Abstract
Carbon plasmas generated by excimer laser ablation are often applied for deposition (in vacuum or under controlled atmosphere) of high-technological interest nanostructures and thin films. For specific excimer irradiation conditions, these transient plasmas can exhibit peculiar behaviors when probed by fast time- and space-resolved optical and electrical methods. We propose here a fractal approach to simulate this peculiar dynamics. In our model, the complexity of the interactions between the transient plasma particles (in the Euclidean space) is substituted by the nondifferentiability (fractality) of the motion curves of the same particles, but in a fractal space. For plane symmetry and particular boundary conditions, stationary geodesic equations at a fractal scale resolution give a fractal velocity field with components expressed by means of nonlinear solutions (soliton type, kink type, etc.). The theoretical model successfully reproduces the (surprising) formation of V-like radiating plasma structures (consisting of two lateral arms of high optical emissivity and a fast-expanding central part of low emissivity) experimentally observed.
Highlights
Plasma structures are often assimilated into complex systems, when considering their functionality and structures [1, 2]
We propose here a fractal approach to simulate this peculiar dynamics
For plane symmetry and particular boundary conditions, stationary geodesic equations at a fractal scale resolution give a fractal velocity field with components expressed by means of nonlinear solutions
Summary
Plasma structures are often assimilated into complex systems, when considering their functionality and structures [1, 2]. The previous approximation is well applied for complex system dynamics, because the real measurements are done for a finite scale resolution This implies building a physical theory for a new geometric structure, by introducing the scale laws (and the scale transformation invariance) into the motion laws (which already are invariant to transformations of space and time coordinates). These requirements are satisfied by the scale relativity theory (SRT) [6] and more recently by the SRT in an arbitrary constant fractal dimension [7], where the interaction complexity is replaced by nondifferentiability, and motions take place without constraints. Such transient plasmas play a significant role in the production of various nanostructured materials (carbon nanotubes, nanowires, graphene, etc.) [11,12,13], and controlling their properties (expansion velocities, density, and temperature) allows a significant enhancement of the deposition process [14,15,16]
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