New evidence and impact of electron transport non-linearities based on new perturbative inter-modulation analysis

Abstract

Abstract.A new methodology to analyze non-linear components in perturbative transport experiments is introduced. The methodology has been experimentally validated in the Large Helical Device (LHD) for the electron heat transport channel. Electron cyclotron resonance heating (ECRH) with different modulation frequencies by two gyrotrons have been used to directly quantify the amplitude the non-linear component at the inter-modulation frequencies. The measurements show significant quadratic non-linear contributions, but also the absence of cubic and higher order components. The non-linear component is analyzed using Volterra series, which is the non-linear generalization of transfer functions. This allows to study the radial distribution of the non-linearity of the plasma and to reconstruct linear profiles in the case the measurements were not distorted by non-linearities. The reconstructed linear profiles are significantly different from the measured profiles showing the significant impact the non-linearity can have.

A systematic approach to optimize excitations for perturbative transport experiments

“…This test has also been experimentally applied and can be found in Ref. 21. There, it is shown that indeed if the perturbation is chosen relatively small even for a small perturbation, one can observe non-linear components.…”

“…This can be done using natural interaction between sawtooth and modulated electron cyclotron heating (ECH) 19 or using directly two modulated ECH sources. 20,21 Analyzing higher harmonics can specifically be used to test the linearity of the experiment, which is a necessary condition when compared to linearized physics models.…”

Heat flux reconstruction and effective diffusion estimation from perturbative experiments using advanced filtering and confidence analysis

“…The calculated standard deviations are very similar (note the logarithmic scale). Only at low-frequency there is some deviation due to the transient, which could be further improved using the LPM-method introduced in [20,21]. Methods number (II) or (III) are used to calculate the variance, i.e., the SNRs, of the individual harmonic components.…”

“…Then, the variance of the integral based on propagation of uncertainty and averaging of noise (factor 2) is calculated as follows t) . (20) Given that at small ρ only a few samples are available, it is important to remember that there is an additional error on the estimate based on the formula for the trapezoidal approximation, i.e.,…”

“…Therefore, we will not further consider these errors in (21), but focus purely on the stochastic uncertainties. The 95% confidence bounds based on (20) assuming Gaussian distributed noise is shown in Fig. 8.…”