Reliability of the two-point measurement of the spatial correlation length from Gaussian-shaped fluctuating signals in fusion-grade plasmas

TL;DR

This paper evaluates the reliability and accuracy of a statistical two-point measurement method for estimating the spatial correlation length of Gaussian-shaped fluctuating signals in fusion plasmas, using analytical, synthetic, and experimental data.

Contribution

It provides an analytical framework to assess the variance and bias of two-point correlation measurements, validated with synthetic and real plasma data.

Findings

Analytical expression for the standard deviation of correlation estimates.

Validation with synthetic data confirms theoretical predictions.

Application to experimental data demonstrates practical utility.

Abstract

A statistical method for the estimation of spatial correlation lengths of Gaussian-shaped fluctuating signals with two measurement points is examined to quantitatively evaluate its reliability (variance) and accuracy (bias error). The standard deviation of the correlation value is analytically derived for randomly distributed Gaussian shaped fluctuations satisfying stationarity and homogeneity, allowing us to evaluate, as a function of fluctuation-to-noise ratios, sizes of averaging time windows and ratios of the distance between the two measurement points to the true correlation length, the goodness of the two-point measurement for estimating the spatial correlation length. Analytic results are confirmed with numerically generated synthetic data and real experimental data obtained with the KSTAR beam emission spectroscopy diagnostic. Our results can be applied to Gaussian-shaped fluctuating signals where a correlation length must be measured with only two measurement points.