On possibilities to characterize turbulence in plasma torches by correlation dimensions

The method of time embedding reconstruction of phase portraits can be used for analysis of chaotic data and nonlinear phenomena in various dynamic models, simulations and experiments including investigations of plasma dynamics. Thermal plasma jets are experimental systems which afford according to the turbulence stage experimental data characterized by a changing portion of regular, chaotic and noise components and their characterization by correlation dimensions could become an interesting tool for further investigations of turbulence and transition to turbulence in various experimental conditions. Parameters of chaotic dynamics such as correlation dimension and Lyapunov exponents can also have strong practical applications. For example it has been shown that they are related to the average size of the produced nanostructures during nanosynthesis. In our experiments we have used for the generation of a thermal plasma jet a dc argon plasma torch with a transparent arc chamber walls. In such arrangement it was possible to observe both the electric arc and the generated plasma flow. Strong gradients of temperature, velocity and density in the generated plasma jet lead to turbulent phenomena manifesting themselves both in fluctuations of the plasma jet optical radiation and in oscillations of arc current and voltage. Electric arc inside the plasma torch and generated plasma jet were observed optically by arrays of photodiodes from 4 directions. Arc voltage and current were recorded simultaneously with the optical radiation. A standard method of time-delayed coordinates was used for the analysis of these records. In our previous work we have shown that resulting phase portraits of the dynamics embedded in three dimensions exhibit some structures and reflect stability of the plasma jet. In this paper we estimate correlation dimensions of phase portraits by Grassberger-Procaccia algorithm for both arc current records and records of optical radiation of arc and plasma jet. Results show that the correlation dimension increases with increasing argon flow rate and can thus be used as an indicator of dynamics complexity and stability.