Conditions for generating synthetic data to investigate characteristics of fluctuating quantities

Abstract

Synthetic data describing coherent random fluctuations have widely been used to validate numerical simulations against experimental observations or to examine the reliability of extracting statistical properties of plasma turbulence via correlation functions. Estimating correlation time or lengths based on correlation functions implicitly assumes that the observed data are stationary and homogeneous. It is, therefore, important that numerically generated synthetic data also satisfy the stationary process and homogeneous state. Based on the synthetic data with randomly generated moving Gaussian shaped fluctuations both in time and space, the correlation function depending on the size of averaging time window is analytically derived. Then, the smallest possible spatial window size of synthetic data satisfying the stationary process and homogeneous state is proposed, thereby reducing the computation time to generate proper synthetic data and providing a constraint on the minimum size of simulation domains when using synthetic diagnostics to compare with experiment. This window size is also numerically confirmed with 1D synthetic data with various parameter scans.

Experimental determination of the correlation properties of plasma turbulence using 2D BES systems

“…However, because the integration domain, spatial scales and velocity of the perturbations are all kept constant throughout the study of varying fluctuation amplitudes in Section 6.2.1, these effects simply cause the resulting fluctuation amplitude to be reduced by a constant factor [42]. Therefore, because we already have an arbitrary free parameter κ, we can rescale the analytic expression for the fluctuation amplitude (B.41) to match the value measured from the numerically generated fluctuating field.…”

“…The black solid lines correspond to the laboratory-frame relations (B.41), (15), (28), (17)(18), (25), and (27) in each of the panels, respectively. The coloured lines correspond to the Gaussian-model PSF calculations (47), (39), (40), (42)(43), (49), and (48), respectively, which are discussed in Section 6.3. The lowest numerical values of Ω, from (45), are given in each panel for each PSF case.…”

Evolution of magnetic Kubo number of stochastic magnetic fields during the edge pedestal collapse simulation

“…Experimental measurements of correlation lengths in fusion-grade hot plasmas are typically performed by replacing the ensemble average operator with a temporaldomain average operator assuming that the data are ergodic, stationary and homogeneous. [35][36][37] Since we only have 201 points in time in the simulation data, i.e., τ A = [0, 1, 2, ..., 199, 200], the temporal-domain average is not suitable to obtain statistically valid results. Furthermore, running tens of the same simulation to obtain the ensemble average is computationally too expensive.…”

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

“…Later on, we show that F ∼ O (1) ensures the generated signal to have the square of the fluctuation level indeed of the order of A 2 as specified. More detailed descriptions on the model of the fluctuating signal can be found elsewhere [21,23].…”

“…where the approximation in the last line is valid for τ ac /∆T sub 1. ∆T sub is much smaller than ∆T allowing many of ∆T sub to exist within ∆T (for an ensemble average [23]) but still much larger than τ ac , the usual auto-correlation time of the fluctuating signal in the lab frame defined as [30]…”