Finite ion orbit width effect on the neoclassical tearing mode threshold in a tokamak plasma

Abstract

A new drift kinetic theory for the response of ions to small magnetic islands in toroidal plasma is presented. Islands whose width w is comparable to the ion poloidal Larmor radius are considered, expanding the ion response solution in terms of , where r is the minor radius. In this limit, the ion distribution can be represented as a function of toroidal canonical momentum, . With effects of grad-B and curvature drifts taken into account, the ion distribution function is a constant on a ‘drift island’ structure, which is identical to the magnetic island but radially shifted by . The distribution is then flattened across the drift island, rather than the magnetic island. For small islands , the pressure gradient is maintained across the magnetic island, suppressing the bootstrap current drive for the neoclassical tearing mode (NTM) growth. As , the ions are largely unperturbed. However, the electrons respond to the electrostatic potential required for quasi-neutrality and this provides a stabilizing contribution to the NTM evolution. This gives a new physical understanding of the NTM threshold mechanism, with implications for the design of NTM control systems for future tokamaks such as ITER.

On the triggerless onset of 2/1 neoclassical tearing modes in TCV

“…where ρ mn ∆ ohmic0 represents the stability of the ohmic plasma at zero island width, I cd,tot stands for the total current driven by all EC beams and k Icd,tot Ip refers to the modification of the linear stability by co-ECCD beams (destabilizing hence k > 0). Interpretative simulations with ASTRA suggest that the magnetic shear at the 2/1 surface increases with increasing I cd,tot (under constant I p ) in the discharges, which justifies equation (11) to some extent. More theoretical inputs are desired to explain this dependence more accurately.…”

“…More theoretical inputs are desired to explain this dependence more accurately. Note that equation (11) accounts for the change of ∆ through a global change of the q profile by ECCD, given the relatively short timescale in TCV (with a resistive time of 50 ∼ 100 ms in the test discharges) and the strong co-ECCD involved here ( Icd,tot Ip = 35% ∼ 90% depending on the density and EC power levels used). This is different from the effect of small off-axis EC depositions on ∆ discussed in [39,40] and has been used for example in [23] for NTM prevention and stabilization studies.…”

“…Similarly, the range of k can be estimated through the statistics of simulations and observations in the experiments. As defined in equation (11), k represents the contribution of EC beams to the modification of ∆ 0 and is positive. The fact that no mode has been observed in similar plasmas with lower co-ECCD power or no EC power (i.e.…”

“…The stabilizing effects at small island width (w) that contribute to w crit have also been investigated in detail. w crit has mainly been explained by the incomplete flattening of the pressure profile at small w and/or by the polarization cur rent depending on the relative rotation of the NTM in a frame where the radial electrical field vanishes [3,[9][10][11].…”

Drift kinetic theory of neoclassical tearing modes in a low collisionality tokamak plasma: magnetic island threshold physics

“…k ∥ = k ϑ w/L s , where L s = Rq/s is the shear length scale with s = (r/q)dq/dr being the magnetic shear, k ϑ = m/r s . We extend our previous results [34][35][36] to treat the electrons with the same drift kinetic formalism that we use for the ions, while considering magnetic islands at rest in the plasma E × B frame (ω = 0, where ω is the island propagation frequency in that frame). Earlier work on the ion bootstrap flow considered small islands of w ∼ ρ bi by solving the drift kinetic equation through a Monte Carlo computational approach [37,38].…”