Development of a Novel Method for Determination of Momentum Transport Parameters

The toroidal momentum pinch velocity V$_{\varphi}$ and diffusivity $\chi_{\varphi}$ in NSTX were previously determined from the transient response of the toroidal rotation $\Omega $ following applied n$=$3 magnetic perturbations that brake the plasma [1,2]. Assuming $\Pi =$nmR$^{2}$(-$\chi_{\phi}\nabla \Omega +$V$_{\phi}\Omega$), where the momentum flux $\Pi $ is determined using TRANSP, these local analyses used fits to $\Omega $ and $\nabla \Omega $ to obtain $\chi_{\phi}$ and V$_{\phi}$ one flux surface at a time. This work attempts to improve the accuracy of the inferred $\chi_{\phi}$(r) and V$_{\phi}$(r) profiles by utilizing many flux surfaces simultaneously. We employ nonlinear least-squares minimization that compares the entire perturbed rotation profile evolution $\Omega $(r,t) against the profile evolution generated by solving the momentum transport equation. We compare the local and integrated approaches and discuss their limitations. We also apply the integrated approach to determine whether an additional residual stress contribution (independent of $\Omega$ or $\nabla \Omega$) can be inferred given experimental uncertainties.\\[4pt] [1] W. Solomon et al., Phys. Rev. Lett. \textbf{101}, 065004 (2008).\\[0pt] [2] Kaye et al., Nucl. Fusion \textbf{49}, 045010 (2009).