Edge profile analysis of Joint European Torus (JET) Thomson scattering data: Quantifying the systematic error due to edge localised mode synchronisation

Abstract

The Joint European Torus (JET) high resolution Thomson scattering (HRTS) system measures radial electron temperature and density profiles. One of the key capabilities of this diagnostic is measuring the steep pressure gradient, termed the pedestal, at the edge of JET plasmas. The pedestal is susceptible to limiting instabilities, such as Edge Localised Modes (ELMs), characterised by a periodic collapse of the steep gradient region. A common method to extract the pedestal width, gradient, and height, used on numerous machines, is by performing a modified hyperbolic tangent (mtanh) fit to overlaid profiles selected from the same region of the ELM cycle. This process of overlaying profiles, termed ELM synchronisation, maximises the number of data points defining the pedestal region for a given phase of the ELM cycle. When fitting to HRTS profiles, it is necessary to incorporate the diagnostic radial instrument function, particularly important when considering the pedestal width. A deconvolved fit is determined by a forward convolution method requiring knowledge of only the instrument function and profiles. The systematic error due to the deconvolution technique incorporated into the JET pedestal fitting tool has been documented by Frassinetti et al. [Rev. Sci. Instrum. 83, 013506 (2012)]. This paper seeks to understand and quantify the systematic error introduced to the pedestal width due to ELM synchronisation. Synthetic profiles, generated with error bars and point-to-point variation characteristic of real HRTS profiles, are used to evaluate the deviation from the underlying pedestal width. We find on JET that the ELM synchronisation systematic error is negligible in comparison to the statistical error when assuming ten overlaid profiles (typical for a pre-ELM fit to HRTS profiles). This confirms that fitting a mtanh to ELM synchronised profiles is a robust and practical technique for extracting the pedestal structure.

Studies of the pedestal structure and inter-ELM pedestal evolution in JET with the ITER-like wall

“…The pre-ELM quantities are those relating to the 80-99% ELM interval and are used for the pedestal width scaling studies in section 3. In the pedestal region the spatial sampling of the HRTS diagnostic is ~8 mm and the FWHM is ~1 cm [11], which is smaller than the minimum pedestal width observed on JET [12], but larger than the inter-chord spacing. Therefore, the instrument function is numerically calculated and convolved with the mtanh function when fitting the profiles for an accurate estimate of the pedestal width [11,12].…”

“…In the pedestal region the spatial sampling of the HRTS diagnostic is ~8 mm and the FWHM is ~1 cm [11], which is smaller than the minimum pedestal width observed on JET [12], but larger than the inter-chord spacing. Therefore, the instrument function is numerically calculated and convolved with the mtanh function when fitting the profiles for an accurate estimate of the pedestal width [11,12]. In addition, the spatial resolution in the pedestal changes from shot to shot as it is related to the number of HRTS profiles included in the composite profile.…”

Isotope dependence of the type I ELMy H-mode pedestal in JET-ILW hydrogen and deuterium plasmas

“…The pedestal structure analysis is carried out for the pre-ELM phase (namely the last 20 % of the ELM cycle) and is based on the mtanh [23] fitted electron density (n e ) and temperature (T e ) profiles as measured by Thomson scattering (TS) [24]. The kinetic profiles, collected from a steady time window of the discharge, are ELM-synchronised to improve signal statistics [25,26]. The width and height of the pedestal electron density and temperature are taken directly from the mtanh fit.…”

Bayesian modelling of Thomson scattering and multichannel interferometer diagnostics using Gaussian processes

“…Figure 4(a) shows an example of the parasitic signals obtained by firing many laser pulses (different colours) before a single plasma discharge, and (b) shows the linear relation between the signal mean and the variance over many laser pulses with the estimated slope of a = 2.01 × 10 −4 . Here, the photon noise is assumed to be the dominant contribution to the signal fluctuation [36]. Once we have the value of a, then the photon noise can be estimated as…”

“…Specifically, we use the hyperparameter model developed by [32] (denoted as σ f,Te , σ x,Te , σ f,ne and σ x,ne in figure 1) whose details are explained in section 2.3. Since we use a nonparametric model, our method does not depend on any predefined parametric model [20,21,[33][34][35][36] such as a modified hyperbolic tangent function [33] which often limit our knowledge on the profiles from measurements. Moreover, Gaussian processes avoid imposing assumptions such as monotonicity [30,37].…”