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.
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