Identifying Transitions with Topological Data Analysis of Noisy Turbulence in Plasmas*

Cross-field transport and heat loss in a magnetically confined plasma is determined by turbulence driven by perpendicular (to the magnetic field) pressure gradients [1]. The heat losses from turbulence can make it difficult to maintain the energy density required to reach and maintain the conditions necessary for fusion. Self-organization of turbulence into intermediate scale so-called zonal flows can reduce the radial heat losses, however identifying when the transition occurs and any precursors to the transition is still a challenge. We introduce the concept of Topological Data Analysis (TDA) which is used to extract topological features from point cloud data to develop a methodology to identify the transition from turbulent dominant to zonal flow dominant. This method clearly identifies the transition by showing a large change in the persistence diagrams and number of topological features [2]. To expand this to experimental observations, we find that TDA is very susceptible to noise, which can easily be mistaken as small-scale features and crowd out legitimate topology. We explore techniques to mitigate the effects of noise in the use of TDA on plasma data. First, TDA will be applied to simulation data with additive noise, and a methodology will be developed to identify characteristic topology of turbulent and zonal regimes despite noisy or incomplete data. Finally, we will apply this methodology on experimental image data.

[1] Garbet, Xavier. "Introduction to turbulent transport in fusion plasmas." Comptes Rendus Physique 7.6 (2006): 573-583

[2] Stanish Sage, "Counting Holes in Physical Systems - Applications of Computational Homology to Systems in Physics -" (2022). Undergraduate Honors Theses. William & Mary. Paper 1785.