# Rotation and Neoclassical Ripple Transport in ITER

## TL;DR

This study models neoclassical ripple transport and torque in ITER, showing ferritic inserts significantly reduce toroidal viscosity and impact plasma rotation, with detailed calculations accounting for various plasma and magnetic field factors.

## Contribution

It provides the first comprehensive calculation of NTV in ITER considering realistic 3D magnetic equilibria, ripple effects, and ferromagnetic structures, improving understanding of plasma rotation damping.

## Key findings

- NTV torque is dominated by the 8 ripple component.
- Ferritic inserts reduce NTV torque by about 75% near the edge.
- Ripple-trapping may be a significant NTV mechanism in ITER.

## Abstract

Neoclassical transport in the presence of non-axisymmetric magnetic fields causes a toroidal torque known as neoclassical toroidal viscosity (NTV). The toroidal symmetry of ITER will be broken by the finite number of toroidal field coils and by test blanket modules (TBMs). The addition of ferritic inserts (FIs) will decrease the magnitude of the toroidal field ripple. 3D magnetic equilibria with toroidal field ripple and ferromagnetic structures are calculated for an ITER steady-state scenario using the Variational Moments Equilibrium Code (VMEC). Neoclassical transport quantities in the presence of these error fields are calculated using the Stellarator Fokker-Planck Iterative Neoclassical Conservative Solver (SFINCS). These calculations fully account for $E_r$, flux surface shaping, multiple species, magnitude of ripple, and collisionality rather than applying approximate analytic NTV formulae. As NTV is a complicated nonlinear function of $E_r$, we study its behavior over a plausible range of $E_r$. We estimate the toroidal flow, and hence $E_r$, using a semi-analytic turbulent intrinsic rotation model and NUBEAM calculations of neutral beam torque. The NTV from the $\rvert n \rvert = 18$ ripple dominates that from lower $n$ perturbations of the TBMs. With the inclusion of FIs, the magnitude of NTV torque is reduced by about 75% near the edge. We present comparisons of several models of tangential magnetic drifts, finding appreciable differences only for superbanana-plateau transport at small $E_r$. We find the scaling of calculated NTV torque with ripple magnitude to indicate that ripple-trapping may be a significant mechanism for NTV in ITER. The computed NTV torque without ferritic components is comparable in magnitude to the NBI and intrinsic turbulent torques and will likely damp rotation, but the NTV torque is significantly reduced by the planned ferritic inserts.