Abstract
A new drift kinetic theory for the plasma response to the neoclassical tearing mode (NTM) magnetic perturbation is presented. Small magnetic islands of width, (a is the tokamak minor radius) are assumed, retaining the limit w ∼ ρ bi (ρ bi is the ion banana orbit width) to include finite orbit width effects. When collisions are small, the ions/electrons follow streamlines in phase space; for passing particles, these lie in surfaces that reproduce the magnetic island structure but have a radial shift by an amount, proportional to , where is the ion/electron poloidal Larmor radius. This shift is associated with the curvature and ∇B drifts and is found to be in opposite directions for , where is the component of velocity parallel to the magnetic field. The particle distribution function is then found to be flattened across these shifted or drift islands rather than the magnetic island. This results in the pressure gradient being sustained across the magnetic island for and hence reduces the neoclassical drive for NTMs when w is small. This provides a physics basis for the NTM threshold, which is quantified. In Imada et al (2019 Nucl. Fusion 59 046016, and references therein), a 4D drift kinetic non-linear code has been applied to describe these modes. In the present paper, the drift island formalism is employed. Valid at low collisionality, it allows a dimensionality reduction to a 3D problem, simplifying the numerical task and efficiently resolving the collisional boundary layer across the trapped-passing boundary. An improved model is adopted for the magnetic drift frequency. This decreases the NTM threshold, compared to the results shown in Imada et al (2019 Nucl. Fusion 59 046016, and references therein), making it in quantitative agreement with experimental observations, with , where w c is the threshold magnetic island half-width, or 2.85ρ bi for the full threshold island width, predicted for our equilibrium.
Highlights
Neoclassical tearing modes (NTM) [1, 2] are classified as large scale resistive magnetohydrodynamic (MHD) plasma instabilities [3]
A new theory is required to determine all the modified Rutherford equation (MRE) neoclassical contributions allowing the limit of w ∼ ρbi, which is crucial in providing the neoclassical tearing mode (NTM) threshold island width scaling for ITER and other future tokamak devices
The electron/ion distribution function is found to be flattened across the so called drift islands, which are radially shifted by a value, proportional to ρθe/i/w, compared to the magnetic island
Summary
Neoclassical tearing modes (NTM) [1, 2] are classified as large scale resistive magnetohydrodynamic (MHD) plasma instabilities [3]. A new theory is required to determine all the MRE neoclassical contributions allowing the limit of w ∼ ρbi, which is crucial in providing the NTM threshold island width scaling for ITER and other future tokamak devices. The analytic reduction described here explains the physical origin of the density gradient across the island and provides a new NTM threshold model that arises from both, ion and electron plasma responses. It provides the self-consistent electrostatic potential, Φ, required to ensure quasi-neutrality. More detailed information, including benchmarking against other models, can be found in appendices A–C
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