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We report certain complex behaviors of a nanosecond Nd:YAG laser produced plasma on a Ni target. For high laser fluences, a split in the transversal expansion plane along with oscillatory regimes of the ablation plasma were observed and investigated. These complex phenomena, which take place at various interaction time scales, are described using a fractal theoretical model based on continuous but non-differentiable curves of particle movement.

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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.

An innovative theoretical model is developed on the backbone of a classical Lorenz system. A mathematical representation of a differential Lorenz system is transposed into a fractal space and reduced to an integral form. In such a conjecture, the Lorenz variables will operate simultaneously on two manifolds, generating two transformation groups, one corresponding to the space coordinates transformation and another one to the scale resolution transformation. Since these groups are isomorphs various types isometries become functional. The Lorenz system was further adapted to describe the dynamics of ejected particles as a result of laser matter interaction in a fractal paradigm. The simulations were focused on the dynamics of charged particles, and showcase the presence of current oscillations, a heterogenous velocity distribution and multi-structuring at different interaction scales. The theoretical predictions were compared with the experimental data acquired with noninvasive diagnostic techniques. The experimental data confirm the multi-structure scenario and the oscillatory behavior predicted by the mathematical model.