Experimentally testing the dependence of momentum transport on second derivatives using Gaussian process regression

It remains an open question to explain the dramatic change in intrinsic rotation induced by slight changes in electron density (White et al 2013 Phys. Plasmas20 056106). One proposed explanation is that momentum transport is sensitive to the second derivatives of the temperature and density profiles (Lee et al 2015 Plasma Phys. Control. Fusion57 125006), but it is widely considered to be impossible to measure these higher derivatives. In this paper, we show that it is possible to estimate second derivatives of electron density and temperature using a nonparametric regression technique known as Gaussian process regression. This technique avoids over-constraining the fit by not assuming an explicit functional form for the fitted curve. The uncertainties, obtained rigorously using Markov chain Monte Carlo sampling, are small enough that it is reasonable to explore hypotheses which depend on second derivatives. It is found that the differences in the second derivatives of and between the peaked and hollow rotation cases are rather small, suggesting that changes in the second derivatives are not likely to explain the experimental results.