Elucidating plasma dynamics in Hasegawa–Wakatani turbulence by information geometry

Abstract

The impact of adiabatic electrons on drift-wave turbulence, modeled by the Hasegawa–Wakatani equations, is studied using information length. Information length is a novel theoretical method for measuring distances between statistical states represented by different probability distribution functions (PDFs) along the path of a system and represents the total number of statistically different states that a system evolves through in time. Specifically, the time-dependent PDFs of turbulent fluctuations for a given adiabatic index A are computed. The changes in fluctuation statistics are then quantified in time by using information length. The numerical results provide time traces exhibiting intermittent plasma dynamics, and such behavior is identified by a rapid change in the information length. The effects of A are discussed.

Time-dependent probability density functions and information geometry of the low-to-high confinement transition in fusion plasma

“…Practically, to apply our method to experimental data, time-dependent PDFs can be calculated by sampling the data in the time-series of different variables (fluctuating density, electric field, etc.) by using moving-time windows, as was done in a Hasagawa-Wakatani turbulence model [26] where information length was shown to be a novel methodology of assessing the effects of coherent structures and turbulent dynamics in plasmas, e.g., quantifying the decorrelation of the flux between different spatial positions due to coherent structures. Therefore, one promising future work will be to utilise our method to predict undesirable plasmas events (e.g.…”

“…ELMs, eruptions) well before other methods can, so that the occurrence of such events can be avoided or else controlled to some degree. It will also be of great interest to apply this methodology to understand the temporal-spatial dynamics in other L-H transition turbulence models as well as experimental data to quantify correlations at different spatial positions [26,28].…”

“…We begin by summarizing how to calculate the change in statistical states for a stochastic variable x which has a time-dependent PDF p(x, t). By calculating an infinitesimal relative entropy between p(x, t) and p(x, t + δt) as δt → 0, and then summing the square root of the infinitesimal relative entropy along the path, we define the (dimensionless) information length L(t) [19,[21][22][23][24][25][26][27][28]…”

Causal Information Rate

“…This is because Equations (3)-(5) can be calculated from any (numerical or experimental) data as long as time-dependent (marginal, joint) PDFs can be constructed. For instance, we used a time-sliding window method to construct time-dependent PDFs of different variables and then calculated E and L to analyze numerically generated time-series data for fusion turbulence [26], time-series music data [20], and numerically generated time-series data for global circulation model [28]. However, it is not always clear how many hidden variables are in a given data set.…”

“…We have recently proposed information-geometric theory as a powerful tool to understand non-equilibrium stochastic processes that often involve high temporal variabilities and large fluctuations [20][21][22][23][24][25][26][27][28][29][30][31][32], as often the case of rare, extreme events. This is based on the surprisal rate, r(x, t) = ∂ t s(x, t) = −∂ t ln p(x, t), where p(x, t) is a probability density function (PDF) of a random variable x at time t, and s(x, t) = − ln p(x, t) is a local entropy.…”