model was obtained by using normalized variables of the particle density, velocities, current density, etc., and by choosing adequate scale resolutions.…”

“…This allows us to re-write the dependencies of the plasma dynamic variables on the external factors as follows [76]:…”

“…In its compact form, we were able for the first time [76] to define some clear associations between fractal model variables and specific plasma parameters (electron temperature, thermal velocity, particle density). Moreover, when compared with experimental data depicting the temporal evolution of the plasma parameters determined though the Langmuir probe method, the model satisfactorily reproduces the experimental traces.…”

Investigations of Laser Produced Plasmas Generated by Laser Ablation on Geomaterials. Experimental and Theoretical Aspects

“…Considering that all the collision impact points are an uncountable set of point, it results that the trajectories of the plasma particles become continuous but non-differentiable curves (fractal curves). Since in these conditions the non-differentiability (fractality) appears as a fundamental property of the ablation plasma dynamics it seems necessary to construct a corresponding non-differentiable plasma physics model, for example in the form of fractal hydrodynamics model [46]. The mathematics behind this model as well as some applications of the model were development in a systematic manner by our group in [28,29,46,47].…”

“…Since in these conditions the non-differentiability (fractality) appears as a fundamental property of the ablation plasma dynamics it seems necessary to construct a corresponding non-differentiable plasma physics model, for example in the form of fractal hydrodynamics model [46]. The mathematics behind this model as well as some applications of the model were development in a systematic manner by our group in [28,29,46,47]. In the following, a fractal analysis will prove a multi-structuring of the ablation plasma in the form of Coulomb, thermal and cluster structures.…”