Drift-kinetic simulations of Neoclassical Tearing Mode instabilities in finite collisionality tokamak plasmas

Neoclassical tearing modes are resistive magnetohydrodynamic instabilities caused by filamentation of magnetic field-parallel current density, reconfiguring the field to form ’magnetic island’ structures. Islands enhance radial transport, remove parallel bootstrap current and self-amplify, degrading confinement. Experiments indicate island growth occurs only when both a threshold island half-width wc and poloidal beta are exceeded, the former comparable to the trapped ion banana orbit width ρb,i . Identifying the physical influences on wc would inform NTM control methods in future tokamaks like ITER, where NTMs are anticipated. In this work, a new numerical simulation code ”kokuchou” is developed to model the plasma response to a threshold-size magnetic island in a circular cross section, low inverse aspect ratio ε ≪ 1 tokamak under an ITER-like collisional banana regime, at the length scale ρb,i ∼ w ≪ rs where rs is the minor radius of the rational surface where the island forms. Ions are iteratively tracked via a 4D drift-kinetic equation, then combined with an analytic electron response to self-consistently derive the electrostatic potential and ion flow-like momentum conservation term, both part of the 4D equation. Objectives included: (1) validation and verification of the new code, (2) studying the ion response from four full-scale runs at varying island half-width ŵ[rs] and plasma collisionality ν⋆, and (3) calculating the island growth rate across varying ŵ, ν⋆ and ion poloidal gyroradius ρ̂θ,i[rs]. A novel result for the threshold width dependence on both ion poloidal gyroradius and collisionality is obtained: wc [rs] ≈ 0.440ρ̂θ,i[rs] + 0.0178ν⋆ − 7.54 × 10−5 , over the range ν⋆ = 0.005 − 0.020. The interacting effects of collisions and “drift island” dynamics on island growth and their relevance to the computational problem are explored.