Using visibility graphs to characterize non-Maxwellian turbulent plasmas

The Visibility Graph, a technique for mapping time series into complex networks, is employed to research underlying physical mechanisms in collisionless, turbulent plasmas. We analyze four distinct time series of magnetic field fluctuations obtained from Particle in Cell (PIC) simulations, initialized varying the κ parameter of its particle velocity distributions to explore departures from thermodynamic equilibrium. All studied cases exhibit a power law behavior in the degree distribution of the nodes. The critical exponent of this distribution unveils information about network properties, including particle correlations and heterogeneity. We compute the γ exponent for the degree distribution of the scale-free network and observe its evolution according to κ, peaking at κ=3. This trend suggests that long-range correlations are more prominent in plasmas far from thermal equilibrium, while short-range correlations dominate in thermal plasmas following a Maxwellian distribution. These findings align with previous non-collisional plasma studies. Additionally, we investigate the μ and ν exponents associated with the slopes of power spectra of the magnetic fluctuations, obtaining insights into the energy dissipation and temporal persistence of the time series. Our findings reveal that low-frequency fluctuations exhibit the sharpest energy dissipation in thermal equilibrium environments, while high-frequency fluctuations dominate in systems described by velocity distributions with small κ. When comparing the correlation between these exponents and γ as a function of κ, we find a direct correlation for the exponent ν associated with high-frequencies, and an anticorrelation for the low-frequencies exponent μ. This finding underscores the connection between long- and short-range correlations and the Debye sphere of the plasma, revealing that the γ metric of the Visibility Graph is only able to see the smaller scales of a time series.