Strong gradient neoclassical transport in the plateau regime

Abstract

Strong gradient regions in tokamaks such as the pedestal or internal transport barriers are regions of reduced turbulence where neoclassical transport can play a dominant role. In pedestals, gradient lengths comparable to the ion poloidal gyroradius have been measured. Standard neoclassical theory can miss important strong gradient effects in these regions because it assumes that the gradient length scales of density, temperature and potential are larger than the ion poloidal gyroradius. We extend plateau regime neoclassical theory into regions of gradients of the order of the ion poloidal gyroradius to capture strong gradient effects on transport processes in the pedestal and internal transport barriers. The fundamental idea behind our new framework is to keep a scale separation between the orbit widths and the gradient length scales by performing a large aspect ratio expansion. In the plateau regime, strong gradients cause poloidal variation that is in-out as well as up-down asymmetric. We study two different test cases assuming either radial force balance or the absence of turbulence and show that strong gradient effects can enhance or reduce standard neoclassical theory predictions in the plateau regime in strong gradient regions.

Figures (9)

• Figure 1: Input profiles for normalised ion and electron temperature and density from \ref{['input']}. The strong gradient region is indicated by vertical dashed lines. We compare two different input profiles for the mean parallel flow of the form \ref{['Vinput']}.
• Figure 2: The radial electric field as determined by radial force balance \ref{['radialForceBalance']}.
• Figure 3: The ion neoclassical particle flux is mostly positive for $\alpha=-0.25$ and negative for $\alpha=0.59$. The ion neoclassical energy flux exceeds the weak gradient energy flux in the strong gradient region.
• Figure 4: On the left is the poloidal variation of the electric potential $\bar{\phi}_\theta=\bar{\phi}_c\cos\theta+\bar{\phi}_s\sin\theta$ for $\alpha=0.59$, and on the right for $\alpha=-0.25$. Both cases show in-out and up-down asymmetry. The corresponding amplitudes $\bar{\phi}_c$ and $\bar{\phi}_s$ are shown as a function of $\bar{\psi}$ below the respective two dimensional plots.
• Figure 5: The bootstrap current is almost identical to weak gradient neoclassical theory for $\alpha=-0.25$ but smaller than weak gradient neoclassical predictions for $\alpha=0.59$. The electron neoclassical particle flux is closer to the weak gradient limit for $\alpha=0.59$ and larger for $\alpha=-0.25$.